# Patent

## Title
Signal processing device, signal processing method, program, and recording medium

## Abstract

A signal processing device and signal processing method, and program and recording medium, whereby images and the like closer approximating real world signals can be obtained. An actual world estimating unit estimates the actual world function, assuming that the pixel value of each pixel corresponding to a position in the x direction of image data wherein real world light signals are projected on a plurality of pixels each having the time-space integration effects, and part of the continuity of the real world light signals has been lost is a pixel value acquired by integrating the actual world function corresponding to the real world light signals approximated with a spline function in the x direction. An image generating unit generates an image by integrating the actual world function in the x direction in predetermined increments.

## Background
TECHNICAL FIELD
The present invention relates to a signal processing device and signal processing method, and a program and recording medium, and in particular relates to a signal processing device and signal processing method, and a program and recording medium, enabling images and the like with closer approximation to real world signals.
BACKGROUND ART
Technology for detecting phenomena in the actual world (real world) with sensors and processing sampling data output from the sensors is widely used. For example, image processing technology wherein the actual world is imaged with an imaging sensor and sampling data which is the image data is processed, is widely employed.
Also, arrangements are known having second dimensions with fewer dimensions than first dimensions obtained by detecting with sensors first signals, which are signals of the real world having first dimensions, obtaining second signals including distortion as to the first signals, and performing signal processing based on the second signals, thereby generating third signals with alleviated distortion as compared to the second signals (e.g., Japanese Unexamined Patent Application Publication No. 2001-250119).
However, conventionally, signal processing taking into consideration the continuity of real world signals had not been performed, so obtaining images and the like which closer approximate real world signals has been difficult.
DISCLOSURE OF INVENTION
The present invention has been made in light of the situation as described above, and provides for obtaining of images and the like which closer approximate real world signals.
A signal processing device according to the present invention comprises: actual world estimating means for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of image data wherein the real world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the realworld light signal continuity is lost is a pixel value acquired by integrating the actual world function corresponding to the actual world light signal approximated with the spline function in at least the one-dimensional direction; and image generating means for generating an image by integrating the actual world function in at least the one-dimensional direction in predetermined increments.
A signal processing method according to the present invention comprises: an actual world estimating step for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of image data wherein the real world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the realworld light signal continuity is lost is a pixel value acquired by integrating the actual world function corresponding to the actual world light signal approximated with the spline function in at least the one-dimensional direction; and an image generating step for generating an image by integrating the actual world function in at least the one-dimensional direction in predetermined increments.
A program according to the present invention comprises: an actual world estimating step for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of image data wherein the real world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the realworld light signal continuity is lost is a pixel value acquired by integrating the actual world function corresponding to the actual world light signal approximated with the spline function in at least the one-dimensional direction; and an image generating step for generating an image by integrating the actual world function in at least the one-dimensional direction in predetermined increments.
A recording medium according to the present invention stores a program comprising: an actual world estimating step for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of image data wherein the real world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the realworld light signal continuity is lost is a pixel value acquired by integrating the actual world function corresponding to the real world light signal approximated with the spline function in at least the one-dimensional direction; and an image generating step for generating an image by integrating the actual world function in at least the one-dimensional direction in predetermined increments.
With the signal processing device, signal processing method, program, and recording medium according to the present invention, an actual world function is estimated assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of image data wherein the real world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the realworld light signal continuity is lost is a pixel value acquired by integrating the actual world function corresponding to the actual world light signal approximated with the spline function in at least the one-dimensional direction, an image is generated by integrating the actual world function in at least the one-dimensional direction in predetermined increments.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram illustrating the principle of the present invention.
FIG. 2 is a block diagram illustrating an example of the hardware configuration of a signal processing device 4.
FIG. 3 is a block diagram illustrating a configuration example of an embodiment of the signal processing device 4 shown in FIG. 1.
FIG. 4 is a diagram describing in detail the principle of the signal processing performed by the signal processing device 4.
FIG. 5 is a diagram for describing an example of array of pixels on an image sensor.
FIG. 6 is a diagram for describing the operations of a detecting device which is a CCD.
FIG. 7 is a diagram for describing the relation between light cast into detecting elements corresponding to pixel D through pixel F, and pixel values.
FIG. 8 is a diagram describing the relation between elapsing of time, light cast into a detecting element corresponding to one pixel, and pixel values.
FIG. 9 is a diagram illustrating an example of an image of a linear object in the actual world 1.
FIG. 10 is a diagram illustrating an example of pixel values of image data obtained by actual imaging.
FIG. 11 is a diagram illustrating an example of an image of the actual world 1, of an object which is of a color different from that of the background, having a monotone and linear edge.
FIG. 12 is a diagram illustrating an example of pixel values of image data obtained by actual imaging.
FIG. 13 is a schematic diagram of image data.
FIG. 14 is a diagram for describing estimation of a model 161 with M pieces of data 162.
FIG. 15 is a diagram for describing the relationship between signals of the actual world 1 and data 3.
FIG. 16 is a diagram illustrating an example of data 3 of interest at the time of creating an Expression.
FIG. 17 is a diagram for describing signals for two objects in the actual world 1, and values belonging to a mixed region at the time of creating an expression.
FIG. 18 is a diagram for describing continuity represented by Expression (18), Expression (19), and Expression (22).
FIG. 19 is a diagram illustrating an example of M pieces of data 162 extracted from data 3.
FIG. 20 is a diagram for describing integration of signals of the actual world 1 in the time direction and two-dimensional spatial direction, in the data 3.
FIG. 21 is a diagram for describing an integration region at the time of generating high-resolution data with higher resolution in the spatial direction.
FIG. 22 is a diagram for describing an integration region at the time of generating high-resolution data with higher resolution in the time direction.
FIG. 23 is a diagram for describing an integration region at the time of generating high-resolution data with higher resolution in the time-spatial directions.
FIG. 24 is a diagram illustrating the original image of the input image.
FIG. 25 is a diagram illustrating an example of an input image.
FIG. 26 is a diagram illustrating an image obtained by applying conventional class classification adaptation processing.
FIG. 27 is a diagram illustrating results of detecting a fine line region.
FIG. 28 is a diagram illustrating an example of an output image output from the signal processing device 4.
FIG. 29 is a flowchart for describing signal processing with the signal processing device 4.
FIG. 30 is a block diagram illustrating the configuration of a data continuity detecting unit 101.
FIG. 31 is a diagram illustrating an image in the actual world 1 with a fine line in front of the background.
FIG. 32 is a diagram for describing approximation of a background with a plane.
FIG. 33 is a diagram illustrating the cross-sectional shape of image data regarding which the image of a fine line has been projected.
FIG. 34 is a diagram illustrating the cross-sectional shape of image data regarding which the image of a fine line has been projected.
FIG. 35 is a diagram illustrating the cross-sectional shape of image data regarding which the image of a fine line has been projected.
FIG. 36 is a diagram for describing the processing for detecting a peak and detecting of monotonous increase/decrease regions.
FIG. 37 is a diagram for describing the processing for detecting a fine line region wherein the pixel value of the peak exceeds a threshold, while the pixel value of the adjacent pixel is equal to or below the threshold value.
FIG. 38 is a diagram representing the pixel value of pixels arrayed in the direction indicated by dotted line AA′ in FIG. 37.
FIG. 39 is a diagram for describing processing for detecting continuity in a monotonous increase/decrease region.
FIG. 40 is a diagram illustrating an example of other processing for detecting regions where an image of a fine line has been projected.
FIG. 41 is a flowchart for describing continuity detection processing.
FIG. 42 is a diagram for describing processing for detecting continuity of data in the time direction.
FIG. 43 is a block diagram illustrating the configuration of a non-continuity component extracting unit 201.
FIG. 44 is a diagram for describing the number of time of rejections.
FIG. 45 is a flowchart describing the processing for extracting the non-continuity component.
FIG. 46 is a flowchart describing the processing for extracting the continuity component.
FIG. 47 is a flowchart describing other processing for extracting the continuity component.
FIG. 48 is a flowchart describing still other processing for extracting the continuity component.
FIG. 49 is a block diagram illustrating another configuration of a continuity component extracting unit 101.
FIG. 50 is a diagram for describing the activity in an input image having data continuity.
FIG. 51 is a diagram for describing a block for detecting activity.
FIG. 52 is a diagram for describing the angle of data continuity as to activity.
FIG. 53 is a block diagram illustrating a detailed configuration of the data continuity detecting unit 101.
FIG. 54 is a diagram describing a set of pixels.
FIG. 55 is a diagram describing the relation between the position of a pixel set and the angle of data continuity.
FIG. 56 is a flowchart for describing processing for detecting data continuity.
FIG. 57 is a diagram illustrating a set of pixels extracted when detecting the angle of data continuity in the time direction and space direction.
FIG. 58 is a diagram for describing the principle of function approximation, which is an example of an embodiment of the actual world estimating unit shown in FIG. 3.
FIG. 59 is a diagram for describing integration effects in the event that the sensor is a CCD.
FIG. 60 is a diagram for describing a specific example of the integration effects of the sensor shown in FIG. 59.
FIG. 61 is a diagram for describing another specific example of the integration effects of the sensor shown in FIG. 59.
FIG. 62 is a diagram representing a fine-line-inclusive actual world region shown in FIG. 60.
FIG. 63 is a diagram for describing the principle of an example of an embodiment of the actual world estimating unit shown in FIG. 3, in comparison with the example shown in FIG. 58.
FIG. 64 is a diagram representing the fine-line-inclusive data region shown in FIG. 60.
FIG. 65 is a diagram wherein each of the pixel values contained in the fine-line-inclusive data region shown in FIG. 64 is plotted on a graph.
FIG. 66 is a diagram wherein an approximation function, approximating the pixel values contained in the fine-line-inclusive data region shown in FIG. 65, is plotted on a graph.
FIG. 67 is a diagram for describing the continuity in the spatial direction which the fine-line-inclusive actual world region shown in FIG. 60 has.
FIG. 68 is a diagram wherein each of the pixel values contained in the fine-line-inclusive data region shown in FIG. 64 is plotted on a graph.
FIG. 69 is a diagram for describing a state wherein each of the input pixel values indicated in FIG. 68 are shifted by a predetermined shift amount.
FIG. 70 is a diagram wherein an approximation function, approximating the pixel values contained in the fine-line-inclusive data region shown in FIG. 65, is plotted on a graph, taking into consideration the spatial-direction continuity.
FIG. 71 is a diagram for describing space-mixed region.
FIG. 72 is a diagram for describing an approximation function approximating actual-world signals in a space-mixed region.
FIG. 73 is a diagram wherein an approximation function, approximating the actual world signals corresponding to the fine-line-inclusive data region shown in FIG. 65, is plotted on a graph, taking into consideration both the sensor integration properties and the spatial-direction continuity.
FIG. 74 is a block diagram for describing a configuration example of the actual world estimating unit using, of function approximation techniques having the principle shown in FIG. 58, primary polynomial approximation.
FIG. 75 is a flowchart for describing actual world estimation processing which the actual world estimating unit of the configuration shown in FIG. 74 executes.
FIG. 76 is a diagram for describing a tap range.
FIG. 77 is a diagram for describing actual world signals having continuity in the spatial direction.
FIG. 78 is a diagram for describing integration effects in the event that the sensor is a CCD.
FIG. 79 is a diagram for describing distance in the cross-sectional direction.
FIG. 80 is a block diagram for describing a configuration example of the actual world estimating unit using, of function approximation techniques having the principle shown in FIG. 58, quadratic polynomial approximation.
FIG. 81 is a flowchart for describing actual world estimation processing which the actual world estimating unit of the configuration shown in FIG. 81 executes.
FIG. 82 is a diagram for describing a tap range.
FIG. 83 is a diagram for describing direction of continuity in the time-spatial direction.
FIG. 84 is a diagram for describing integration effects in the event that the sensor is a CCD.
FIG. 85 is a diagram for describing actual world signals having continuity in the spatial direction.
FIG. 86 is a diagram for describing actual world signals having continuity in the space-time directions.
FIG. 87 is a block diagram for describing a configuration example of the actual world estimating unit using, of function approximation techniques having the principle shown in FIG. 58, cubic polynomial approximation.
FIG. 88 is a flowchart for describing actual world estimation processing which the actual world estimating unit of the configuration shown in FIG. 87 executes.
FIG. 89 is a diagram for describing the principle of re-integration, which is an example of an embodiment of the image generating unit shown in FIG. 3.
FIG. 90 is a diagram for describing an example of an input pixel and an approximation function for approximation of an actual world signal corresponding to the input pixel.
FIG. 91 is a diagram for describing an example of creating four high-resolution pixels in the one input pixel shown in FIG. 90, from the approximation function shown in FIG. 90.
FIG. 92 is a block diagram for describing a configuration example of an image generating unit using, of re-integration techniques having the principle shown in FIG. 89, one-dimensional re-integration technique.
FIG. 93 is a flowchart for describing the image generating processing which the image generating unit of the configuration shown in FIG. 92 executes.
FIG. 94 is a diagram illustrating an example of the original image of the input image.
FIG. 95 is a diagram illustrating an example of image data corresponding to the image shown in FIG. 94.
FIG. 96 is a diagram representing an example of an input image.
FIG. 97 is a diagram representing an example of image data corresponding to the image shown in FIG. 96.
FIG. 98 is a diagram illustrating an example of an image obtained by subjecting an input image to conventional class classification adaptation processing.
FIG. 99 is a diagram representing an example of image data corresponding to the image shown in FIG. 98.
FIG. 100 is a diagram illustrating an example of an image obtained by subjecting an input image to the one-dimensional re-integration technique according to the present invention.
FIG. 101 is a diagram illustrating an example of image data corresponding to the image shown in FIG. 100.
FIG. 102 is a diagram for describing actual-world signals having continuity in the spatial direction.
FIG. 103 is a block diagram for describing a configuration example of an image generating unit which uses, of the re-integration techniques having the principle shown in FIG. 89, a two-dimensional re-integration technique.
FIG. 104 is a diagram for describing distance in the cross-sectional direction.
FIG. 105 is a flowchart for describing the image generating processing which the image generating unit of the configuration shown in FIG. 103 executes.
FIG. 106 is a diagram for describing an example of an input pixel.
FIG. 107 is a diagram for describing an example of creating four high-resolution pixels in the one input pixel shown in FIG. 106, with the two-dimensional re-integration technique.
FIG. 108 is a diagram for describing the direction of continuity in the space-time directions.
FIG. 109 is a block diagram for describing a configuration example of the image generating unit which uses, of the re-integration techniques having the principle shown in FIG. 89, a three-dimensional re-integration technique.
FIG. 110 is a flowchart for describing the image generating processing which the image generating unit of the configuration shown in FIG. 109 executes.
FIG. 111 is a block diagram illustrating a configuration example of another embodiment of the signal processing device 4 shown in FIG. 1.
FIG. 112 is a flowchart for describing the processing of the signal processing device 4 shown in FIG. 111.
FIG. 113 is a block diagram illustrating a configuration example of another applied embodiment of the signal processing device 4 shown in FIG. 111.
FIG. 114 is a diagram for describing types of signal processing.
FIG. 115 is a flowchart for describing the processing of the signal processing device 4 shown in FIG. 113.
FIG. 116 is a diagram for describing the integration effects of the image sensor.
FIG. 117 is a diagram for describing the integration effects of the image sensor.
FIG. 118 is a diagram illustrating a scene of capturing a background object in a stationary state, and a foreground object moving in front thereof.
FIG. 119 is a diagram describing a foreground region, a background region, and a mixed region.
FIG. 120 is a block diagram illustrating a configuration example of a device equivalent to the signal processing device 4 in FIG. 113 for removing movement blurring.
FIG. 121 is a flowchart for describing the processing of the device shown in FIG. 120.
FIG. 122 is a diagram illustrating a foreground region, a background region, and a mixed region.
FIG. 123 is a diagram illustrating foreground components and background components.
FIG. 124 is a diagram illustrating a three-dimensional spline function.
FIG. 125 is a diagram illustrating a physical model for approximating an optical signal function F(x) with a spline function Ck(x).
FIG. 126 is a diagram for describing pixel values obtained in the physical model in FIG. 125.
FIG. 127 is a diagram illustrating an integration range in a pixel.
FIG. 128 is a diagram illustrating an integration range for calculating a pixel value component S1.
FIG. 129 is a diagram illustrating an integration range for calculating a pixel value component S2.
FIG. 130 is a diagram illustrating an integration range for calculating pixel value components S3,P.
FIG. 131 is a diagram for describing a spline function to be integrated for calculating pixel value components S3,P.
FIG. 132 is a diagram illustrating an integration range for calculating pixel value components S3,P.
FIG. 133 is a diagram illustrating an integration range for calculating pixel value components S4,P.
FIG. 134 is a diagram illustrating an integration range for calculating pixel value components S4,P.
FIG. 135 is a diagram for describing an integration method for obtaining a pixel value of which movement blurring is removed.
FIG. 136 is a diagram for describing an integration method for obtaining a high-resolution pixel value of which movement blurring is removed.
FIG. 137 is a block diagram illustrating a configuration example of a movement blurring adjusting unit 17035 shown in FIG. 120.
FIG. 138 is a flowchart for describing the processing of the movement blurring adjusting unit 17035 shown in FIG. 137.
FIG. 139 is a diagram for describing constraining conditions.
FIG. 140 is a diagram for describing a method for estimating the actual world using a constraint conditional expression.
FIG. 141 is a block diagram illustrating another configuration example of the movement blurring adjusting unit 17035 shown in FIG. 120.
FIG. 142 is a flowchart for describing the processing of the movement blurring adjusting unit 17035 shown in FIG. 141.
FIG. 143 is a block diagram illustrating an actual processing unit 17100 for performing actual processing.
FIG. 144 is a block diagram illustrating a configuration example of the actual processing unit 17100 shown in FIG. 143.
FIG. 145 is a flowchart for describing the processing of the actual processing unit 17100 shown in FIG. 144.
FIG. 146 is a block diagram illustrating another configuration example of the actual processing unit 17100 shown in FIG. 143.
FIG. 147 is a flowchart for describing the processing of the actual processing unit 17100 shown in FIG. 146.
FIG. 148 is a diagram illustrating a physical model assuming that the movement amount v of the physical model in FIG. 125 is 0.
FIG. 149 is a diagram for describing an integration method for obtaining a high-resolution pixel value.
FIG. 150 is a block diagram illustrating yet another configuration example of the actual processing unit 17100 shown in FIG. 143.
FIG. 151 is a flowchart for describing the processing of the actual processing unit 17100 shown in FIG. 150.
FIG. 152 is a flowchart for describing the processing of the signal processing device 4 shown in FIG. 113.
FIG. 153 is a diagram for describing operations of a user I/F 17006 by the user.
FIG. 154 is a block diagram illustrating a configuration example of a device equivalent to the signal processing device 4 shown in FIG. 113.
FIG. 155 is a flowchart for describing the processing of the device shown in FIG. 154.
FIG. 156 is a block diagram illustrating a configuration example of a movement blurring removal processing unit 17303 shown in FIG. 154.
FIG. 157 is a flowchart for describing the processing of the movement blurring removal processing unit 17303 shown in FIG. 156.
FIG. 158 is a block diagram illustrating another configuration example of the movement blurring removal processing unit 17303 shown in FIG. 154.
FIG. 159 is a flowchart for describing the processing of the movement blurring removal processing unit 17303 shown in FIG. 158.
FIG. 160 is a block diagram illustrating a configuration example of a continuity setting unit 17002.
FIG. 161 is a diagram for describing the amount of movement.
FIG. 162 is a diagram illustrating pixel values of an image output from a camera, taken by the camera while a foreground object passes in front of a background object.
FIG. 163 is a diagram illustrating difference values of the pixel values of pixels in the image shown in FIG. 162.
FIG. 164 is a flowchart for describing processing for detecting amount of movement.
FIG. 165 is a flowchart for describing processing for detecting correlation.



BEST MODE FOR CARRYING OUT THE INVENTION
FIG. 1 illustrates the principle of the present invention. As shown in the drawing, events (phenomena) in an actual world 1 having dimensions of space, time, and mass, are acquired by a sensor 2, and formed into data. Events in the actual world 1 refer to light (images), sound, pressure, temperature, mass, humidity, brightness/darkness, or smells, and so forth. The events in the actual world 1 are distributed in the space-time directions. For example, an image of the actual world 1 is a distribution of the intensity of light of the actual world 1 in the space-time directions.
Taking note of the sensor 2, of the events in the actual world 1 having the dimensions of space, time, and mass, the events in the actual world 1 which the sensor 2 can acquire, are converted into data 3 by the sensor 2. It can be said that information indicating events in the actual world 1 are acquired by the sensor 2.
That is to say, the sensor 2 converts information indicating events in the actual world 1, into data 3. It can be said that signals which are information indicating the events (phenomena) in the actual world 1 having dimensions of space, time, and mass, are acquired by the sensor 2 and formed into data.
Hereafter, the distribution of events such as images, sound, pressure, temperature, mass, humidity, brightness/darkness, or smells, and so forth, in the actual world 1, will be referred to as signals of the actual world 1, which are information indicating events. Also, signals which are information indicating events of the actual world 1 will also be referred to simply as signals of the actual world 1. In the present Specification, signals are to be understood to include phenomena and events, and also include those wherein there is no intent on the transmitting side.
The data 3 (detected signals) output from the sensor 2 is information obtained by projecting the information indicating the events of the actual world 1 on a space-time having a lower dimension than the actual world 1. For example, the data 3 which is image data of a moving image, is information obtained by projecting an image of the three-dimensional space direction and time direction of the actual world 1 on the time-space having the two-dimensional space direction and time direction. Also, in the event that the data 3 is digital data for example, the data 3 is rounded off according to the sampling increments. In the event that the data 3 is analog data, information of the data 3 is either compressed according to the dynamic range, or a part of the information has been deleted by a limiter or the like.
Thus, by projecting the signals shown are information indicating events in the actual world 1 having a predetermined number of dimensions onto data 3 (detection signals), a part of the information indicating events in the actual world 1 is dropped. That is to say, a part of the information indicating events in the actual world 1 is dropped from the data 3 which the sensor 2 outputs.
However, even though a part of the information indicating events in the actual world 1 is dropped due to projection, the data 3 includes useful information for estimating the signals which are information indicating events (phenomena) in the actual world 1.
With the present invention, information having continuity contained in the actual world 1 or the data 3 is used as useful information for estimating the signals which is information of the actual world 1. Continuity is a concept which is newly defined.
Taking note of the actual world 1, events in the actual world 1 include characteristics which are constant in predetermined dimensional directions. For example, an object (corporeal object) in the actual world 1 either has shape, pattern, or color that is continuous in the space direction or time direction, or has repeated patterns of shape, pattern, or color.
Accordingly, the information indicating the events in actual world 1 includes characteristics constant in a predetermined dimensional direction.
With a more specific example, a linear object such as a string, cord, or rope, has a characteristic which is constant in the length-wise direction, i.e., the spatial direction, that the cross-sectional shape is the same at arbitrary positions in the length-wise direction. The constant characteristic in the spatial direction that the cross-sectional shape is the same at arbitrary positions in the length-wise direction comes from the characteristic that the linear object is long.
Accordingly, an image of the linear object has a characteristic which is constant in the length-wise direction, i.e., the spatial direction, that the cross-sectional shape is the same, at arbitrary positions in the length-wise direction.
Also, a monotone object, which is a corporeal object, having an expanse in the spatial direction, can be said to have a constant characteristic of having the same color in the spatial direction regardless of the part thereof.
In the same way, an image of a monotone object, which is a corporeal object, having an expanse in the spatial direction, have a constant characteristic of having the same color in the spatial direction regardless of the part thereof.
In this way, events in the actual world 1 (real world) have characteristics which are constant in predetermined dimensional directions, so signals of the actual world 1 have characteristics which are constant in predetermined dimensional directions.
In the present Specification, such characteristics which are constant in predetermined dimensional directions will be called continuity. Continuity of the signals of the actual world 1 (real world) means the characteristics which are constant in predetermined dimensional directions which the signals indicating the events of the actual world 1 (real world) have.
Countless such continuities exist in the actual world 1 (real world).
Next, taking note of the data 3, the data 3 is obtained by signals which is information indicating events of the actual world 1 having predetermined dimensions being projected by the sensor 2, and includes continuity corresponding to the continuity of signals in the real world. It can be said that the data 3 includes continuity wherein the continuity of actual world signals has been projected.
However, as described above, in the data 3 output from the sensor 2, a part of the information of the actual world 1 has been lost, so a part of the continuity contained in the signals of the actual world 1 (real world) may be lost from the data.
In other words, the data 3 contains at least a part of the continuity within the continuity of the signals of the actual world 1 (real world) as data continuity. Data continuity means characteristics which are constant in predetermined dimensional directions, which the data 3 has.
With the present invention, continuity of the actual world 1 signals, or the data continuity which the data 3 has, is used as significant data for estimating signals which are information indicating events of the actual world 1.
For example, with the signal processing device 4, information indicating an event in the actual world 1 which has been lost is generated by signals processing of the data 3, using data continuity.
Now, with the signal processing device 4, of the length (space), time, and mass, which are dimensions of signals serving as information indicating events in the actual world 1, continuity in the spatial direction or time direction, are used.
In FIG. 1, the sensor 2 is formed of, for example, a digital still camera, a video camera, or the like, and takes images of the actual world 1, and outputs the image data which is the obtained data 3, to a signal processing device 4. The sensor 2 may also be a thermography device, a pressure sensor using photo-elasticity, or the like.
The signal processing device 4 is configured of, for example, a personal computer or the like, and performs signal processing with regard to the data 3.
The signal processing device 4 is configured as shown in FIG. 2, for example. A CPU (Central Processing Unit) 21 executes various types of processing following programs stored in ROM (Read Only Memory) 22 or the storage unit 28. RAM (Random Access Memory) 23 stores programs to be executed by the CPU 21, data, and so forth, as suitable. The CPU 21, ROM 22, and RAM 23, are mutually connected by a bus 24.
Also connected to the CPU 21 is an input/output interface 25 via the bus 24. An input device 26 made up of a keyboard, mouse, microphone, and so forth, and an output unit 27 made up of a display, speaker, and so forth, are connected to the input/output interface 25. The CPU 21 executes various types of processing corresponding to commands input from the input unit 26. The CPU 21 then outputs images and audio and the like obtained as a result of processing to the output unit 27.
A storage unit 28 connected to the input/output interface 25 is configured of a hard disk for example, and stores the programs and various types of data which the CPU 21 executes. A communication unit 29 communicates with external devices via the Internet and other networks. In the case of this example, the communication unit 29 acts as an acquiring unit for capturing data 3 output from the sensor 2.
Also, an arrangement may be made wherein programs are obtained via the communication unit 29 and stored in the storage unit 28.
A drive 30 connected to the input/output interface 25 drives a magnetic disk 51, optical disk 52, magneto-optical disk 53, or semiconductor memory 54 or the like mounted thereto, and obtains programs and data recorded therein. The obtained programs and data are transferred to the storage unit 28 as necessary and stored.
FIG. 3 is a block diagram illustrating a signal processing device 4.
Note that whether the functions of the signal processing device 4 are realized by hardware or realized by software is irrelevant. That is to say, the block diagrams in the present Specification may be taken to be hardware block diagrams or may be taken to be software function block diagrams.
With the signal processing device 4 of which the configuration is shown in FIG. 3, image data which is an example of the data 3 is input, and the continuity of the data is detected from the input image data (input image). Next, the signals of the actual world 1 acquired by the sensor 2 are estimated from the continuity of the data detected. Then, based on the estimated signals of the actual world 1, an image is generated, and the generated image (output image) is output. That is to say, FIG. 3 is a diagram illustrating the configuration of the signal processing device 4 which is an image processing device.
The input image (image data which is an example of the data 3) input to the signal processing device 4 is supplied to a data continuity detecting unit 101 and actual world estimating unit 102.
The data continuity detecting unit 101 detects the continuity of the data from the input image, and supplies data continuity information indicating the detected continuity to the actual world estimating unit 102 and an image generating unit 103. The data continuity information includes, for example, the position of a region of pixels having continuity of data, the direction of a region of pixels having continuity of data (the angle or gradient of the time direction and space direction), or the length of a region of pixels having continuity of data, or the like in the input image. Detailed configuration of the data continuity detecting unit 101 will be described later.
The actual world estimating unit 102 estimates the signals of the actual world 1, based on the input image and the data continuity information supplied from the data continuity detecting unit 101. That is to say, the actual world estimating unit 102 estimates an image which is the signals of the actual world cast into the sensor 2 at the time that the input image was acquired. The actual world estimating unit 102 supplies the actual world estimation information indicating the results of the estimation of the signals of the actual world 1, to the image generating unit 103. The detailed configuration of the actual world estimating unit 102 will be described later.
The image generating unit 103 generates signals further approximating the signals of the actual world 1, based on the actual world estimation information indicating the estimated signals of the actual world 1, supplied from the actual world estimating unit 102, and outputs the generated signals. Or, the image generating unit 103 generates signals further approximating the signals of the actual world 1, based on the data continuity information supplied from the data continuity detecting unit 101, and the actual world estimation information indicating the estimated signals of the actual world 1, supplied from the actual world estimating unit 102, and outputs the generated signals.
That is to say, the image generating unit 103 generates an image further approximating the image of the actual world 1 based on the actual world estimation information, and outputs the generated image as an output image. Or, the image generating unit 103 generates an image further approximating the image of the actual world 1 based on the data continuity information and actual world estimation information, and outputs the generated image as an output image.
For example, the image generating unit 103 generates an image with higher resolution in the spatial direction or time direction in comparison with the input image, by integrating the estimated image of the actual world 1 within a desired range of the spatial direction or time direction, based on the actual world estimation information, and outputs the generated image as an output image. For example, the image generating unit 103 generates an image by extrapolation/interpolation, and outputs the generated image as an output image.
Detailed configuration of the image generating unit 103 will be described later.
Next, the principle of the present invention will be described with reference to FIG. 4.
For example, signals of the actual world 1, which are an image for example, are imaged on the photoreception face of a CCD (Charge Coupled Device) which is an example of the sensor 2. The CCD, which is an example of the sensor 2, has integration properties, so difference is generated in the data 3 output from the CCD as to the image of the actual world 1. Details of the integration properties of the sensor 2 will be described later.
With the signal processing by the signal processing device 4, the relationship between the image of the actual world 1 obtained by the CCD, and the data 3 taken by the CCD and output, is explicitly taken into consideration. That is to say, the relationship between the data 3 and the signals which is information of the actual world obtained by the sensor 2, is explicitly taken into consideration.
More specifically, as shown in FIG. 4, the signal processing device 4 uses a model 161 to approximate (describe) the actual world 1. The model 161 is represented by, for example, N variables. More accurately, the model 161 approximates (describes) signals of the actual world 1.
In order to predict the model 161, the signal processing device 4 extracts M pieces of data 162 from the data 3. At the time of extracting the M pieces of data 162 from the data 3, the signal processing device 4 uses the continuity of the data contained in the data 3, for example. In other words, the signal processing device 4 extracts data 162 for predicting the model 161, based on the continuity of the data contained in the data 3. Consequently, in this case, the model 161 is constrained by the continuity of the data.
That is to say, the model 161 approximates (information (signals) indicating) events of the actual world 1 having continuity (constant characteristics in a predetermined dimensional direction), which generates the data continuity in the data 3 when acquired with the sensor 2.
Now, in the event that the number M of the data 162 is N or more, which is the number of variables of the model, the model 161 represented by the N variables can be predicted, from the M pieces of the data 162.
In this way, the signal processing device 4 can take into consideration the signals which are information of the actual world 1, by predicting the model 161 approximating (describing) the (signals of the) actual world 1.
Next, the integration effects of the sensor 2 will be described.
An image sensor such as a CCD or CMOS (Complementary Metal-Oxide Semiconductor) sensor or the like, which is the sensor 2 for taking images, projects signals, which are information of the real world, onto two-dimensional data, at the time of imaging the real world. The pixels of the image sensor each have a predetermined area, as a so-called photoreception face (photoreception region). Incident light to the photoreception face having a predetermined area is integrated in the space direction and time direction for each pixel, and is converted into a single pixel value for each pixel.
The space-time integration of images will be described with reference to FIG. 5 through FIG. 8.
An image sensor images a subject (object) in the real world, and outputs the obtained image data as a result of imagining in increments of single frames. That is to say, the image sensor acquires signals of the actual world 1 which is light reflected off of the subject of the actual world 1, and outputs the data 3.
For example, the image sensor outputs image data of 30 frames per second. In this case, the exposure time of the image sensor can be made to be 1/30 seconds. The exposure time is the time from the image sensor starting conversion of incident light into electric charge, to ending of the conversion of incident light into electric charge. Hereafter, the exposure time will also be called shutter time.
FIG. 5 is a diagram describing an example of a pixel array on the image sensor. In FIG. 5, A through I denote individual pixels. The pixels are placed on a plane corresponding to the image displayed by the image data. A single detecting element corresponding to a single pixel is placed on the image sensor. At the time of the image sensor taking images of the actual world 1, the one detecting element outputs one pixel value corresponding to the one pixel making up the image data. For example, the position in the spatial direction X (X coordinate) of the detecting element corresponds to the horizontal position on the image displayed by the image data, and the position in the spatial direction Y (Y coordinate) of the detecting element corresponds to the vertical position on the image displayed by the image data.
Distribution of intensity of light of the actual world 1 has expanse in the three-dimensional spatial directions and the time direction, but the image sensor acquires light of the actual world 1 in two-dimensional spatial directions and the time direction, and generates data 3 representing the distribution of intensity of light in the two-dimensional spatial directions and the time direction.
As shown in FIG. 6, the detecting device which is a CCD for example, converts light cast onto the photoreception face (photoreception region) (detecting region) into electric charge during a period corresponding to the shutter time, and accumulates the converted charge. The light is information (signals) of the actual world 1 regarding which the intensity is determined by the three-dimensional spatial position and point-in-time. The distribution of intensity of light of the actual world 1 can be represented by a function F(x, y, z, t), wherein position x, y, z, in three-dimensional space, and point-in-time t, are variables.
The amount of charge accumulated in the detecting device which is a CCD is approximately proportionate to the intensity of the light cast onto the entire photoreception face having two-dimensional spatial expanse, and the amount of time that light is cast thereupon. The detecting device adds the charge converted from the light cast onto the entire photoreception face, to the charge already accumulated during a period corresponding to the shutter time. That is to say, the detecting device integrates the light cast onto the entire photoreception face having a two-dimensional spatial expanse, and accumulates a change of an amount corresponding to the integrated light during a period corresponding to the shutter time. The detecting device can also be said to have an integration effect regarding space (photoreception face) and time (shutter time).
The charge accumulated in the detecting device is converted into a voltage value by an unshown circuit, the voltage value is further converted into a pixel value such as digital data or the like, and is output as data 3. Accordingly, the individual pixel values output from the image sensor have a value projected on one-dimensional space, which is the result of integrating the portion of the information (signals) of the actual world 1 having time-space expanse with regard to the time direction of the shutter time and the spatial direction of the photoreception face of the detecting device.
That is to say, the pixel value of one pixel is represented as the integration of F(x, y, t). F(x, y, t) is a function representing the distribution of light intensity on the photoreception face of the detecting device. For example, the pixel value P is represented by Expression (1).




  
    
      
        P
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In Expression (1), x1 represents the spatial coordinate at the left-side boundary of the photoreception face of the detecting device (X coordinate). x2 represents the spatial coordinate at the right-side boundary of the photoreception face of the detecting device (X coordinate). In Expression (1), y1 represents the spatial coordinate at the top-side boundary of the photoreception face of the detecting device (Y coordinate). y2 represents the spatial coordinate at the bottom-side boundary of the photoreception face of the detecting device (Y coordinate). Also, t1 represents the point-in-time at which conversion of incident light into an electric charge was started. t2 represents the point-in-time at which conversion of incident light into an electric charge was ended.
Note that actually, the gain of the pixel values of the image data output from the image sensor is corrected for the overall frame, for example.
Each of the pixel values of the image data are integration values of the light cast on the photoreception face of each of the detecting elements of the image sensor, and of the light cast onto the image sensor, waveforms of light of the actual world 1 finer than the photoreception face of the detecting element are hidden in the pixel value as integrated values.
Hereafter, in the present Specification, the waveform of signals represented with a predetermined dimension as a reference may be referred to simply as waveforms.
Thus, the image of the actual world 1 (light signals) is integrated in the spatial direction and time direction in increments of pixels, so a part of the continuity of the image of the actual world 1 drops out from the image data, so another part of the continuity of the image of the actual world 1 is left in the image data. Or, there may be cases wherein continuity which has changed from the continuity of the image of the actual world 1 is included in the image data.
Further description will be made regarding the integration effect in the spatial direction for an image taken by an image sensor having integration effects.
FIG. 7 is a diagram describing the relationship between incident light to the detecting elements corresponding to the pixel D through pixel F, and the pixel values. F(x) in FIG. 7 is an example of a function representing the distribution of light intensity of the actual world 1, having the coordinate x in the spatial direction X in space (on the detecting device) as a variable. In other words, F(x) is an example of a function representing the distribution of light intensity of the actual world 1, with the spatial direction Y and time direction constant. In FIG. 7, L indicates the length in the spatial direction X of the photoreception face of the detecting device corresponding to the pixel D through pixel F.
The pixel value of a single pixel is represented as the integral of F(x). For example, the pixel value P of the pixel E is represented by Expression (2).




  
    
      
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In the Expression (2), x1 represents the spatial coordinate in the spatial direction X at the left-side boundary of the photoreception face of the detecting device corresponding to the pixel E. x2 represents the spatial coordinate in the spatial direction X at the right-side boundary of the photoreception face of the detecting device corresponding to the pixel E.
In the same way, further description will be made regarding the integration effect in the time direction for an image taken by an image sensor having integration effects.
FIG. 8 is a diagram for describing the relationship between time elapsed, the incident light to a detecting element corresponding to a single pixel, and the pixel value. F(t) in FIG. 8 is a function representing the distribution of light intensity of the actual world 1, having the point-in-time t as a variable. In other words, F(t) is an example of a function representing the distribution of light intensity of the actual world 1, with the spatial direction Y and the spatial direction X constant. Ts represents the shutter time.
The frame #n−1 is a frame which is previous to the frame #n time-wise, and the frame #n+1 is a frame following the frame #n time-wise. That is to say, the frame #n−1, frame #n, and frame #n+1, are displayed in the order of frame #n−1, frame #n, and frame #n+1.
Note that in the example shown in FIG. 8, the shutter time ts and the frame intervals are the same.
The pixel value of a single pixel is represented as the integral of F(t). For example, the pixel value P of the pixel of frame #n is represented by Expression (3).




  
    
      
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In the Expression (3), t1 represents the time at which conversion of incident light into an electric charge was started. t2 represents the time at which conversion of incident light into an electric charge was ended.
Hereafter, the integration effect in the spatial direction by the sensor 2 will be referred to simply as spatial integration effect, and the integration effect in the time direction by the sensor 2 also will be referred to simply as time integration effect. Also, space integration effects or time integration effects will be simply called integration effects.
Next, description will be made regarding an example of continuity of data included in the data 3 acquired by the image sensor having integration effects.
FIG. 9 is a diagram illustrating a linear object of the actual world 1 (e.g., a fine line), i.e., an example of distribution of light intensity. In FIG. 9, the position to the upper side of the drawing indicates the intensity (level) of light, the position to the upper right side of the drawing indicates the position in the spatial direction X which is one direction of the spatial directions of the image, and the position to the right side of the drawing indicates the position in the spatial direction Y which is the other direction of the spatial directions of the image.
The image of the linear object of the actual world 1 includes predetermined continuity. That is to say, the image shown in FIG. 9 has continuity in that the cross-sectional shape (the change in level as to the change in position in the direction orthogonal to the length direction), at any arbitrary position in the length direction.
FIG. 10 is a diagram illustrating an example of pixel values of image data obtained by actual image-taking, corresponding to the image shown in FIG. 9.
That is to say, FIG. 10 is a model diagram of the image data obtained by imaging, with the image sensor, an image of a linear object having a diameter shorter than the length L of the photoreception face of each pixel, and extending in a direction offset from the array of the pixels of the image sensor (the vertical or horizontal array of the pixels). The image cast into the image sensor at the time that the image data shown in FIG. 10 was acquired is an image of the linear object of the actual world 1 shown in FIG. 9.
In FIG. 10, the position to the upper side of the drawing indicates the pixel value, the position to the upper right side of the drawing indicates the position in the spatial direction X which is one direction of the spatial directions of the image, and the position to the right side of the drawing indicates the position in the spatial direction Y which is the other direction of the spatial directions of the image. The direction indicating the pixel value in FIG. 10 corresponds to the direction of level in FIG. 9, and the spatial direction X and spatial direction Y in FIG. 10 also are the same as the directions in FIG. 9.
In the event of taking an image of a linear object having a diameter shorter than the length L of the photoreception face of each pixel with the image sensor, the linear object is represented in the image data obtained as a result of the image-taking as multiple arc shapes (half-discs) having a predetermined length which are arrayed in a diagonally-offset fashion, in a model representation, for example. The arc shapes are of approximately the same shape. One arc shape is formed on one row of pixels vertically, or is formed on one row of pixels horizontally. For example, one arc shape shown in FIG. 10 is formed on one row of pixels vertically.
Thus, with the image data taken and obtained by the image sensor for example, the continuity in that the cross-sectional shape in the spatial direction Y at any arbitrary position in the length direction is the same, which the linear object image of the actual world 1 had, is lost. Also, it can be said that the continuity, which the linear object image of the actual world 1 had, has changed into continuity in that arc shapes of the same shape formed on one row of pixels vertically or formed on one row of pixels horizontally are arrayed at predetermined intervals.
FIG. 11 is a diagram illustrating an image in the actual world 1 of an object having a straight edge, and is of a monotone color different from that of the background, i.e., an example of distribution of light intensity. In FIG. 11, the position to the upper side of the drawing indicates the intensity (level) of light, the position to the upper right side of the drawing indicates the position in the spatial direction X which is one direction of the spatial directions of the image, and the position to the right side of the drawing indicates the position in the spatial direction Y which is the other direction of the spatial directions of the image.
The image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, includes predetermined continuity. That is to say, the image shown in FIG. 11 has continuity in that the cross-sectional shape (the change in level as to the change in position in the direction orthogonal to the edge) is the same at any arbitrary position in the length direction of the edge.
FIG. 12 is a diagram illustrating an example of pixel values of the image data obtained by actual image-taking, corresponding to the image shown in FIG. 11. As shown in FIG. 12, the image data is in a stepped shape, since the image data is made up of pixel values in increments of pixels.
FIG. 13 is a model diagram illustrating the image data shown in FIG. 12.
The model diagram shown in FIG. 13 is a model diagram of image data obtained by taking, with the image sensor, an image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, and extending in a direction offset from the array of the pixels of the image sensor (the vertical or horizontal array of the pixels). The image cast into the image sensor at the time that the image data shown in FIG. 13 was acquired is an image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, shown in FIG. 11.
In FIG. 13, the position to the upper side of the drawing indicates the pixel value, the position to the upper right side of the drawing indicates the position in the spatial direction X which is one direction of the spatial directions of the image, and the position to the right side of the drawing indicates the position in the spatial direction Y which is the other direction of the spatial directions of the image. The direction indicating the pixel value in FIG. 13 corresponds to the direction of level in FIG. 11, and the spatial direction X and spatial direction Y in FIG. 13 also are the same as the directions in FIG. 11.
In the event of taking an image of an object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background with an image sensor, the straight edge is represented in the image data obtained as a result of the image-taking as multiple pawl shapes having a predetermined length which are arrayed in a diagonally-offset fashion, in a model representation, for example. The pawl shapes are of approximately the same shape. One pawl shape is formed on one row of pixels vertically, or is formed on one row of pixels horizontally. For example, one pawl shape shown in FIG. 13 is formed on one row of pixels vertically.
Thus, the continuity of image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, in that the cross-sectional shape is the same at any arbitrary position in the length direction of the edge, for example, is lost in the image data obtained by imaging with an image sensor. Also, it can be said that the continuity, which the image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background had, has changed into continuity in that pawl shapes of the same shape formed on one row of pixels vertically or formed on one row of pixels horizontally are arrayed at predetermined intervals.
The data continuity detecting unit 101 detects such data continuity of the data 3 which is an input image, for example. For example, the data continuity detecting unit 101 detects data continuity by detecting regions having a constant characteristic in a predetermined dimensional direction. For example, the data continuity detecting unit 101 detects a region wherein the same arc shapes are arrayed at constant intervals, such as shown in FIG. 10. Also, for example, the data continuity detecting unit 101 detects a region wherein the same pawl shapes are arrayed at constant intervals, such as shown in FIG. 13.
Also, the data continuity detecting unit 101 detects continuity of the data by detecting angle (gradient) in the spatial direction, indicating an array of the same shapes.
Also, for example, the data continuity detecting unit 101 detects continuity of data by detecting angle (movement) in the space direction and time direction, indicating the array of the same shapes in the space direction and the time direction.
Further, for example, the data continuity detecting unit 101 detects continuity in the data by detecting the length of the region having constant characteristics in a predetermined dimensional direction.
Hereafter, the portion of data 3 where the sensor 2 has projected the image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, will also be called a two-valued edge.
Now, with conventional signal processing, desired high-resolution data, for example, is generated from the data 3.
Conversely, with the signal processing by the signal processing device 4, the actual world 1 is estimated from the data 3, and the high-resolution data is generated based on the estimation results. That is to say, the actual world 1 is estimated from the data 3, and the high-resolution data is generated based on the estimated actual world 1, taking into consideration the data 3.
In order to generate the high-resolution data from the actual world 1, there is the need to take into consideration the relationship between the actual world 1 and the data 3. For example, how the actual world 1 is projected on the data 3 by the sensor 2 which is a CCD, is taken into consideration.
The sensor 2 which is a CCD has integration properties as described above. That is to say, one unit of the data 3 (e.g., pixel value) can be calculated by integrating a signal of the actual world 1 with a detection region (e.g., photoreception face) of a detection device (e.g., CCD) of the sensor 2.
Applying this to the high-resolution data, the high-resolution data can be obtained by applying processing, wherein a virtual high-resolution sensor projects signals of the actual world 1 to the data 3, to the estimated actual world 1.
In other words, if the signals of the actual world 1 can be estimated from the data 3, one value contained in the high-resolution data can be obtained by integrating signals of the actual world 1 for each detection region of the detecting elements of the virtual high-resolution sensor (in the time-space direction).
For example, in the event that the change in signals of the actual world 1 are smaller than the size of the detection region of the detecting elements of the sensor 2, the data 3 cannot expresses the small changes in the signals of the actual world 1. Accordingly, high-resolution data indicating small change of the signals of the actual world 1 can be obtained by integrating the signals of the actual world 1 estimated from the data 3 with each region (in the time-space direction) that is smaller in comparison with the change in signals of the actual world 1.
That is to say, integrating the signals of the estimated actual world 1 with the detection region with regard to each detecting element of the virtual high-resolution sensor enables the high-resolution data to be obtained.
With the signal processing device 4, the image generating unit 103 generates the high-resolution data by integrating the signals of the estimated actual world 1 in the time-space direction regions of the detecting elements of the virtual high-resolution sensor, for example.
Next, in order to estimate the actual world 1 from the data 3, at the signal processing device 4, the relationship between the data 3 and the actual world 1, continuity, and a spatial or temporal mixture in the data 3 (space mixture or time mixture), are used.
Here, a mixture means a value in the data 3 wherein the signals of two objects in the actual world 1 are mixed to yield a single value.
A space mixture means the mixture of the signals of two objects in the spatial direction due to the spatial integration effects of the sensor 2. Time mixture will be described later.
The actual world 1 itself is made up of countless events, and accordingly, in order to represent the actual world 1 itself with mathematical expressions, for example, there is the need to have an infinite number of variables. It is impossible to predict all events of the actual world 1 from the data 3.
In the same way, it is impossible to predict all of the signals of the actual world 1 from the data 3.
Accordingly, with the signal processing device 4, of the signals of the actual world 1, a portion which has continuity and which can be expressed by the function f(x, y, z, t) is taken note of, and the portion of the signals of the actual world 1 which can be represented by the function f(x, y, z, t) and has continuity is approximated with a model 161 represented by N variables. As shown in FIG. 14, the model 161 is predicted from the M pieces of data 162 in the data 3.
In order to enable the model 161 to be predicted from the M pieces of data 162, first, there is the need to represent the model 161 with N variables based on the continuity, and second, to generate an expression using the N variables which indicates the relationship between the model 161 represented by the N variables and the M pieces of data 162 based on the integral properties of the sensor 2. Since the model 161 is represented by the N variables, based on the continuity, it can be said that the expression using the N variables that indicates the relationship between the model 161 represented by the N variables and the M pieces of data 162, describes the relationship between the part of the signals of the actual world 1 having continuity, and the part of the data 3 having data continuity.
In other words, the part of the signals of the actual world 1 having continuity, that is approximated by the model 161 represented by the N variables, generates data continuity in the data 3.
The data continuity detecting unit 101 detects the part of the data 3 where data continuity has been generated by the part of the signals of the actual world 1 having continuity, and the characteristics of the part where data continuity has been generated.
For example, as shown in FIG. 15, in an image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background, the edge at the position of interest indicated by A in FIG. 15, has a gradient. The arrow B in FIG. 15 indicates the gradient of the edge. A predetermined edge gradient can be represented as an angle as to a reference axis or as a direction as to a reference position. For example, a predetermined edge gradient can be represented as the angle between the coordinates axis of the spatial direction X and the edge. For example, the predetermined edge gradient can be represented as the direction indicated by the length of the spatial direction X and the length of the spatial direction Y.
At the time that the image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background is obtained at the sensor 2 and the data 3 is output, pawl shapes corresponding to the edge are arrayed in the data 3 at the position corresponding to the position of interest (A) of the edge in the image of the actual world 1, which is indicated by A′ in FIG. 15, and pawl shapes corresponding to the edge are arrayed in the direction corresponding to the gradient of the edge of the image in the actual world 1, in the direction of the gradient indicated by B′ in FIG. 15.
The model 161 represented with the N variables approximates such a portion of the signals of the actual world 1 generating data continuity in the data 3.
At the time of formulating an expression using the N variables indicating the relationship between the model 161 represented with the N variables and the M pieces of data 162, the values of part where data continuity is generated in the data 3 are used.
In this case, in the data 3 shown in FIG. 16, taking note of the values where data continuity is generated and which belong to a mixed region, an expression is formulated with a value integrating the signals of the actual world 1 as being equal to a value output by the detecting element of the sensor 2. For example, multiple expressions can be formulated regarding the multiple values in the data 3 where data continuity is generated.
In FIG. 16, A denotes the position of interest of the edge, and A′ denotes (the position of) the pixel corresponding to the position (A) of interest of the edge in the image of the actual world 1.
Now, a mixed region means a region of data in the data 3 wherein the signals for two objects in the actual world 1 are mixed and become one value. For example, a pixel value wherein, in the image of the object of the actual world 1 which has a straight edge and is of a monotone color different from that of the background in the data 3, the image of the object having the straight edge and the image of the background are integrated, belongs to a mixed region.
FIG. 17 is a diagram describing signals for two objects in the actual world 1 and values belonging to a mixed region, in a case of formulating an expression.
FIG. 17 illustrates, to the left, signals of the actual world 1 corresponding to two objects in the actual world 1 having a predetermined expansion in the spatial direction X and the spatial direction Y, which are acquired at the detection region of a single detecting element of the sensor 2. FIG. 17 illustrates, to the right, a pixel value P of a single pixel in the data 3 wherein the signals of the actual world 1 illustrated to the left in FIG. 17 have been projected by a single detecting element of the sensor 2. That is to say, illustrates a pixel value P of a single pixel in the data 3 wherein the signals of the actual world 1 corresponding to two objects in the actual world 1 having a predetermined expansion in the spatial direction X and the spatial direction Y which are acquired by a single detecting element of the sensor 2, have been projected.
L in FIG. 17 represents the level of the signal of the actual world 1 which is shown in white in FIG. 17, corresponding to one object in the actual world 1. R in FIG. 17 represents the level of the signal of the actual world 1 which is shown hatched in FIG. 17, corresponding to the other object in the actual world 1.
Here, the mixture ratio α is the ratio of (the area of) the signals corresponding to the two objects cast into the detecting region of the one detecting element of the sensor 2 having a predetermined expansion in the spatial direction X and the spatial direction Y. For example, the mixture ratio α represents the ratio of area of the level L signals cast into the detecting region of the one detecting element of the sensor 2 having a predetermined expansion in the spatial direction X and the spatial direction Y, as to the area of the detecting region of a single detecting element of the sensor 2.
In this case, the relationship between the level L, level R, and the pixel value P, can be represented by Expression (4).

α×L+f(1−α)×R=P  (4)

Note that there may be cases wherein the level R may be taken as the pixel value of the pixel in the data 3 positioned to the right side of the pixel of interest, and there may be cases wherein the level L may be taken as the pixel value of the pixel in the data 3 positioned to the left side of the pixel of interest.
Also, the time direction can be taken into consideration in the same way as with the spatial direction for the mixture ratio α and the mixed region. For example, in the event that an object in the actual world 1 which is the object of image-taking, is moving as to the sensor 2, the ratio of signals for the two objects cast into the detecting region of the single detecting element of the sensor 2 changes in the time direction. The signals for the two objects regarding which the ratio changes in the time direction, that have been cast into the detecting region of the single detecting element of the sensor 2, are projected into a single value of the data 3 by the detecting element of the sensor 2.
The mixture of signals for two objects in the time direction due to time integration effects of the sensor 2 will be called time mixture.
The data continuity detecting unit 101 detects regions of pixels in the data 3 where signals of the actual world 1 for two objects in the actual world 1, for example, have been projected. The data continuity detecting unit 101 detects gradient in the data 3 corresponding to the gradient of an edge of an image in the actual world 1, for example.
The actual world estimating unit 102 estimates the signals of the actual world 1 by formulating an expression using N variables, representing the relationship between the model 161 represented by the N variables and the M pieces of data 162, based on the region of the pixels having a predetermined mixture ratio α detected by the data continuity detecting unit 101 and the gradient of the region, for example, and solving the formulated expression.
Description will be made further regarding specific estimation of the actual world 1.
Of the signals of the actual world represented by the function F(x, y, z, t) let us consider approximating the signals of the actual world represented by the function F(x, y, t) at the cross-section in the spatial direction Z (the position of the sensor 2), with an approximation function f(x, y, t) determined by a position x in the spatial direction X, a position y in the spatial direction Y, and a point-in-time t.
Now, the detection region of the sensor 2 has an expanse in the spatial direction X and the spatial direction Y. In other words, the approximation function f(x, y, t) is a function approximating the signals of the actual world 1 having an expanse in the spatial direction and time direction, which are acquired with the sensor 2.
Let us say that projection of the signals of the actual world 1 from the sensor 2 yields a value P(x, y, t) of the data 3. The value P(x, y, t) of the data 3 is a pixel value which the sensor 2 which is an image sensor outputs, for example.
Now, in the event that the projection by the sensor 2 can be formulated, the value obtained by projecting the approximation function f(x, y, t) can be represented as a projection function S(x, y, t).
Obtaining the projection function S(x, y, t) has the following problems.
First, generally, the function F(x, y, z, t) representing the signals of the actual world 1 can be a function with an infinite number of orders.
Second, even if the signals of the actual world could be described as a function, the projection function S(x, y, t) via projection of the sensor 2 generally cannot be determined. That is to say, the action of projection by the sensor 2, in other words, the relationship between the input signals and output signals of the sensor 2, is unknown, so the projection function S(x, y, t) cannot be determined.
With regard to the first problem, let us consider expressing the function f(x, y, t) approximating signals of the actual world 1 with the sum of products of the function fi(x, y, t) which is a describable function (e.g., a function with a finite number of orders) and variables wi.
Also, with regard to the second problem, formulating projection by the sensor 2 allows us to describe the function Si(x, y, t) from the description of the function fi(x, y, t).
That is to say, representing the function f(x, y, t) approximating signals of the actual world 1 with the sum of products of the function fi(x, y, t) and variables wi, the Expression (5) can be obtained.




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ,
              y
              ,
              t
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              1
            
            N
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                f
                i
              
              ⁡
              
                (
                
                  x
                  ,
                  y
                  ,
                  t
                
                )
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




For example, as indicated in Expression (6), the relationship between the data 3 and the signals of the actual world can be formulated as shown in Expression (7) from Expression (5) by formulating the projection of the sensor 2.




  
    
      
        
          
            S
            i
          
          ⁡
          
            (
            
              x
              ,
              y
              ,
              t
            
            )
          
        
        =
        
          ∫
          
            ∫
            
              ∫
              
                
                  
                    f
                    i
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                      ,
                      t
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
                ⁢
                
                  d
                  t
                
              
            
          
        
      
    
    
      
        (
        6
        )
      
    
  
  
    
      
        
          
            P
            j
          
          ⁡
          
            (
            
              
                x
                j
              
              ,
              
                y
                j
              
              ,
              
                t
                j
              
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              1
            
            N
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                S
                i
              
              ⁡
              
                (
                
                  
                    x
                    j
                  
                  ,
                  
                    y
                    j
                  
                  ,
                  
                    t
                    j
                  
                
                )
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




In Expression (7), j represents the index of the data.
In the event that M data groups (j=1 through M) common with the N variables wi (i=1 through N) exists in Expression (7), Expression (8) is satisfied, so the model 161 of the actual world can be obtained from data 3.

N≦M  (8)

N is the number of variables representing the model 161 approximating the actual world 1. M is the number of pieces of data 162 include in the data 3.
Representing the function f(x, y, t) approximating the actual world 1 signals with Expression (5) allows the variable portion wi to be handled independently. At this time, i represents the number of variables. Also, the form of the function represented by fi can be handed independently, and a desired function can be used for fi.
Accordingly, the number N of the variables wi can be defined without dependence on the function fi, and the variables wi can be obtained from the relationship between the number N of the variables wi and the number of pieces of data M.
That is to say, using the following three allows the actual world 1 to be estimated from the data 3.
First, the N variables are determined. That is to say, Expression (5) is determined. This enables describing the actual world 1 using continuity. For example, the signals of the actual world 1 can be described with a model 161 wherein a cross-section is expressed with a polynomial, and the same cross-sectional shape continues in a constant direction.
Second, for example, projection by the sensor 2 is formulated, describing Expression (7). For example, this is formulated such that the results of integration of the signals of the actual world 2 are data 3.
Third, M pieces of data 162 are collected to satisfy Expression (8). For example, the data 162 is collected from a region having data continuity that has been detected with the data continuity detecting unit 101. For example, data 162 of a region wherein a constant cross-section continues, which is an example of continuity, is collected.
In this way, the relationship between the data 3 and the actual world 1 is described with the Expression (5), and M pieces of data 162 are collected, thereby satisfying Expression (8), and the actual world 1 can be estimated.
More specifically, in the event of N=M, the number of variables N and the number of expressions M are equal, so the variables wi can be obtained by formulating a simultaneous equation.
Also, in the event that N<M, various solving methods can be applied. For example, the variables wi can be obtained by least-square.
Now, the solving method by least-square will be described in detail.
First, an Expression (9) for predicting data 3 from the actual world 1 will be shown according to Expression (7).




  
    
      
        
          P
          j
          ′
        
        =
        
          
            (
            
              
                x
                j
              
              ,
              
                y
                j
              
              ,
              
                t
                j
              
            
            )
          
          =
          
            
              ∑
              
                i
                =
                1
              
              N
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                
                  S
                  i
                
                ⁡
                
                  (
                  
                    
                      x
                      j
                    
                    ,
                    
                      y
                      j
                    
                    ,
                    
                      t
                      j
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




In Expression (9), P′j(xj, yj, tj) is a prediction value.
The sum of squared differences E for the prediction value P′ and observed value P is represented by Expression (10).




  
    
      
        E
        =
        
          
            ∑
            
              j
              =
              1
            
            M
          
          ⁢
          
            
              (
              
                
                  
                    P
                    j
                  
                  ⁡
                  
                    (
                    
                      
                        x
                        j
                      
                      ,
                      
                        y
                        j
                      
                      ,
                      
                        t
                        j
                      
                    
                    )
                  
                
                -
                
                  
                    P
                    j
                    ′
                  
                  ⁡
                  
                    (
                    
                      
                        x
                        j
                      
                      ,
                      
                        y
                        j
                      
                      ,
                      
                        t
                        j
                      
                    
                    )
                  
                
              
              )
            
            2
          
        
      
    
    
      
        (
        10
        )
      
    
  




The variables wi are obtained such that the sum of squared differences E is the smallest. Accordingly, the partial differential value of Expression (10) for each variable wk is 0. That is to say, Expression (11) holds.




  
    
      
        
          
            
              
                
                  ∂
                  E
                
                
                  ∂
                  
                    w
                    k
                  
                
              
              =
              
                
                  
                    -
                    2
                  
                  ⁢
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        w
                        i
                      
                      ⁢
                      
                        
                          S
                          k
                        
                        ⁡
                        
                          (
                          
                            
                              x
                              j
                            
                            ,
                            
                              y
                              j
                            
                            ,
                            
                              t
                              j
                            
                          
                          )
                        
                      
                      ⁢
                      
                        (
                        
                          
                            
                              P
                              j
                            
                            ⁡
                            
                              (
                              
                                
                                  x
                                  
                                    
                                      
                                    
                                    ⁢
                                    j
                                  
                                
                                ,
                                
                                  y
                                  
                                    
                                      
                                    
                                    ⁢
                                    j
                                  
                                
                                ,
                                
                                  t
                                  
                                    
                                      
                                    
                                    ⁢
                                    j
                                  
                                
                              
                              )
                            
                          
                          -
                          
                            
                              ∑
                              
                                i
                                ⁢
                                
                                  
                                
                                =
                                
                                  
                                
                                ⁢
                                1
                              
                              
                                
                                  
                                
                                ⁢
                                N
                              
                            
                            ⁢
                            
                              
                                w
                                
                                  
                                    
                                  
                                  ⁢
                                  i
                                
                              
                              ⁢
                              
                                
                                  S
                                  
                                    
                                      
                                    
                                    ⁢
                                    i
                                  
                                
                                ⁡
                                
                                  (
                                  
                                    
                                      
                                        x
                                        
                                          
                                            
                                          
                                          ⁢
                                          j
                                        
                                      
                                      ⁢
                                      
                                        y
                                        
                                          
                                            
                                          
                                          ⁢
                                          j
                                        
                                      
                                    
                                    ,
                                    
                                      t
                                      j
                                    
                                  
                                  )
                                
                              
                            
                          
                        
                        )
                      
                    
                  
                
                =
                0
              
            
          
        
        
          
            
              
            
          
        
      
    
    
      
        (
        11
        )
      
    
  




Expression (11) yields Expression (12).




  
    
      
        
          
            ∑
            
              j
              =
              1
            
            M
          
          ⁢
          
            (
            
              
                
                  S
                  k
                
                ⁡
                
                  (
                  
                    
                      x
                      j
                    
                    ,
                    
                      y
                      j
                    
                    ,
                    
                      t
                      j
                    
                  
                  )
                
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    1
                  
                  N
                
                ⁢
                
                  
                    w
                    i
                  
                  ⁢
                  
                    
                      S
                      i
                    
                    ⁡
                    
                      (
                      
                        
                          x
                          j
                        
                        ,
                        
                          y
                          j
                        
                        ,
                        
                          t
                          j
                        
                      
                      )
                    
                  
                
              
            
            )
          
        
        =
        
          
            ∑
            
              j
              =
              1
            
            M
          
          ⁢
          
            
              
                S
                k
              
              ⁡
              
                (
                
                  
                    x
                    j
                  
                  ,
                  
                    y
                    j
                  
                  ,
                  
                    t
                    j
                  
                
                )
              
            
            ⁢
            
              
                P
                j
              
              ⁡
              
                (
                
                  
                    x
                    j
                  
                  ,
                  
                    y
                    j
                  
                  ,
                  
                    t
                    j
                  
                
                )
              
            
          
        
      
    
    
      
        (
        12
        )
      
    
  




When Expression (12) holds with K=1 through N, the solution by least-square is obtained. The normal equation thereof is shown in Expression (13).




  
    
      
        
          
            (
            
              
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋰
                
                
                  ⋮
                
              
              
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          2
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          N
                        
                        ⁡
                        
                          (
                          j
                          )
                        
                      
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    w
                    1
                  
                
              
              
                
                  
                    
                  
                
              
              
                
                  
                    w
                    2
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    w
                    N
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        2
                      
                      ⁢
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        N
                      
                      ⁢
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        13
        )
      
    
  




Note that in Expression (13), Si(xj, yj, tj) is described as Si(j).




  
    
      
        
          S
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋰
              
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        14
        )
      
    
  








  
    
      
        
          W
          MAT
        
        =
        
          (
          
            
              
                
                  w
                  1
                
              
            
            
              
                
                  
                
              
            
            
              
                
                  w
                  2
                
              
            
            
              
                ⋮
              
            
            
              
                
                  w
                  N
                
              
            
          
          )
        
      
    
    
      
        (
        15
        )
      
    
  
  
    
      
        
          P
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        2
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      j
                      =
                      1
                    
                    M
                  
                  ⁢
                  
                    
                      
                        S
                        N
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                    ⁢
                    
                      
                        P
                        j
                      
                      ⁡
                      
                        (
                        j
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        16
        )
      
    
  




From Expression (14) through Expression (16). Expression (13) can be expressed as SMATWMAT=PMAT.
In Expression (13), Si represents the projection of the actual world 1. In Expression (13), Pj represents the data 3. In Expression (13), wi represents variables for describing and obtaining the characteristics of the signals of the actual world 1.
Accordingly, inputting the data 3 into Expression (13) and obtaining WMAT by a matrix solution or the like enables the actual world 1 to be estimated. That is to say, the actual world 1 can be estimated by computing Expression (17).




  
    
      
        
          W
          MAT
        
        =
        
          
            S
            MAT
            
              -
              1
            
          
          ⁢
          
            P
            MAT
          
        
      
    
    
      
        (
        17
        )
      
    
  




Note that in the event that SMAT is not regular, a transposed matrix of SMAT can be used to obtain WMAT.
The actual world estimating unit 102 estimates the actual world 1 by, for example, inputting the data 3 into Expression (13) and obtaining WMAT by a matrix solution or the like.
Now, an even more detailed example will be described. For example, the cross-sectional shape of the signals of the actual world 1, i.e., the change in level as to the change in position, will be described with a polynomial. Let us assume that the cross-sectional shape of the signals of the actual world 1 is constant, and that the cross-section of the signals of the actual world 1 moves at a constant speed. Projection of the signals of the actual world 1 from the sensor 2 to the data 3 is formulated by three-dimensional integration in the time-space direction of the signals of the actual world 1.
The assumption that the cross-section of the signals of the actual world 1 moves at a constant speed yields Expression (18) and Expression (19).




  
    
      
        
          
            d
            x
          
          
            d
            t
          
        
        =
        
          v
          x
        
      
    
    
      
        (
        18
        )
      
    
  
  
    
      
        
          
            d
            y
          
          
            d
            t
          
        
        =
        
          v
          y
        
      
    
    
      
        (
        19
        )
      
    
  




Here, vx and vy are constant.
Using Expression (18) and Expression (19), the cross-sectional shape of the signals of the actual world 1 can be represented as in Expression (20).

f(x′,y′)=f(x+vxt,y+vyt)  (20)

Formulating projection of the signals of the actual world 1 from the sensor 2 to the data 3 by three-dimensional integration in the time-space direction of the signals of the actual world 1 yields Expression (21).




  
    
      
        
          
            
              
                S
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                    ,
                    t
                  
                  )
                
              
              =
              
                
                  ∫
                  
                    x
                    s
                  
                  
                    x
                    e
                  
                
                ⁢
                
                  
                    ∫
                    
                      y
                      s
                    
                    
                      y
                      e
                    
                  
                  ⁢
                  
                    
                      ∫
                      
                        t
                        s
                      
                      
                        t
                        e
                      
                    
                    ⁢
                    
                      
                        f
                        ⁡
                        
                          (
                          
                            
                              x
                              ′
                            
                            ,
                            
                              y
                              ′
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        x
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        y
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
          
        
        
          
            
              =
              
                
                  ∫
                  
                    x
                    s
                  
                  
                    x
                    e
                  
                
                ⁢
                
                  
                    ∫
                    
                      y
                      s
                    
                    
                      y
                      e
                    
                  
                  ⁢
                  
                    
                      ∫
                      
                        t
                        s
                      
                      
                        t
                        e
                      
                    
                    ⁢
                    
                      
                        f
                        ⁡
                        
                          (
                          
                            
                              x
                              +
                              
                                
                                  v
                                  x
                                
                                ⁢
                                t
                              
                            
                            ,
                            
                              y
                              +
                              
                                
                                  v
                                  y
                                
                                ⁢
                                t
                              
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        x
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        y
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        21
        )
      
    
  




In Expression (21), S(x, y, t) represents an integrated value the region from position xs to position xe for the spatial direction X, from position ys to position ye for the spatial direction Y, and from point-in-time ts to point-in-time te for the time direction t, i.e., the region represented as a space-time cuboid.
Solving Expression (13) using a desired function f(x′, y′) whereby Expression (21) can be determined enables the signals of the actual world 1 to be estimated.
In the following, we will use the function indicated in Expression (22) as an example of the function f(x′, y′).




  
    
      
        
          
            
              
                f
                ⁡
                
                  (
                  
                    
                      x
                      ′
                    
                    ,
                    
                      y
                      ′
                    
                  
                  )
                
              
              =
              
                
                  
                    w
                    1
                  
                  ⁢
                  
                    x
                    ′
                  
                
                +
                
                  
                    w
                    2
                  
                  ⁢
                  
                    y
                    ′
                  
                
                +
                
                  w
                  3
                
              
            
          
        
        
          
            
              =
              
                
                  
                    w
                    1
                  
                  ⁡
                  
                    (
                    
                      x
                      +
                      
                        
                          v
                          x
                        
                        ⁢
                        t
                      
                    
                    )
                  
                
                +
                
                  
                    w
                    2
                  
                  ⁡
                  
                    (
                    
                      y
                      +
                      
                        
                          v
                          y
                        
                        ⁢
                        t
                      
                    
                    )
                  
                
                +
                
                  w
                  3
                
              
            
          
        
      
    
    
      
        (
        22
        )
      
    
  




That is to say, the signals of the actual world 1 are estimated to include the continuity represented in Expression (18), Expression (19), and Expression (22). This indicates that the cross-section with a constant shape is moving in the space-time direction as shown in FIG. 18.
Substituting Expression (22) into Expression (21) yields Expression (23).




  
    
      
        
          
            
              
                S
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                    ,
                    t
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∫
                  
                    x
                    s
                  
                  
                    x
                    e
                  
                
                ⁢
                
                  
                    ∫
                    
                      y
                      s
                    
                    
                      y
                      e
                    
                  
                  ⁢
                  
                    
                      ∫
                      
                        t
                        s
                      
                      
                        t
                        e
                      
                    
                    ⁢
                    
                      
                        f
                        ⁡
                        
                          (
                          
                            
                              x
                              +
                              
                                
                                  v
                                  x
                                
                                ⁢
                                t
                              
                            
                            ,
                            
                              y
                              +
                              
                                
                                  v
                                  y
                                
                                ⁢
                                t
                              
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        x
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        y
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                Volume
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    
                      
                        
                          w
                          0
                        
                        2
                      
                      ⁢
                      
                        (
                        
                          
                            x
                            e
                          
                          +
                          
                            x
                            s
                          
                          +
                          
                            
                              v
                              x
                            
                            ⁡
                            
                              (
                              
                                
                                  t
                                  e
                                
                                +
                                
                                  t
                                  s
                                
                              
                              )
                            
                          
                        
                        )
                      
                    
                    +
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    
                      w
                      1
                    
                    2
                  
                  ⁢
                  
                    (
                    
                      
                        y
                        e
                      
                      +
                      
                        y
                        s
                      
                      +
                      
                        
                          v
                          y
                        
                        ⁡
                        
                          (
                          
                            
                              t
                              e
                            
                            +
                            
                              t
                              s
                            
                          
                          )
                        
                      
                    
                    )
                  
                
                +
                
                  w
                  2
                
              
              )
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    w
                    0
                  
                  ⁢
                  
                    
                      S
                      0
                    
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                        ,
                        t
                      
                      )
                    
                  
                
                +
                
                  
                    w
                    1
                  
                  ⁢
                  
                    
                      S
                      1
                    
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                        ,
                        t
                      
                      )
                    
                  
                
                +
                
                  
                    w
                    2
                  
                  ⁢
                  
                    
                      S
                      2
                    
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                        ,
                        t
                      
                      )
                    
                  
                
              
            
          
        
      
    
    
      
        (
        23
        )
      
    
  




wherein
Volume=(xe−xs) (ye−ys) (te−ts)
S0(x, y, t)=Volume/2×(xe+xs+vx(te+ts))
S1(x, y, t)=Volume/2×(ye+ys+vy(te+ts))
S2(x, y, t)=1
holds.
FIG. 19 is a diagram illustrating an example of the M pieces of data 162 extracted from the data 3. For example, let us say that 27 pixel values are extracted as the data 162, and that the extracted pixel values are Pj(x, y, t). In this case, j is 0 through 26.
In the example shown in FIG. 19, in the event that the pixel value of the pixel corresponding to the position of interest at the point-in-time t which is n is P13(x, y, t), and the direction of array of the pixel values of the pixels having the continuity of data (e.g., the direction in which the same-shaped pawl shapes detected by the data continuity detecting unit 101 are arrayed) is a direction connecting P4 (x, y, t), P13(x, y, t), and P22(x, y, t), the pixel values P9(x, y, t) through P17(x, y, t) at the point-in-time t which is n, the pixel values P0(x, y, t) through P8(x, y, t) at the point-in-time t which is n−1 which is earlier in time than n, and the pixel values P18(x, y, t) through P26(x, y, t) at the point-in-time t which is n+1 which is later in time than n, are extracted.
Now, the region regarding which the pixel values, which are the data 3 output from the image sensor which is the sensor 2, have been obtained, have a time-direction and two-dimensional spatial direction expansion. Now, for example, the center of gravity of the cuboid corresponding to the pixel values (the region regarding which the pixel values have been obtained) can be used as the position of the pixel in the space-time direction.
Generating Expression (13) from the 27 pixel values P0(x, y, t) through P26(x, y, t) and from Expression (23), and obtaining W, enables the actual world 1 to be estimated.
In this way, the actual world estimating unit 102 generates Expression (13) from the 27 pixel values P0(x, y, t) through P26(x, y, t) and from Expression (23), and obtains W, thereby estimating the signals of the actual world 1.
Note that a Gaussian function, a sigmoid function, or the like, can be used for the function fi(x, y, t).
An example of processing for generating high-resolution data with even higher resolution, corresponding to the data 3, from the estimated actual world 1 signals, will be described with reference to FIG. 20 through FIG. 23.
As shown in FIG. 20, the data 3 has a value wherein signals of the actual world 1 are integrated in the time direction and two-dimensional spatial directions. For example, a pixel value which is data 3 that has been output from the image sensor which is the sensor 2 has a value wherein the signals of the actual world 1, which is light cast into the detecting device, are integrated by the shutter time which is the detection time in the time direction, and integrated by the photoreception region of the detecting element in the spatial direction.
Conversely, as shown in FIG. 21, the high-resolution data with even higher resolution in the spatial direction is generated by integrating the estimated actual world 1 signals in the time direction by the same time as the detection time of the sensor 2 which has output the data 3, and also integrating in the spatial direction by a region narrower in comparison with the photoreception region of the detecting element of the sensor 2 which has output the data 3.
Note that at the time of generating the high-resolution data with even higher resolution in the spatial direction, the region where the estimated signals of the actual world 1 are integrated can be set completely disengaged from photoreception region of the detecting element of the sensor 2 which has output the data 3. For example, the high-resolution data can be provided with resolution which is that of the data 3 magnified in the spatial direction by an integer, of course, and further, can be provided with resolution which is that of the data 3 magnified in the spatial direction by a rational number such as 5/3 times, for example.
Also, as shown in FIG. 22, the high-resolution data with even higher resolution in the time direction is generated by integrating the estimated actual world 1 signals in the spatial direction by the same region as the photoreception region of the detecting element of the sensor 2 which has output the data 3, and also integrating in the time direction by a time shorter than the detection time of the sensor 2 which has output the data 3.
Note that at the time of generating the high-resolution data with even higher resolution in the time direction, the time by which the estimated signals of the actual world 1 are integrated can be set completely disengaged from shutter time of the detecting element of the sensor 2 which has output the data 3. For example, the high-resolution data can be provided with resolution which is that of the data 3 magnified in the time direction by an integer, of course, and further, can be provided with resolution which is that of the data 3 magnified in the time direction by a rational number such as 7/4 times, for example.
High-resolution data with movement blurring removed is generated by integrating the estimated actual world 1 signals only in the spatial direction and not in the time direction.
Further, as shown in FIG. 23, high-resolution data with higher resolution in the time direction and space direction is generated by integrating the estimated actual world 1 signals in the spatial direction by a region narrower in comparison with the photoreception region of the detecting element of the sensor 2 which has output the data 3, and also integrating in the time direction by a time shorter in comparison with the detection time of the sensor 2 which has output the data 3.
In this case, the region and time for integrating the estimated actual world 1 signals can be set completely unrelated to the photoreception region and shutter time of the detecting element of the sensor 2 which has output the data 3.
Thus, the image generating unit 103 generates data with higher resolution in the time direction or the spatial direction, by integrating the estimated actual world 1 signals by a desired space-time region, for example.
Accordingly, data which is more accurate with regard to the signals of the actual world 1, and which has higher resolution in the time direction or the space direction, can be generated by estimating the signals of the actual world 1.
FIG. 24 through FIG. 28 illustrate an example of an input image and an example of the results of processing with the signal processing device 4 used for signal processing.
FIG. 24 is a diagram illustrating an original image of an input image (equivalent to light signals of the actual world 1). FIG. 25 is a diagram illustrating an example of an input image. The input image shown in FIG. 25 is an image generated by taking the average value of pixel values of pixels belonging to blocks made up of 2 by 2 pixels of the image shown in FIG. 24, as the pixel value of a single pixel. That is to say, the input image is an image obtained by applying spatial direction integration to the image shown in FIG. 24, imitating the integrating properties of the sensor.
The original image shown in FIG. 24 contains an image of a fine line inclined at approximately 5 degrees in the clockwise direction from the vertical direction. In the same way, the input image shown in FIG. 25 contains an image of a fine line inclined at approximately 5 degrees in the clockwise direction from the vertical direction.
FIG. 26 is a diagram illustrating an image obtained by applying conventional class classification adaptation processing to the input image shown in FIG. 25. Now, class classification processing is made up of class classification processing and adaptation processing, wherein the data is classified based on the nature thereof by the class classification adaptation processing, and subjected to adaptation processing for each class. In the adaptation processing, a low-image quality or standard image quality image, for example, is converted into a high image quality image by being subjected to mapping (mapping) using a predetermined tap coefficient.
That is to say, with adaptation processing, first data is converted into second data by being mapped (mapping) using a predetermined tap coefficient.
Now, adaptation processing will be described with regard to a mapping method using the tap coefficient, wherein for example, a linear combination model is used, and also a low-resolution image or standard resolution SD (Standard Definition) image obtained by filtering a high-resolution HD (High Definition) image with a low-pass filter is used as the first data, and the HD image used for obtaining the SD image is used as the second data.
Now, under the above-described conditions, an HD pixel y making up the HD image can be obtained with the following linear expression (linear combination) using multiple SD pixels extracted from SD pixels making up the SD image, as a prediction tap for predicting the HD image, and the tap coefficient.




  
    
      
        y
        =
        
          
            ∑
            
              n
              =
              1
            
            N
          
          ⁢
          
            
              w
              n
            
            ⁢
            
              x
              n
            
          
        
      
    
    
      
        (
        24
        )
      
    
  




Wherein, in Expression (24), xn represents the pixel value of the n'th pixel in the SD image, making up a prediction tap regarding the HD pixel y, and wn represents the n'th tap coefficient to be multiplied by (the pixel value of) the n'th SD pixel. Note that in Expression (24), a prediction tap is made up of an N number of SD pixels x1, x2, . . . , xN.
Now, the pixel value y of the HD pixel can be obtained by a quadratic expression or higher, instead of the linear expression shown in Expression (24).
Now, in the HD image, saying that Yk represents the true value of (the pixel value of) the k'th HD pixel, and Yk′ represents a prediction value of the true value Yk obtained by the Expression (24), the prediction error ek thereof is as expressed in the following Expression, for example.

ek=yk−yk′  (25)

The prediction value yk′ in Expression (25) is obtained according to Expression (24), so substituting the yk′ in Expression (25) according Expression (24) yields the following Expression.




  
    
      
        
          e
          k
        
        =
        
          
            y
            k
          
          -
          
            (
            
              
                ∑
                
                  n
                  =
                  1
                
                N
              
              ⁢
              
                
                  w
                  n
                
                ⁢
                
                  x
                  
                    n
                    ,
                    k
                  
                
              
            
            )
          
        
      
    
    
      
        (
        26
        )
      
    
  




Wherein, in Expression (26), Xn,k represents the n'th SD pixel making up the prediction tap for the k'th HD pixel.
While a tap coefficient wn wherein the prediction error ek is 0 in Expression (26) is optimal for predicting the HD pixel, obtaining such a tap coefficient wn for all HD pixels is generally difficult.
Accordingly, as a rule representing the tap coefficient wn as being optimal, employing the least-square method for example, means that the optimal tap coefficient wn can be obtained by minimizing the summation E of squared errors represented in the following Expression for example, as a statistical error.




  
    
      
        E
        =
        
          
            ∑
            
              k
              =
              1
            
            K
          
          ⁢
          
            e
            k
            2
          
        
      
    
    
      
        (
        27
        )
      
    
  




Wherein, in Expression (27), K represents the number of samples of sets made up of an HD pixel yk and SD pixels X1,k, X2,k, . . . , XN,k making up a prediction tap regarding that HD pixel yk.
The tap coefficient Wn which makes the summation E of squared errors in Expression (27) smallest (the minimum) is such that the partial differentiation of the summation E by the tap coefficient wn yields 0. Accordingly, the following Expression must be satisfied.




  
    
      
        
          
            ∂
            E
          
          
            ∂
            
              w
              n
            
          
        
        =
        
          
            
              
                e
                1
              
              ⁢
              
                
                  ∂
                  
                    e
                    1
                  
                
                
                  ∂
                  
                    w
                    n
                  
                
              
            
            +
            
              
                e
                2
              
              ⁢
              
                
                  ∂
                  
                    e
                    2
                  
                
                
                  ∂
                  
                    w
                    n
                  
                
              
            
            +
            ...
            +
            
              
                e
                k
              
              ⁢
              
                
                  ∂
                  
                    e
                    
                      k
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                
                
                  ∂
                  
                    w
                    n
                  
                
              
            
          
          =
          
            0
            ⁢
            
              
            
            ⁢
            
              (
              
                
                  n
                  =
                  1
                
                ,
                2
                ,
                ...
                ⁢
                
                  
                
                ,
                N
              
              )
            
          
        
      
    
    
      
        (
        28
        )
      
    
  




Now, partial differentiation of the above Expression (26) by the tap coefficient wn yields the following Expression.




  
    
      
        
          
            
              ∂
              
                e
                k
              
            
            
              ∂
              
                w
                1
              
            
          
          =
          
            -
            
              X
              
                1
                ,
                k
              
            
          
        
        ,
        
          
            
              ∂
              
                e
                k
              
            
            
              ∂
              
                w
                2
              
            
          
          =
          
            -
            
              X
              
                2
                ,
                k
              
            
          
        
        ,
        ...
        ⁢
        
          
        
        ,
        
          
            
              ∂
              
                e
                k
              
            
            
              ∂
              
                w
                
                  n
                  ⁢
                  
                    
                  
                
              
            
          
          =
          
            -
            
              X
              
                N
                ,
                k
              
            
          
        
        ,
        
          (
          
            
              k
              =
              1
            
            ,
            2
            ,
            ...
            ⁢
            
              
            
            ,
            K
          
          )
        
      
    
    
      
        (
        29
        )
      
    
  




Expressions (28) and (29) yield the following Expression.




  
    
      
        
          
            
              ∑
              
                k
                =
                1
              
              k
            
            ⁢
            
              
                e
                k
              
              ⁢
              
                X
                
                  1
                  ,
                  k
                
              
            
          
          =
          0
        
        ,
        
          
            
              ∑
              
                k
                =
                1
              
              k
            
            ⁢
            
              
                e
                k
              
              ⁢
              
                X
                
                  2
                  ,
                  k
                
              
            
          
          =
          0
        
        ,
        
          
            ...
            ⁢
            
              
            
            ⁢
            
              
                ∑
                
                  k
                  =
                  1
                
                k
              
              ⁢
              
                
                  e
                  k
                
                ⁢
                
                  X
                  
                    N
                    ,
                    k
                  
                
              
            
          
          =
          0
        
      
    
    
      
        (
        30
        )
      
    
  




Substituting Expression (26) for ek in Expression (30) allows Expression (30) to be expressed in the form of the normal equation in Expression (31).




  
    
      
        
          
            [
            
              
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
                
                  ⋯
                
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            N
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
              
              
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            2
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            2
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            2
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
                
                  ⋯
                
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            2
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            N
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋰
                
                
                  ⋮
                
              
              
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            N
                            ,
                            k
                          
                        
                        ⁢
                        
                          X
                          
                            1
                            ,
                            k
                          
                        
                      
                    
                    )
                  
                
                
                  
                    (
                    
                      
                        ∑
                        
                          k
                          =
                          1
                        
                        k
                      
                      ⁢
                      
                        
                          X
                          
                            N
                            ,
                            k
                          
                        
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Preparing a certain number of sets of the HD pixel yk and SD pixels xn,k allows as many of the normal equations in Expression (31) to be formulated as the number of tap coefficients wn to be obtained, and solving Expression (31) allows optimal tap coefficients wn to be obtained. Note that sweeping (Gauss-Jordan elimination) or the like, for example, can be used for solving Expression (31).
As described above, adaptation processing involves taking a great number of HD pixels y1, y2, . . . , yK as tutor data to serve as a tutor for learning for tap coefficients, and also taking SD pixels X1,k, X2,k, . . . , XN,k making up a prediction tap regarding each HD pixel yk as student data to serve as a student for learning for tap coefficients, and solving Expression (31), thereby performing learning for obtaining an optimal tap coefficient wn, and further using the optimal tap coefficient wn to perform mapping (conversion) of an SD image into an HD image according to Expression (24).
Now, for the SD pixels X1,k, X2,k, . . . XN,k making up the prediction tap regarding the HD pixels yk, an SD pixel close to a position on the SD image corresponding to the HD pixel yk, either spatially or temporally, can be used.
Also, with class classification adaptation processing, learning of the tap coefficient wn and mapping using the tap coefficient wn are performed by class. With class classification adaptation processing, class classification processing is performed with regard to the HD pixel yk of interest, and learning of the tap coefficient wn and mapping using the tap coefficient wn are performed for each class obtained by the class classification processing.
An example of class classification processing with regard to the HD pixel yk is to extract multiple SD pixels from the SD image to serve as a class tap used for class classification of the HD pixel yk, and to perform M-bit ADRC (Adaptive Dynamic Range Coding) using the class tap made up of the multiple SD pixels.
In M-bit ADRC processing, the maximum value MAX and minimum value MIN of the SD pixels making up the class tap are detected, DR=MAX−MIN is set as a local dynamic range, and the SD pixels making up the class tap are re-quantized into K bits, based on this dynamic range DR. That is to say, the minimum value MIN is subtracted from the SD pixels making up the class tap, and the subtraction value is divided by DR/2K (quantized). Accordingly, in the event that a class tap is subjected to 1-bit ADRC processing for example, each SD pixel making up the class tap is one bit. In this case, a bit string obtained by arraying in a predetermined order the 1-bit pixel values regarding each SD pixel making up the class tap that have been obtained as described above is output as ADRC code, and the ADRC code is taken as a class code representing the class.
Note that class classification adaptation processing differs from simple interpolation processing or the like, for example, in that components not included in the SD image but are included in the HD image are reproduced. That is to say, with class classification adaptation processing, it would seem by looking at Expression (24) alone that this is the same as interpolation processing using a so-called interpolation filter, but the tap coefficient wn which is equivalent to the tap coefficient of the interpolation filter has been obtained by learning using an HD image serving as tutor data and an SD image serving as student data, so the component contained in the HD image can be reproduced.
Now, tap coefficients wn which perform various types of conversion can be obtained in the tap coefficient wn learning, depending on what sort of combination of tutor data y and student data x is employed.
That is to say, in a case of taking a high-resolution HD image as the tutor data y and taking an SD image wherein the resolution of the HD image has been deteriorated as the student data x, for example, a tap coefficient wn for mapping an image into an image with the resolution improved, can be obtained. Further, in a case of taking an HD image as the tutor data y and taking an SD image wherein the number of pixels of the HD image has been reduced as the student data x, for example, a tap coefficient wn for mapping an image into an image with an increased number of pixels making up the image, can be obtained.
FIG. 26 is an image obtained by subjecting the input image shown in FIG. 25 to mapping by the class classification adaptation processing such as described above. It can be understood in the image shown in FIG. 26 that the image of the fine line is different to that of the original image in FIG. 24.
FIG. 27 is a diagram illustrating the results of detecting the fine line regions from the input image shown in the example in FIG. 25, by the data continuity detecting unit 101. In FIG. 27, the white region indicates the fine line region, i.e., the region wherein the arc shapes shown in FIG. 10 are arrayed.
FIG. 28 is a diagram illustrating an example of the output image obtained by performing signal processing at the signal processing device 4, with the image shown in FIG. 25 as the input image. As shown in FIG. 28, the signals processing device 4 yields an image closer to the fine line image of the original image shown in FIG. 24.
FIG. 29 is a flowchart for describing the processing of signals with the signal processing device 4.
In step S101, the data continuity detecting unit 101 executes the processing for detecting continuity. The data continuity detecting unit 101 detects data continuity contained in the input image which is the data 3, and supplies the data continuity information indicating the detected data continuity to the actual world estimating unit 102 and the image generating unit 103.
The data continuity detecting unit 101 detects the continuity of data corresponding to the continuity of the signals of the actual world. In the processing in step S101, the continuity of data detected by the data continuity detecting unit 101 is either part of the continuity of the image of the actual world 1 contained in the data 3, or continuity which has changed from the continuity of the signals of the actual world 1.
For example, the data continuity detecting unit 101 detects the data continuity by detecting a region having a constant characteristic in a predetermined dimensional direction. Also, for example, the data continuity detecting unit 101 detects data continuity by detecting angle (gradient) in the spatial direction indicating the an array of the same shape.
Details of the continuity detecting processing in step S101 will be described later.
Note that the data continuity information can be used as features, indicating the characteristics of the data 3.
In step S102, the actual world estimating unit 102 executes processing for estimating the actual world. That is to say, the actual world estimating unit 102 estimates the signals of the actual world based on the input image and the data continuity information supplied from the data continuity detecting unit 101. In the processing in step S102 for example, the actual world estimating unit 102 estimates the signals of the actual world 1 by predicting a model 161 approximating (describing) the actual world 1. The actual world estimating unit 102 supplies the actual world estimation information indicating the estimated signals of the actual world 1 to the image generating unit 103.
For example, the actual world estimating unit 102 estimates the actual world 1 signals by predicting the width of the linear object. Also, for example, the actual world estimating unit 102 estimates the actual world 1 signals by predicting a level indicating the color of the linear object.
Details of processing for estimating the actual world in step S102 will be described later.
Note that the actual world estimation information can be used as features, indicating the characteristics of the data 3.
In step S103, the image generating unit 103 performs image generating processing, and the processing ends. That is to say, the image generating unit 103 generates an image based on the actual world estimation information, and outputs the generated image. Or, the image generating unit 103 generates an image based on the data continuity information and actual world estimation information, and outputs the generated image.
For example, in the processing in step S103, the image generating unit 103 integrates the estimated real world light in the spatial direction, based on the actual world estimated information, thereby generating an image with higher resolution in the spatial direction in comparison with the input image, and outputs the generated image. For example, the image generating unit 103 integrates estimated real world light in the time-space direction, based on the actual world estimated information, hereby generating an image with higher resolution in the time direction and the spatial direction in comparison with the input image, and outputs the generated image. The details of the image generating processing in step S103 will be described later.
Thus, the signal processing device 4 detects data continuity from the data 3, and estimates the actual world 1 from the detected data continuity. The signal processing device 4 then generates signals closer approximating the actual world 1 based on the estimated actual world 1.
As described above, in the event of performing the processing for estimating signals of the real world, accurate and highly-precise processing results can be obtained.
Also, in the event that first signals which are real world signals having first dimensions are projected, the continuity of data corresponding to the lost continuity of the real world signals is detected for second signals of second dimensions, having a number of dimensions fewer than the first dimensions, from which a part of the continuity of the signals of the real world has been lost, and the first signals are estimated by estimating the lost real world signals continuity based on the detected data continuity, accurate and highly-precise processing results can be obtained as to the events in the real world.
Next, the details of the configuration of the data continuity detecting unit 101 will be described.
FIG. 30 is a block diagram illustrating the configuration of the data continuity detecting unit 101.
Upon taking an image of an object which is a fine line, the data continuity detecting unit 101, of which the configuration is shown in FIG. 30, detects the continuity of data contained in the data 3, which is generated from the continuity in that the cross-sectional shape which the object has is the same. That is to say, the data continuity detecting unit 101 of the configuration shown in FIG. 30 detects the continuity of data contained in the data 3, which is generated from the continuity in that the change in level of light as to the change in position in the direction orthogonal to the length-wise direction is the same at an arbitrary position in the length-wise direction, which the image of the actual world 1 which is a fine line, has.
More specifically, the data continuity detecting unit 101 of which configuration is shown in FIG. 30 detects the region where multiple arc shapes (half-disks) having a predetermined length are arrayed in a diagonally-offset adjacent manner, within the data 3 obtained by taking an image of a fine line with the sensor 2 having spatial integration effects.
The data continuity detecting unit 101 extracts the portions of the image data (hereafter referred to as con-continuity component) other than the portion of the image data where the image of the fine line having data continuity has been projected (hereafter, the portion of the image data where the image of the fine line having data continuity has been projected will also be called continuity component, and the other portions will be called non-continuity component), from an input image which is the data 3, detects the pixels where the image of the fine line of the actual world 1 has been projected, from the extracted non-continuity component and the input image, and detects the region of the input image made up of pixels where the image of the fine line of the actual world 1 has been projected.
A non-continuity component extracting unit 201 extracts the non-continuity component from the input image, and supplies the non-continuity component information indicating the extracted non-continuity component to a peak detecting unit 202 and a monotonous increase/decrease detecting unit 203 along with the input image.
For example, as shown in FIG. 31, in the event that an image of the actual world 1 wherein a fine line exists in front of a background with an approximately constant light level is projected on the data 3, the non-continuity component extracting unit 201 extracts the non-continuity component which is the background, by approximating the background in the input image which is the data 3, on a plane, as shown in FIG. 32. In FIG. 32, the solid line indicates the pixel values of the data 3, and the dotted line illustrates the approximation values indicated by the plane approximating the background. In FIG. 32, A denotes the pixel value of the pixel where the image of the fine line has been projected, and the PL denotes the plane approximating the background.
In this way, the pixel values of the multiple pixels at the portion of the image data having data continuity are discontinuous as to the non-continuity component.
The non-continuity component extracting unit 201 detects the discontinuous portion of the pixel values of the multiple pixels of the image data which is the data 3, where an image which is light signals of the actual world 1 has been projected and a part of the continuity of the image of the actual world 1 has been lost.
Details of the processing for extracting the non-continuity component with the non-continuity component extracting unit 201 will be described later.
The peak detecting unit 202 and the monotonous increase/decrease detecting unit 203 remove the non-continuity component from the input image, based on the non-continuity component information supplied from the non-continuity component extracting unit 201. For example, the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203 remove the non-continuity component from the input image by setting the pixel values of the pixels of the input image where only the background image has been projected, to 0. Also, for example, the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203 remove the non-continuity component from the input image by subtracting values approximated by the plane PL from the pixel values of each pixel of the input image.
Since the background can be removed from the input image, the peak detecting unit 202 through continuousness detecting unit 204 can process only the portion of the image data where the fine line has be projected, thereby further simplifying the processing by the peak detecting unit 202 through the continuousness detecting unit 204.
Note that the non-continuity component extracting unit 201 may supply image data wherein the non-continuity component has been removed from the input image, to the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203.
In the example of processing described below, the image data wherein the non-continuity component has been removed from the input image, i.e., image data made up from only pixel containing the continuity component, is the object.
Now, description will be made regarding the image data upon which the fine line image has been projected, which the peak detecting unit 202 through continuousness detecting unit 204 are to detect.
In the event that there is no optical LPF, the cross-dimensional shape in the spatial direction Y (change in the pixel values as to change in the position in the spatial direction) of the image data upon which the fine line image has been projected as shown in FIG. 31 can be thought to be the trapezoid shown in FIG. 33, or the triangle shown in FIG. 34, from the spatial; integration effects of the image sensor which is the sensor 2. However, ordinary image sensors have an optical LPF with the image sensor obtaining the image which has passed through the optical LPF and projects the obtained image on the data 3, so in reality, the cross-dimensional shape of the image data with fine lines in the spatial direction Y has a shape resembling Gaussian distribution, as shown in FIG. 35.
The peak detecting unit 202 through continuousness detecting unit 204 detect a region made up of pixels upon which the fine line image has been projected wherein the same cross-sectional shape (change in the pixel values as to change in the position in the spatial direction) is arrayed in the vertical direction in the screen at constant intervals, and further, detect a region made up of pixels upon which the fine line image has been projected which is a region having data continuity, by detecting regional connection corresponding to the length-wise direction of the fine line of the actual world 1. That is to say, the peak detecting unit 202 through continuousness detecting unit 204 detect regions wherein arc shapes (half-disc shapes) are formed on a single vertical row of pixels in the input image, and determine whether or not the detected regions are adjacent in the horizontal direction, thereby detecting connection of regions where arc shapes are formed, corresponding to the length-wise direction of the fine line image which is signals of the actual world 1.
Also, the peak detecting unit 202 through continuousness detecting unit 204 detect a region made up of pixels upon which the fine line image has been projected wherein the same cross-sectional shape is arrayed in the horizontal direction in the screen at constant intervals, and further, detect a region made up of pixels upon which the fine line image has been projected which is a region having data continuity, by detecting connection of detected regions corresponding to the length-wise direction of the fine line of the actual world 1. That is to say, the peak detecting unit 202 through continuousness detecting unit 204 detect regions wherein arc shapes are formed on a single horizontal row of pixels in the input image, and determine whether or not the detected regions are adjacent in the vertical direction, thereby detecting connection of regions where arc shapes are formed, corresponding to the length-wise direction of the fine line image, which is signals of the actual world 1.
First, description will be made regarding processing for detecting a region of pixels upon which the fine line image has been projected wherein the same arc shape is arrayed in the vertical direction in the screen at constant intervals.
The peak detecting unit 202 detects a pixel having a pixel value greater than the surrounding pixels, i.e., a peak, and supplies peak information indicating the position of the peak to the monotonous increase/decrease detecting unit 203. In the event that pixels arrayed in a single vertical direction row in the screen are the object, the peak detecting unit 202 compares the pixel value of the pixel position upwards in the screen and the pixel value of the pixel position downwards in the screen, and detects the pixel with the greater pixel value as the peak. The peak detecting unit 202 detects one or multiple peaks from a single image, e.g., from the image of a single frame.
A single screen contains frames or fields. This holds true in the following description as well.
For example, the peak detecting unit 202 selects a pixel of interest from pixels of an image of one frame which have not yet been taken as pixels of interest, compares the pixel value of the pixel of interest with the pixel value of the pixel above the pixel of interest, compares the pixel value of the pixel of interest with the pixel value of the pixel below the pixel of interest, detects a pixel of interest which has a greater pixel value than the pixel value of the pixel above and a greater pixel value than the pixel value of the pixel below, and takes the detected pixel of interest as a peak. The peak detecting unit 202 supplies peak information indicating the detected peak to the monotonous increase/decrease detecting unit 203.
There are cases wherein the peak detecting unit 202 does not detect a peak. For example, in the event that the pixel values of all of the pixels of an image are the same value, or in the event that the pixel values decrease in one or two directions, no peak is detected. In this case, no fine line image has been projected on the image data.
The monotonous increase/decrease detecting unit 203 detects a candidate for a region made up of pixels upon which the fine line image has been projected wherein the pixels are vertically arrayed in a single row as to the peak detected by the peak detecting unit 202, based upon the peak information indicating the position of the peak supplied from the peak detecting unit 202, and supplies the region information indicating the detected region to the continuousness detecting unit 204 along with the peak information.
More specifically, the monotonous increase/decrease detecting unit 203 detects a region made up of pixels having pixel values monotonously decreasing with reference to the peak pixel value, as a candidate of a region made up of pixels upon which the image of the fine line has been projected. Monotonous decrease means that the pixel values of pixels which are farther distance-wise from the peak are smaller than the pixel values of pixels which are closer to the peak.
Also, the monotonous increase/decrease detecting unit 203 detects a region made up of pixels having pixel values monotonously increasing with reference to the peak pixel value, as a candidate of a region made up of pixels upon which the image of the fine line has been projected. Monotonous increase means that the pixel values of pixels which are farther distance-wise from the peak are greater than the pixel values of pixels which are closer to the peak.
In the following, the processing regarding regions of pixels having pixel values monotonously increasing is the same as the processing regarding regions of pixels having pixel values monotonously decreasing, so description thereof will be omitted. Also, with the description regarding processing for detecting a region of pixels upon which the fine line image has been projected wherein the same arc shape is arrayed horizontally in the screen at constant intervals, the processing regarding regions of pixels having pixel values monotonously increasing is the same as the processing regarding regions of pixels having pixel values monotonously decreasing, so description thereof will be omitted.
For example, the monotonous increase/decrease detecting unit 203 obtains pixel values of each of the pixels in a vertical row as to a peak, the difference as to the pixel value of the pixel above, and the difference as to the pixel value of the pixel below. The monotonous increase/decrease detecting unit 203 then detects a region wherein the pixel value monotonously decreases by detecting pixels wherein the sign of the difference changes.
Further, the monotonous increase/decrease detecting unit 203 detects, from the region wherein pixel values monotonously decrease, a region made up of pixels having pixel values with the same sign as that of the pixel value of the peak, with the sign of the pixel value of the peak as a reference, as a candidate of a region made up of pixels upon which the image of the fine line has been projected.
For example, the monotonous increase/decrease detecting unit 203 compares the sign of the pixel value of each pixel with the sign of the pixel value of the pixel above and sign of the pixel value of the pixel below, and detects the pixel where the sign of the pixel value changes, thereby detecting a region of pixels having pixel values of the same sign as the peak within the region where pixel values monotonously decrease.
Thus, the monotonous increase/decrease detecting unit 203 detects a region formed of pixels arrayed in a vertical direction wherein the pixel values monotonously decrease as to the peak and have pixels values of the same sign as the peak.
FIG. 36 is a diagram describing processing for peak detection and monotonous increase/decrease region detection, for detecting the region of pixels wherein the image of the fine line has been projected, from the pixel values as to a position in the spatial direction Y.
In FIG. 36 through FIG. 38, P represents a peak. In the description of the data continuity detecting unit 101 of which the configuration is shown in FIG. 30, P represents a peak.
The peak detecting unit 202 compares the pixel values of the pixels with the pixel values of the pixels adjacent thereto in the spatial direction Y, and detects the peak P by detecting a pixel having a pixel value greater than the pixel values of the two pixels adjacent in the spatial direction Y.
The region made up of the peak P and the pixels on both sides of the peak P in the spatial direction Y is a monotonous decrease region wherein the pixel values of the pixels on both sides in the spatial direction Y monotonously decrease as to the pixel value of the peak P. In FIG. 36, the arrow denoted A and the arrow denoted by B represent the monotonous decrease regions existing on either side of the peak P.
The monotonous increase/decrease detecting unit 203 obtains the difference between the pixel values of each pixel and the pixel values of the pixels adjacent in the spatial direction Y, and detects pixels where the sign of the difference changes. The monotonous increase/decrease detecting unit 203 takes the boundary between the detected pixel where the sign of the difference changes and the pixel immediately prior thereto (on the peak P side) as the boundary of the fine line region made up of pixels where the image of the fine line has been projected.
In FIG. 36, the boundary of the fine line region which is the boundary between the pixel where the sign of the difference changes and the pixel immediately prior thereto (on the peak P side) is denoted by C.
Further, the monotonous increase/decrease detecting unit 203 compares the sign of the pixel values of each pixel with the pixel values of the pixels adjacent thereto in the spatial direction Y, and detects pixels where the sign of the pixel value changes in the monotonous decrease region. The monotonous increase/decrease detecting unit 203 takes the boundary between the detected pixel where the sign of the pixel value changes and the pixel immediately prior thereto (on the peak P side) as the boundary of the fine line region.
In FIG. 36, the boundary of the fine line region which is the boundary between the pixel where the sign of the pixel value changes and the pixel immediately prior thereto (on the peak P side) is denoted by D.
As shown in FIG. 36, the fine line region F made up of pixels where the image of the fine line has been projected is the region between the fine line region boundary C and the fine line region boundary D.
The monotonous increase/decrease detecting unit 203 obtains a fine line region F which is longer than a predetermined threshold value, from fine line regions F made up of such monotonous increase/decrease regions, i.e., a fine line region F having a greater number of pixels than the threshold value. For example, in the event that the threshold value is 3, the monotonous increase/decrease detecting unit 203 detects a fine line region F including 4 or more pixels.
Further, the monotonous increase/decrease detecting unit 203 compares the pixel value of the peak P, the pixel value of the pixel to the right side of the peak P, and the pixel value of the pixel to the left side of the peak P, from the fine line region F thus detected, each with the threshold value, detects a fine line pixel region F having the peak P wherein the pixel value of the peak P exceeds the threshold value, and wherein the pixel value of the pixel to the right side of the peak P is the threshold value or lower, and wherein the pixel value of the pixel to the left side of the peak P is the threshold value or lower, and takes the detected fine line region F as a candidate for the region made up of pixels containing the component of the fine line image.
In other words, determination is made that a fine line region F having the peak P, wherein the pixel value of the peak P is the threshold value or lower, or wherein the pixel value of the pixel to the right side of the peak P exceeds the threshold value, or wherein the pixel value of the pixel to the left side of the peak P exceeds the threshold value, does not contain the component of the fine line image, and is eliminated from candidates for the region made up of pixels including the component of the fine line image.
That is, as shown in FIG. 37, the monotonous increase/decrease detecting unit 203 compares the pixel value of the peak P with the threshold value, and also compares the pixel value of the pixel adjacent to the peak P in the spatial direction X (the direction indicated by the dotted line AA′) with the threshold value, thereby detecting the fine line region F to which the peak P belongs, wherein the pixel value of the peak P exceeds the threshold value and wherein the pixel values of the pixel adjacent thereto in the spatial direction X are equal to or below the threshold value.
FIG. 38 is a diagram illustrating the pixel values of pixels arrayed in the spatial direction X indicated by the dotted line AA′ in FIG. 37. The fine line region F to which the peak P belongs, wherein the pixel value of the peak P exceeds the threshold value Ths and wherein the pixel values of the pixel adjacent thereto in the spatial direction X are equal to or below the threshold value Ths, contains the fine line component.
Note that an arrangement may be made wherein the monotonous increase/decrease detecting unit 203 compares the difference between the pixel value of the peak P and the pixel value of the background with the threshold value, taking the pixel value of the background as a reference, and also compares the difference between the pixel value of the pixels adjacent to the peak P in the spatial direction X and the pixel value of the background with the threshold value, thereby detecting the fine line region F to which the peak P belongs, wherein the difference between the pixel value of the peak P and the pixel value of the background exceeds the threshold value, and wherein the difference between the pixel value of the pixel adjacent in the spatial direction X and the pixel value of the background is equal to or below the threshold value.
The monotonous increase/decrease detecting unit 203 supplies to the continuousness detecting unit 204 monotonous increase/decrease region information indicating a region made up of pixels of which the pixel value monotonously decrease with the peak P as a reference and the sign of the pixel value is the same as that of the peak P, wherein the peak P exceeds the threshold value and wherein the pixel value of the pixel to the right side of the peak P is equal to or below the threshold value and the pixel value of the pixel to the left side of the peak P is equal to or below the threshold value.
In the event of detecting a region of pixels arrayed in a single row in the vertical direction of the screen where the image of the fine line has been projected, pixels belonging to the region indicated by the monotonous increase/decrease region information are arrayed in the vertical direction and include pixels where the image of the fine line has been projected. That is to say, the region indicated by the monotonous increase/decrease region information includes a region formed of pixels arrayed in a single row in the vertical direction of the screen where the image of the fine line has been projected.
In this way, the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203 detects a continuity region made up of pixels where the image of the fine line has been projected, employing the nature that, of the pixels where the image of the fine line has been projected, change in the pixel values in the spatial direction Y approximates Gaussian distribution.
Of the region made up of pixels arrayed in the vertical direction, indicated by the monotonous increase/decrease region information supplied from the monotonous increase/decrease detecting unit 203, the continuousness detecting unit 204 detects regions including pixels adjacent in the horizontal direction, i.e., regions having similar pixel value change and duplicated in the vertical direction, as continuous regions, and outputs the peak information and data continuity information indicating the detected continuous regions. The data continuity information includes monotonous increase/decrease region information, information indicating the connection of regions, and so forth.
Arc shapes are aligned at constant intervals in an adjacent manner with the pixels where the fine line has been projected, so the detected continuous regions include the pixels where the fine line has been projected.
The detected continuous regions include the pixels where arc shapes are aligned at constant intervals in an adjacent manner to which the fine line has been projected, so the detected continuous regions are taken as a continuity region, and the continuousness detecting unit 204 outputs data continuity information indicating the detected continuous regions.
That is to say, the continuousness detecting unit 204 uses the continuity wherein arc shapes are aligned at constant intervals in an adjacent manner in the data 3 obtained by imaging the fine line, which has been generated due to the continuity of the image of the fine line in the actual world 1, the nature of the continuity being continuing in the length direction, so as to further narrow down the candidates of regions detected with the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203.
FIG. 39 is a diagram describing the processing for detecting the continuousness of monotonous increase/decrease regions.
As shown in FIG. 39, in the event that a fine line region F formed of pixels aligned in a single row in the vertical direction of the screen includes pixels adjacent in the horizontal direction, the continuousness detecting unit 204 determines that there is continuousness between the two monotonous increase/decrease regions, and in the event that pixels adjacent in the horizontal direction are not included, determines that there is no continuousness between the two fine line regions F. For example, a fine line region F−1 made up of pixels aligned in a single row in the vertical direction of the screen is determined to be continuous to a fine line region F0 made up of pixels aligned in a single row in the vertical direction of the screen in the event of containing a pixel adjacent to a pixel of the fine line region F0 in the horizontal direction. The fine line region F0 made up of pixels aligned in a single row in the vertical direction of the screen is determined to be continuous to a fine line region F1 made up of pixels aligned in a single row in the vertical direction of the screen in the event of containing a pixel adjacent to a pixel of the fine line region F1 in the horizontal direction.
In this way, regions made up of pixels aligned in a single row in the vertical direction of the screen where the image of the fine line has been projected are detected by the peak detecting unit 202 through the continuousness detecting unit 204.
As described above, the peak detecting unit 202 through the continuousness detecting unit 204 detect regions made up of pixels aligned in a single row in the vertical direction of the screen where the image of the fine line has been projected, and further detect regions made up of pixels aligned in a single row in the horizontal direction of the screen where the image of the fine line has been projected.
Note that the order of processing is not particularly restricted, and may be executed in parallel, as a matter of course.
That is to say, the peak detecting unit 202, with regard to of pixels aligned in a single row in the horizontal direction of the screen, detects as a peak a pixel which has a pixel value greater in comparison with the pixel value of the pixel situated to the left side on the screen and the pixel value of the pixel situated to the right side on the screen, and supplies peak information indicating the position of the detected peak to the monotonous increase/decrease detecting unit 203. The peak detecting unit 202 detects one or multiple peaks from one image, for example, one frame image.
For example, the peak detecting unit 202 selects a pixel of interest from pixels in the one frame image which has not yet been taken as a pixel of interest, compares the pixel value of the pixel of interest with the pixel value of the pixel to the left side of the pixel of interest, compares the pixel value of the pixel of interest with the pixel value of the pixel to the right side of the pixel of interest, detects a pixel of interest having a pixel value greater than the pixel value of the pixel to the left side of the pixel of interest and having a pixel value greater than the pixel value of the pixel to the right side of the pixel of interest, and takes the detected pixel of interest as a peak. The peak detecting unit 202 supplies peak information indicating the detected peak to the monotonous increase/decrease detecting unit 203.
There are cases wherein the peak detecting unit 202 does not detect a peak.
The monotonous increase/decrease detecting unit 203 detects candidates for a region made up of pixels aligned in a single row in the horizontal direction as to the peak detected by the peak detecting unit 202 wherein the fine line image has been projected, and supplies the monotonous increase/decrease region information indicating the detected region to the continuousness detecting unit 204 along with the peak information.
More specifically, the monotonous increase/decrease detecting unit 203 detects regions made up of pixels having pixel values monotonously decreasing with the pixel value of the peak as a reference, as candidates of regions made up of pixels where the fine line image has been projected.
For example, the monotonous increase/decrease detecting unit 203 obtains, with regard to each pixel in a single row in the horizontal direction as to the peak, the pixel value of each pixel, the difference as to the pixel value of the pixel to the left side, and the difference as to the pixel value of the pixel to the right side. The monotonous increase/decrease detecting unit 203 then detects the region where the pixel value monotonously decreases by detecting the pixel where the sign of the difference changes.
Further, the monotonous increase/decrease detecting unit 203 detects, from a region wherein pixel values monotonously decrease, a region made up of pixels having pixel values with the same sign as the pixel value as the sign of the pixel value of the peak, with reference to the sign of the pixel value of the peak, as a candidate for a region made up of pixels where the fine line image has been projected.
For example, the monotonous increase/decrease detecting unit 203 compares the sign of the pixel value of each pixel with the sign of the pixel value of the pixel to the left side or with the sign of the pixel value of the pixel to the right side, and detects the pixel where the sign of the pixel value changes, thereby detecting a region made up of pixels having pixel values with the same sign as the peak, from the region where the pixel values monotonously decrease.
Thus, the monotonous increase/decrease detecting unit 203 detects a region made up of pixels aligned in the horizontal direction and having pixel values with the same sign as the peak wherein the pixel values monotonously decrease as to the peak.
From a fine line region made up of such a monotonous increase/decrease region, the monotonous increase/decrease detecting unit 203 obtains a fine line region longer than a threshold value set beforehand, i.e., a fine line region having a greater number of pixels than the threshold value.
Further, from the fine line region thus detected, the monotonous increase/decrease detecting unit 203 compares the pixel value of the peak, the pixel value of the pixel above the peak, and the pixel value of the pixel below the peak, each with the threshold value, detects a fine line region to which belongs a peak wherein the pixel value of the peak exceeds the threshold value, the pixel value of the pixel above the peak is within the threshold, and the pixel value of the pixel below the peak is within the threshold, and takes the detected fine line region as a candidate for a region made up of pixels containing the fine line image component.
Another way of saying this is that fine line regions to which belongs a peak wherein the pixel value of the peak is within the threshold value, or the pixel value of the pixel above the peak exceeds the threshold, or the pixel value of the pixel below the peak exceeds the threshold, are determined to not contain the fine line image component, and are eliminated from candidates of the region made up of pixels containing the fine line image component.
Note that the monotonous increase/decrease detecting unit 203 may be arranged to take the background pixel value as a reference, compare the difference between the pixel value of the peak and the pixel value of the background with the threshold value, and also to compare the difference between the pixel value of the background and the pixel values of the pixels adjacent to the peak in the vertical direction with the threshold value, and take a detected fine line region wherein the difference between the pixel value of the peak and the pixel value of the background exceeds the threshold value, and the difference between the pixel value of the background and the pixel value of the pixels adjacent in the vertical direction is within the threshold, as a candidate for a region made up of pixels containing the fine line image component.
The monotonous increase/decrease detecting unit 203 supplies to the continuousness detecting unit 204 monotonous increase/decrease region information indicating a region made up of pixels having a pixel value sign which is the same as the peak and monotonously decreasing pixel values as to the peak as a reference, wherein the peak exceeds the threshold value, and the pixel value of the pixel to the right side of the peak is within the threshold, and the pixel value of the pixel to the left side of the peak is within the threshold.
In the event of detecting a region made up of pixels aligned in a single row in the horizontal direction of the screen wherein the image of the fine line has been projected, pixels belonging to the region indicated by the monotonous increase/decrease region information include pixels aligned in the horizontal direction wherein the image of the fine line has been projected. That is to say, the region indicated by the monotonous increase/decrease region information includes a region made up of pixels aligned in a single row in the horizontal direction of the screen wherein the image of the fine line has been projected.
Of the regions made up of pixels aligned in the horizontal direction indicated in the monotonous increase/decrease region information supplied from the monotonous increase/decrease detecting unit 203, the continuousness detecting unit 204 detects regions including pixels adjacent in the vertical direction, i.e., regions having similar pixel value change and which are repeated in the horizontal direction, as continuous regions, and outputs data continuity information indicating the peak information and the detected continuous regions. The data continuity information includes information indicating the connection of the regions.
At the pixels where the fine line has been projected, arc shapes are arrayed at constant intervals in an adjacent manner, so the detected continuous regions include pixels where the fine line has been projected.
The detected continuous regions include pixels where arc shapes are arrayed at constant intervals in an adjacent manner wherein the fine line has been projected, so the detected continuous regions are taken as a continuity region, and the continuousness detecting unit 204 outputs data continuity information indicating the detected continuous regions.
That is to say, the continuousness detecting unit 204 uses the continuity which is that the arc shapes are arrayed at constant intervals in an adjacent manner in the data 3 obtained by imaging the fine line, generated from the continuity of the image of the fine line in the actual world 1 which is continuation in the length direction, so as to further narrow down the candidates of regions detected by the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203.
Thus, the data continuity detecting unit 101 is capable of detecting continuity contained in the data 3 which is the input image. That is to say, the data continuity detecting unit 101 can detect continuity of data included in the data 3 which has been generated by the actual world 1 image which is a fine line having been projected on the data 3. The data continuity detecting unit 101 detects, from the data 3, regions made up of pixels where the actual world 1 image which is a fine line has been projected.
FIG. 40 is a diagram illustrating an example of other processing for detecting regions having continuity, where a fine line image has been projected, with the data continuity detecting unit 101.
As shown in FIG. 40, the data continuity detecting unit 101 calculates the absolute value of difference of pixel values for each pixel and adjacent pixels. The calculated absolute values of difference are placed corresponding to the pixels. For example, in a situation such as shown in FIG. 40 wherein there are pixels aligned which have respective pixel values of P0, P1, and P2, the data continuity detecting unit 101 calculates the difference d0=P0−P1 and the difference d1=P1−P2. Further, the data continuity detecting unit 101 calculates the absolute values of the difference d0 and the difference d1.
In the event that the non-continuity component contained in the pixel values P0, P1, and P2 are identical, only values corresponding to the component of the fine line are set to the difference d0 and the difference d1.
Accordingly, of the absolute values of the differences placed corresponding to the pixels, in the event that adjacent difference values are identical, the data continuity detecting unit 101 determines that the pixel corresponding to the absolute values of the two differences (the pixel between the two absolute values of difference) contains the component of the fine line. However, the data continuity detecting unit 101 does not need to detect the fine line in the event that the absolute value of difference is small. For example, in the event that the absolute value of difference is equal to or greater than a threshold value, the data continuity detecting unit 101 determines that the pixel contains a fine line component.
The data continuity detecting unit 101 can also detect fine lines with a simple method such as this.
FIG. 41 is a flowchart for describing continuity detection processing.
In step S201, the non-continuity component extracting unit 201 extracts non-continuity component, which is portions other than the portion where the fine line has been projected, from the input image. The non-continuity component extracting unit 201 supplies non-continuity component information indicating the extracted non-continuity component, along with the input image, to the peak detecting unit 202 and the monotonous increase/decrease detecting unit 203. Details of the processing for extracting the non-continuity component will be described later.
In step S202, the peak detecting unit 202 eliminates the non-continuity component from the input image, based on the non-continuity component information supplied from the non-continuity component extracting unit 201, so as to leave only pixels including the continuity component in the input image. Further, in step S202, the peak detecting unit 202 detects peaks.
That is to say, in the event of executing processing with the vertical direction of the screen as a reference, of the pixels containing the continuity component, the peak detecting unit 202 compares the pixel value of each pixel with the pixel values of the pixels above and below, and detects pixels having a greater pixel value than the pixel value of the pixel above and the pixel value of the pixel below, thereby detecting a peak. Also, in step S202, in the event of executing processing with the horizontal direction of the screen as a reference, of the pixels containing the continuity component, the peak detecting unit 202 compares the pixel value of each pixel with the pixel values of the pixels to the right side and left side, and detects pixels having a greater pixel value than the pixel value of the pixel to the right side and the pixel value of the pixel to the left side, thereby detecting a peak.
The peak detecting unit 202 supplies the peak information indicating the detected peaks to the monotonous increase/decrease detecting unit 203.
In step S203, the monotonous increase/decrease detecting unit 203 eliminates the non-continuity component from the input image, based on the non-continuity component information supplied from the non-continuity component extracting unit 201, so as to leave only pixels including the continuity component in the input image. Further, in step S203, the monotonous increase/decrease detecting unit 203 detects the region made up of pixels having data continuity, by detecting monotonous increase/decrease as to the peak, based on peak information indicating the position of the peak, supplied from the peak detecting unit 202.
In the event of executing processing with the vertical direction of the screen as a reference, the monotonous increase/decrease detecting unit 203 detects monotonous increase/decrease made up of one row of pixels aligned vertically where a single fine line image has been projected, based on the pixel value of the peak and the pixel values of the one row of pixels aligned vertically as to the peak, thereby detecting a region made up of pixels having data continuity. That is to say, in step S203, in the event of executing processing with the vertical direction of the screen as a reference, the monotonous increase/decrease detecting unit 203 obtains, with regard to a peak and a row of pixels aligned vertically as to the peak, the difference between the pixel value of each pixel and the pixel value of a pixel above or below, thereby detecting a pixel where the sign of the difference changes. Also, with regard to a peak and a row of pixels aligned vertically as to the peak, the monotonous increase/decrease detecting unit 203 compares the sign of the pixel value of each pixel with the sign of the pixel value of a pixel above or below, thereby detecting a pixel where the sign of the pixel value changes. Further, the monotonous increase/decrease detecting unit 203 compares pixel value of the peak and the pixel values of the pixels to the right side and to the left side of the peak with a threshold value, and detects a region made up of pixels wherein the pixel value of the peak exceeds the threshold value, and wherein the pixel values of the pixels to the right side and to the left side of the peak are within the threshold.
The monotonous increase/decrease detecting unit 203 takes a region detected in this way as a monotonous increase/decrease region, and supplies monotonous increase/decrease region information indicating the monotonous increase/decrease region to the continuousness detecting unit 204.
In the event of executing processing with the horizontal direction of the screen as a reference, the monotonous increase/decrease detecting unit 203 detects monotonous increase/decrease made up of one row of pixels aligned horizontally where a single fine line image has been projected, based on the pixel value of the peak and the pixel values of the one row of pixels aligned horizontally as to the peak, thereby detecting a region made up of pixels having data continuity. That is to say, in step S203, in the event of executing processing with the horizontal direction of the screen as a reference, the monotonous increase/decrease detecting unit 203 obtains, with regard to a peak and a row of pixels aligned horizontally as to the peak, the difference between the pixel value of each pixel and the pixel value of a pixel to the right side or to the left side, thereby detecting a pixel where the sign of the difference changes. Also, with regard to a peak and a row of pixels aligned horizontally as to the peak, the monotonous increase/decrease detecting unit 203 compares the sign of the pixel value of each pixel with the sign of the pixel value of a pixel to the right side or to the left side, thereby detecting a pixel where the sign of the pixel value changes. Further, the monotonous increase/decrease detecting unit 203 compares pixel value of the peak and the pixel values of the pixels to the upper side and to the lower side of the peak with a threshold value, and detects a region made up of pixels wherein the pixel value of the peak exceeds the threshold value, and wherein the pixel values of the pixels to the upper side and to the lower side of the peak are within the threshold.
The monotonous increase/decrease detecting unit 203 takes a region detected in this way as a monotonous increase/decrease region, and supplies monotonous increase/decrease region information indicating the monotonous increase/decrease region to the continuousness detecting unit 204.
In step S204, the monotonous increase/decrease detecting unit 203 determines whether or not processing of all pixels has ended. For example, the non-continuity component extracting unit 201 detects peaks for all pixels of a single screen (for example, frame, field, or the like) of the input image, and whether or not a monotonous increase/decrease region has been detected is determined.
In the event that determination is made in step S204 that processing of all pixels has not ended, i.e., that there are still pixels which have not been subjected to the processing of peak detection and detection of monotonous increase/decrease region, the flow returns to step S202, a pixel which has not yet been subjected to the processing of peak detection and detection of monotonous increase/decrease region is selected as an object of the processing, and the processing of peak detection and detection of monotonous increase/decrease region are repeated.
In the event that determination is made in step S204 that processing of all pixels has ended, i.e., that peaks and monotonous increase/decrease regions have been detected with regard to all pixels, the flow proceeds to step S205, where the continuousness detecting unit 204 detects the continuousness of detected regions, based on the monotonous increase/decrease region information. For example, in the event that monotonous increase/decrease regions made up of one row of pixels aligned in the vertical direction of the screen, indicated by monotonous increase/decrease region information, include pixels adjacent in the horizontal direction, the continuousness detecting unit 204 determines that there is continuousness between the two monotonous increase/decrease regions, and in the event of not including pixels adjacent in the horizontal direction, determines that there is no continuousness between the two monotonous increase/decrease regions. For example, in the event that monotonous increase/decrease regions made up of one row of pixels aligned in the horizontal direction of the screen, indicated by monotonous increase/decrease region information, include pixels adjacent in the vertical direction, the continuousness detecting unit 204 determines that there is continuousness between the two monotonous increase/decrease regions, and in the event of not including pixels adjacent in the vertical direction, determines that there is no continuousness between the two monotonous increase/decrease regions.
The continuousness detecting unit 204 takes the detected continuous regions as continuity regions having data continuity, and outputs data continuity information indicating the peak position and continuity region. The data continuity information contains information indicating the connection of regions. The data continuity information output from the continuousness detecting unit 204 indicates the fine line region, which is the continuity region, made up of pixels where the actual world 1 fine line image has been projected.
In step S206, a continuity direction detecting unit 205 determines whether or not processing of all pixels has ended. That is to say, the continuity direction detecting unit 205 determines whether or not region continuation has been detected with regard to all pixels of a certain frame of the input image.
In the event that determination is made in step S206 that processing of all pixels has not yet ended, i.e., that there are still pixels which have not yet been taken as the object of detection of region continuation, the flow returns to step S205, a pixel which has not yet been subjected to the processing of detection of region continuity is selected as the pixel for processing, and the processing for detection of region continuity is repeated.
In the event that determination is made in step S206 that processing of all pixels has ended, i.e., that all pixels have been taken as the object of detection of region continuity, the processing ends.
Thus, the continuity contained in the data 3 which is the input image is detected. That is to say, continuity of data included in the data 3 which has been generated by the actual world 1 image which is a fine line having been projected on the data 3 is detected, and a region having data continuity, which is made up of pixels on which the actual world 1 image which is a fine line has been projected, is detected from the data 3.
Now, the data continuity detecting unit 101 of which the configuration is shown in FIG. 30 can detect time-directional data continuity, based on the region having data continuity detected from the frame of the data 3.
For example, as shown in FIG. 42, the continuousness detecting unit 204 detects time-directional data continuity by connecting the edges of the region having detected data continuity in frame #n, the region having detected data continuity in frame #n−1, and the region having detected data continuity in frame #n+1.
The frame #n−1 is a frame preceding the frame #n time-wise, and the frame #n+1 is a frame following the frame #n time-wise. That is to say, the frame #n−1, the frame #n, and the frame #n+1, are displayed on the order of the frame #n−1, the frame #n, and the frame #n+1.
More specifically, in FIG. 42, G denotes a movement vector obtained by connecting the one edge of the region having detected data continuity in frame #n, the region having detected data continuity in frame #n−1, and the region having detected data continuity in frame #n+1, and G′ denotes a movement vector obtained by connecting the other edges of the regions having detected data continuity. The movement vector G and the movement vector G′ are an example of data continuity in the time direction.
Further, the data continuity detecting unit 101 of which the configuration is shown in FIG. 30 can output information indicating the length of the region having data continuity as data continuity information.
FIG. 43 is a block diagram illustrating the configuration of the non-continuity component extracting unit 201 which performs planar approximation of the non-continuitycomponent which is the portion of the image data which does not have data continuity, and extracts the non-continuity component.
The non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43 extracts blocks, which are made up of a predetermined number of pixels, from the input image, performs planar approximation of the blocks, so that the error between the block and a planar value is below a predetermined threshold value, thereby extracting the non-continuity component.
The input image is supplied to a block extracting unit 221, and is also output without change.
The block extracting unit 221 extracts blocks, which are made up of a predetermined number of pixels, from the input image. For example, the block extracting unit 221 extracts a block made up of 7×7 pixels, and supplies this to a planar approximation unit 222. For example, the block extracting unit 221 moves the pixel serving as the center of the block to be extracted in raster scan order, thereby sequentially extracting blocks from the input image.
The planar approximation unit 222 approximates the pixel values of a pixel contained in the block on a predetermined plane. For example, the planar approximation unit 222 approximates the pixel value of a pixel contained in the block on a plane expressed by Expression (32).

Z=ax+by+c  (32)

In Expression (32), x represents the position of the pixel in one direction on the screen (the spatial direction X), and y represents the position of the pixel in the other direction on the screen (the spatial direction Y). z represents the application value represented by the plane. a represents the gradient of the spatial direction X of the plane, and b represents the gradient of the spatial direction Y of the plane. In Expression (32), c represents the offset of the plane (intercept).
For example, the planar approximation unit 222 obtains the gradient a, gradient b, and offset c, by regression processing, thereby approximating the pixel values of the pixels contained in the block on a plane expressed by Expression (32). The planar approximation unit 222 obtains the gradient a, gradient b, and offset c, by regression processing including rejection, thereby approximating the pixel values of the pixels contained in the block on a plane expressed by Expression (32).
For example, the planar approximation unit 222 obtains the plane expressed by Expression (32) wherein the error is least as to the pixel values of the pixels of the block using the least-square method, thereby approximating the pixel values of the pixels contained in the block on the plane.
Note that while the planar approximation unit 222 has been described approximating the block on the plane expressed by Expression (32), this is not restricted to the plane expressed by Expression (32), rather, the block may be approximated on a plane represented with a function with a higher degree of freedom, for example, an n-order (wherein n is an arbitrary integer) polynomial.
A repetition determining unit 223 calculates the error between the approximation value represented by the plane upon which the pixel values of the block have been approximated, and the corresponding pixel values of the pixels of the block. Expression (33) is an expression which shows the error ei which is the difference between the approximation value represented by the plane upon which the pixel values of the block have been approximated, and the corresponding pixel values zi of the pixels of the block.

ei=Zi−{circumflex over (Z)}=Zi−(âxi+{circumflex over (b)}yi+ĉ)  (33)

In Expression (33), z-hat (A symbol with ^ over z will be described as z-hat. The same description will be used in the present specification hereafter.) represents an approximation value expressed by the plane on which the pixel values of the block are approximated, a-hat represents the gradient of the spatial direction X of the plane on which the pixel values of the block are approximated, b-hat represents the gradient of the spatial direction Y of the plane on which the pixel values of the block are approximated, and c-hat represents the offset (intercept) of the plane on which the pixel values of the block are approximated.
The repetition determining unit 223 rejects the pixel regarding which the error ei between the approximation value and the corresponding pixel values of pixels of the block is greatest, shown in Expression (33). Thus, pixels where the fine line has been projected, i.e., pixels having continuity, are rejected. The repetition determining unit 223 supplies rejection information indicating the rejected pixels to the planar approximation unit 222.
Further, the repetition determining unit 223 calculates a standard error, and in the event that the standard error is equal to or greater than threshold value which has been set beforehand for determining ending of approximation, and half or more of the pixels of the pixels of a block have not been rejected, the repetition determining unit 223 causes the planar approximation unit 222 to repeat the processing of planar approximation on the pixels contained in the block, from which the rejected pixels have been eliminated.
Pixels having continuity are rejected, so approximating the pixels from which the rejected pixels have been eliminated on a plane means that the plane approximates the non-continuity component.
At the point that the standard error below the threshold value for determining ending of approximation, or half or more of the pixels of the pixels of a block have been rejected, the repetition determining unit 223 ends planar approximation.
With a block made up of 5×5 pixels, the standard error es can be calculated with, for example, Expression (34).




  
    
      
        
          
            
              
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Here, n is the number of pixels.
Note that the repetition determining unit 223 is not restricted to standard error, and may be arranged to calculate the sum of the square of errors for all of the pixels contained in the block, and perform the following processing.
Now, at the time of planar approximation of blocks shifted one pixel in the raster scan direction, a pixel having continuity, indicated by the black circle in the diagram, i.e., a pixel containing the fine line component, will be rejected multiple times, as shown in FIG. 44.
Upon completing planar approximation, the repetition determining unit 223 outputs information expressing the plane for approximating the pixel values of the block (the gradient and intercept of the plane of Expression 32)) as non-continuity information.
Note that an arrangement may be made wherein the repetition determining unit 223 compares the number of times of rejection per pixel with a preset threshold value, and takes a pixel which has been rejected a number of times equal to or greater than the threshold value as a pixel containing the continuity component, and output the information indicating the pixel including the continuity component as continuity component information. In this case, the peak detecting unit 202 through the continuity direction detecting unit 205 execute their respective processing on pixels containing continuity component, indicated by the continuity component information.
The number of times of rejection, the gradient of the spatial direction X of the plane for approximating the pixel values of the pixel of the block, the gradient of the spatial direction Y of the plane for approximating the pixel values of the pixel of the block, approximation values expressed by the plane approximating the pixel values of the pixels of the block, and the error ei, can be used as features of the input image.
FIG. 45 is a flowchart for describing the processing of extracting the non-continuity component with the non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43, corresponding to step S201.
In step S221, the block extracting unit 221 extracts a block made up of a predetermined number of pixels from the input image, and supplies the extracted block to the planar approximation unit 222. For example, the block extracting unit 221 selects one pixel of the pixels of the input pixel which have not been selected yet, and extracts a block made up of 7×7 pixels centered on the selected pixel. For example, the block extracting unit 221 can select pixels in raster scan order.
In step S222, the planar approximation unit 222 approximates the extracted block on a plane. The planar approximation unit 222 approximates the pixel values of the pixels of the extracted block on a plane by regression processing, for example. For example, the planar approximation unit 222 approximates the pixel values of the pixels of the extracted block excluding the rejected pixels on a plane, by regression processing. In step S223, the repetition determining unit 223 executes repetition determination. For example, repetition determination is performed by calculating the standard error from the pixel values of the pixels of the block and the planar approximation values, and counting the number of rejected pixels.
In step S224, the repetition determining unit 223 determines whether or not the standard error is equal to or above a threshold value, and in the event that determination is made that the standard error is equal to or above the threshold value, the flow proceeds to step S225.
Note that an arrangement may be made wherein the repetition determining unit 223 determines in step S224 whether or not half or more of the pixels of the block have been rejected, and whether or not the standard error is equal to or above the threshold value, and in the event that determination is made that half or more of the pixels of the block have not been rejected, and the standard error is equal to or above the threshold value, the flow proceeds to step S225.
In step S225, the repetition determining unit 223 calculates the error between the pixel value of each pixel of the block and the approximated planar approximation value, rejects the pixel with the greatest error, and notifies the planar approximation unit 222. The procedure returns to step S222, and the planar approximation processing and repetition determination processing is repeated with regard to the pixels of the block excluding the rejected pixel.
In step S225, in the event that a block which is shifted one pixel in the raster scan direction is extracted in the processing in step S221, the pixel including the fine line component (indicated by the black circle in the drawing) is rejected multiple times, as shown in FIG. 44.
In the event that determination is made in step S224 that the standard error is not equal to or greater than the threshold value, the block has been approximated on the plane, so the flow proceeds to step S226.
Note that an arrangement may be made wherein the repetition determining unit 223 determines in step S224 whether or not half or more of the pixels of the block have been rejected, and whether or not the standard error is equal to or above the threshold value, and in the event that determination is made that half or more of the pixels of the block have been rejected, or the standard error is not equal to or above the threshold value, the flow proceeds to step S225.
In step S226, the repetition determining unit 223 outputs the gradient and intercept of the plane for approximating the pixel values of the pixels of the block as non-continuity component information.
In step S227, the block extracting unit 221 determines whether or not processing of all pixels of one screen of the input image has ended, and in the event that determination is made that there are still pixels which have not yet been taken as the object of processing, the flow returns to step S221, a block is extracted from pixels not yet been subjected to the processing, and the above processing is repeated.
In the event that determination is made in step S227 that processing has ended for all pixels of one screen of the input image, the processing ends.
Thus, the non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43 can extract the non-continuity component from the input image. The non-continuity component extracting unit 201 extracts the non-continuity component from the input image, so the peak detecting unit 202 and monotonous increase/decrease detecting unit 203 can obtain the difference between the input image and the non-continuity component extracted by the non-continuity component extracting unit 201, so as to execute the processing regarding the difference containing the continuity component.
Note that the standard error in the event that rejection is performed, the standard error in the event that rejection is not performed, the number of times of rejection of a pixel, the gradient of the spatial direction X of the plane (a-hat in Expression (32)), the gradient of the spatial direction Y of the plane (b-hat in Expression (32)), the level of planar transposing (c-hat in Expression (32)), and the difference between the pixel values of the input image and the approximation values represented by the plane, calculated in planar approximation processing, can be used as features.
FIG. 46 is a flowchart for describing processing for extracting the continuity component with the non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43, instead of the processing for extracting the non-continuity component corresponding to step S201. The processing of step S241 through step S245 is the same as the processing of step S221 through step S225, so description thereof will be omitted.
In step S246, the repetition determining unit 223 outputs the difference between the approximation value represented by the plane and the pixel values of the input image, as the continuity component of the input image. That is to say, the repetition determining unit 223 outputs the difference between the planar approximation values and the true pixel values.
Note that the repetition determining unit 223 may be arranged to output the difference between the approximation value represented by the plane and the pixel values of the input image, regarding pixel values of pixels of which the difference is equal to or greater than a predetermined threshold value, as the continuity component of the input image.
The processing of step S247 is the same as the processing of step S227, and accordingly description thereof will be omitted.
The plane approximates the non-continuity component, so the non-continuity component extracting unit 201 can remove the non-continuity component from the input image by subtracting the approximation value represented by the plane for approximating pixel values, from the pixel values of each pixel in the input image. In this case, the peak detecting unit 202 through the continuousness detecting unit 204 can be made to process only the continuity component of the input image, i.e., the values where the fine line image has been projected, so the processing with the peak detecting unit 202 through the continuousness detecting unit 204 becomes easier.
FIG. 47 is a flowchart for describing other processing for extracting the continuity component with the non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43, instead of the processing for extracting the non-continuity component corresponding to step S201. The processing of step S261 through step S265 is the same as the processing of step S221 through step S225, so description thereof will be omitted.
In step S266, the repetition determining unit 223 stores the number of times of rejection for each pixel, the flow returns to step S262, and the processing is repeated.
In step S264, in the event that determination is made that the standard error is not equal to or greater than the threshold value, the block has been approximated on the plane, so the flow proceeds to step S267, the repetition determining unit 223 determines whether or not processing of all pixels of one screen of the input image has ended, and in the event that determination is made that there are still pixels which have not yet been taken as the object of processing, the flow returns to step S261, with regard to a pixel which has not yet been subjected to the processing, a block is extracted, and the above processing is repeated.
In the event that determination is made in step S267 that processing has ended for all pixels of one screen of the input image, the flow proceeds to step S268, the repetition determining unit 223 selects a pixel which has not yet been selected, and determines whether or not the number of times of rejection of the selected pixel is equal to or greater than a threshold value. For example, the repetition determining unit 223 determines in step S268 whether or not the number of times of rejection of the selected pixel is equal to or greater than a threshold value stored beforehand.
In the event that determination is made in step S268 that the number of times of rejection of the selected pixel is equal to or greater than the threshold value, the selected pixel contains the continuity component, so the flow proceeds to step S269, where the repetition determining unit 223 outputs the pixel value of the selected pixel (the pixel value in the input image) as the continuity component of the input image, and the flow proceeds to step S270.
In the event that determination is made in step S268 that the number of times of rejection of the selected pixel is not equal to or greater than the threshold value, the selected pixel does not contain the continuity component, so the processing in step S269 is skipped, and the procedure proceeds to step S270. That is to say, the pixel value of a pixel regarding which determination has been made that the number of times of rejection is not equal to or greater than the threshold value is not output.
Note that an arrangement may be made wherein the repetition determining unit 223 outputs a pixel value set to 0 for pixels regarding which determination has been made that the number of times of rejection is not equal to or greater than the threshold value.
In step S270, the repetition determining unit 223 determines whether or not processing of all pixels of one screen of the input image has ended to determine whether or not the number of times of rejection is equal to or greater than the threshold value, and in the event that determination is made that processing has not ended for all pixels, this means that there are still pixels which have not yet been taken as the object of processing, so the flow returns to step S268, a pixel which has not yet been subjected to the processing is selected, and the above processing is repeated.
In the event that determination is made in step S270 that processing has ended for all pixels of one screen of the input image, the processing ends.
Thus, of the pixels of the input image, the non-continuity component extracting unit 201 can output the pixel values of pixels containing the continuity component, as continuity component information. That is to say, of the pixels of the input image, the non-continuity component extracting unit 201 can output the pixel values of pixels containing the component of the fine line image.
FIG. 48 is a flowchart for describing yet other processing for extracting the continuity component with the non-continuity component extracting unit 201 of which the configuration is shown in FIG. 43, instead of the processing for extracting the non-continuity component corresponding to step S201. The processing of step S281 through step S288 is the same as the processing of step S261 through step S268, so description thereof will be omitted.
In step S289, the repetition determining unit 223 outputs the difference between the approximation value represented by the plane, and the pixel value of a selected pixel, as the continuity component of the input image. That is to say, the repetition determining unit 223 outputs an image wherein the non-continuity component has been removed from the input image, as the continuity information.
The processing of step S290 is the same as the processing of step S270, and accordingly description thereof will be omitted.
Thus, the non-continuity component extracting unit 201 can output an image wherein the non-continuity component has been removed from the input image as the continuity information.
As described above, in a case wherein real world light signals are projected, a non-continuous portion of pixel values of multiple pixels of first image data wherein a part of the continuity of the real world light signals has been lost is detected, data continuity is detected from the detected non-continuous portions, a model (function) is generated for approximating the light signals by estimating the continuity of the real world light signals based on the detected data continuity, and second image data is generated based on the generated function, processing results which are more accurate and have higher precision as to the event in the real world can be obtained.
FIG. 49 is a block diagram illustrating another configuration of the data continuity detecting unit 101.
With the data continuity detecting unit 101 of which the configuration is shown in FIG. 49, change in the pixel value of the pixel of interest which is a pixel of interest in the spatial direction of the input image, i.e. activity in the spatial direction of the input image, is detected, multiple sets of pixels made up of a predetermined number of pixels in one row in the vertical direction or one row in the horizontal direction are extracted for each angle based on the pixel of interest and a reference axis according to the detected activity, the correlation of the extracted pixel sets is detected, and the angle of data continuity based on the reference axis in the input image is detected based on the correlation.
The angle of data continuity means an angle assumed by the reference axis, and the direction of a predetermined dimension where constant characteristics repeatedly appear in the data 3. Constant characteristics repeatedly appearing means a case wherein, for example, the change in value as to the change in position in the data 3, i.e., the cross-sectional shape, is the same, and so forth.
The reference axis may be, for example, an axis indicating the spatial direction X (the horizontal direction of the screen), an axis indicating the spatial direction Y (the vertical direction of the screen), and so forth.
The input image is supplied to an activity detecting unit 401 and data selecting unit 402.
The activity detecting unit 401 detects change in the pixel values as to the spatial direction of the input image, i.e., activity in the spatial direction, and supplies the activity information which indicates the detected results to the data selecting unit 402 and a continuity direction derivation unit 404.
For example, the activity detecting unit 401 detects the change of a pixel value as to the horizontal direction of the screen, and the change of a pixel value as to the vertical direction of the screen, and compares the detected change of the pixel value in the horizontal direction and the change of the pixel value in the vertical direction, thereby detecting whether the change of the pixel value in the horizontal direction is greater as compared with the change of the pixel value in the vertical direction, or whether the change of the pixel value in the vertical direction is greater as compared with the change of the pixel value in the horizontal direction.
The activity detecting unit 401 supplies to the data selecting unit 402 and the continuity direction derivation unit 404 activity information, which is the detection results, indicating that the change of the pixel value in the horizontal direction is greater as compared with the change of the pixel value in the vertical direction, or indicating that the change of the pixel value in the vertical direction is greater as compared with the change of the pixel value in the horizontal direction.
In the event that the change of the pixel value in the horizontal direction is greater as compared with the change of the pixel value in the vertical direction, arc shapes (half-disc shapes) or pawl shapes are formed on one row of pixels in the vertical direction, as indicated by FIG. 50 for example, and the arc shapes or pawl shapes are formed repetitively more in the vertical direction. That is to say, in the event that the change of the pixel value in the horizontal direction is greater as compared with the change of the pixel value in the vertical direction, with the reference axis as the axis representing the spatial direction X, the angle of the data continuity based on the reference axis in the input image is a value of any from 45 degrees to 90 degrees.
In the event that the change of the pixel value in the vertical direction is greater as compared with the change of the pixel value in the horizontal direction, arc shapes or pawl shapes are formed on one row of pixels in the vertical direction, for example, and the arc shapes or pawl shapes are formed repetitively more in the horizontal direction. That is to say, in the event that the change of the pixel value in the vertical direction is greater as compared with the change of the pixel value in the horizontal direction, with the reference axis as the axis representing the spatial direction X, the angle of the data continuity based on the reference axis in the input image is a value of any from 0 degrees to 45 degrees.
For example, the activity detecting unit 401 extracts from the input image a block made up of the 9 pixels, 3×3 centered on the pixel of interest, as shown in FIG. 51. The activity detecting unit 401 calculates the sum of differences of the pixels values regarding the pixels vertically adjacent, and the sum of differences of the pixels values regarding the pixels horizontally adjacent. The sum of differences hdiff of the pixels values regarding the pixels horizontally adjacent can be obtained with Expression (35).




  
    
      
        
          h
          diff
        
        =
        
          ∑
          
            
          
          ⁢
          
            (
            
              
                P
                
                  
                    i
                    +
                    1
                  
                  ,
                  j
                
              
              -
              
                P
                
                  i
                  ,
                  j
                
              
            
            )
          
        
      
    
    
      
        (
        35
        )
      
    
  




In the same way, the sum of differences vdiff of the pixels values regarding the pixels vertically adjacent can be obtained with Expression (36).




  
    
      
        
          v
          diff
        
        =
        
          ∑
          
            
          
          ⁢
          
            (
            
              
                P
                
                  i
                  ,
                  
                    j
                    +
                    1
                  
                
              
              -
              
                P
                
                  i
                  ,
                  j
                
              
            
            )
          
        
      
    
    
      
        (
        36
        )
      
    
  




In Expression (35) and Expression (36), P represents the pixel value, i represents the position of the pixel in the horizontal direction, and j represents the position of the pixel in the vertical direction.
An arrangement may be made wherein the activity detecting unit 401 compares the calculated sum of differences hdiff of the pixels values regarding the pixels horizontally adjacent with the sum of differences vdiff of the pixels values regarding the pixels vertically adjacent, so as to determine the range of the angle of the data continuity based on the reference axis in the input image. That is to say, in this case, the activity detecting unit 401 determines whether a shape indicated by change in the pixel value as to the position in the spatial direction is formed repeatedly in the horizontal direction, or formed repeatedly in the vertical direction.
For example, change in pixel values in the horizontal direction with regard to an arc formed on pixels in one horizontal row is greater than the change of pixel values in the vertical direction, change in pixel values in the vertical direction with regard to an arc formed on pixels in one horizontal row is greater than the change of pixel values in the horizontal direction, and it can be said that the direction of data continuity, i.e., the change in the direction of the predetermined dimension of a constant feature which the input image that is the data 3 has is smaller in comparison with the change in the orthogonal direction too the data continuity. In other words, the difference of the direction orthogonal to the direction of data continuity (hereafter also referred to as non-continuity direction) is greater as compared to the difference in the direction of data continuity.
For example, as shown in FIG. 52, the activity detecting unit 401 compares the calculated sum of differences hdiff of the pixels values regarding the pixels horizontally adjacent with the sum of differences vdiff of the pixels values regarding the pixels vertically adjacent, and in the event that the sum of differences hdiff of the pixels values regarding the pixels horizontally adjacent is greater, determines that the angle of the data continuity based on the reference axis is a value of any from 45 degrees to 135 degrees, and in the event that the sum of differences vdiff of the pixels values regarding the pixels vertically adjacent is greater, determines that the angle of the data continuity based on the reference axis is a value of any from 0 degrees to 45 degrees, or a value of any from 135 degrees to 180 degrees.
For example, the activity detecting unit 401 supplies activity information indicating the determination results to the data selecting unit 402 and the continuity direction derivation unit 404.
Note that the activity detecting unit 401 can detect activity by extracting blocks of arbitrary sizes, such as a block made up of 25 pixels of 5×5, a block made up of 49 pixels of 7×7, and so forth.
The data selecting unit 402 sequentially selects pixels of interest from the pixels of the input image, and extracts multiple sets of pixels made up of a predetermined number of pixels in one row in the vertical direction or one row in the horizontal direction for each angle based on the pixel of interest and the reference axis, based on the activity information supplied from the activity detecting unit 401.
For example, in the event that the activity information indicates that the change in pixel values in the horizontal direction is greater in comparison with the change in pixel values in the vertical direction, this means that the data continuity angle is a value of any from 45 degrees to 135 degrees, so the data selecting unit 402 extracts multiple sets of pixels made up of a predetermined number of pixels in one row in the vertical direction, for each predetermined angle in the range of 45 degrees to 135 degrees, based on the pixel of interest and the reference axis.
In the event that the activity information indicates that the change in pixel values in the vertical direction is greater in comparison with the change in pixel values in the horizontal direction, this means that the data continuity angle is a value of any from 0 degrees to 45 degrees or from 135 degrees to 180 degrees, so the data selecting unit 402 extracts multiple sets of pixels made up of a predetermined number of pixels in one row in the horizontal direction, for each predetermined angle in the range of 0 degrees to 45 degrees or 135 degrees to 180 degrees, based on the pixel of interest and the reference axis.
Also, for example, in the event that the activity information indicates that the angle of data continuity is a value of any from 45 degrees to 135 degrees, the data selecting unit 402 extracts multiple sets of pixels made up of a predetermined number of pixels in one row in the vertical direction, for each predetermined angle in the range of 45 degrees to 135 degrees, based on the pixel of interest and the reference axis.
In the event that the activity information indicates that the angle of data continuity is a value of any from 0 degrees to 45 degrees or from 135 degrees to 180 degrees, the data selecting unit 402 extracts multiple sets of pixels made up of a predetermined number of pixels in one row in the horizontal direction, for each predetermined angle in the range of 0 degrees to 45 degrees or 135 degrees to 180 degrees, based on the pixel of interest and the reference axis.
The data selecting unit 402 supplies the multiple sets made up of the extracted pixels to an error estimating unit 403.
The error estimating unit 403 detects correlation of pixel sets for each angle with regard to the multiple sets of extracted pixels.
For example, with regard to the multiple sets of pixels made up of a predetermined number of pixels in one row in the vertical direction corresponding to one angle, the error estimating unit 403 detects the correlation of the pixels values of the pixels at corresponding positions of the pixel sets. With regard to the multiple sets of pixels made up of a predetermined number of pixels in one row in the horizontal direction corresponding to one angle, the error estimating unit 403 detects the correlation of the pixels values of the pixels at corresponding positions of the sets.
The error estimating unit 403 supplies correlation information indicating the detected correlation to the continuity direction derivation unit 404. The error estimating unit 403 calculates the sum of the pixel values of pixels of a set including the pixel of interest supplied from the data selecting unit 402 as values indicating correlation, and the absolute value of difference of the pixel values of the pixels at corresponding positions in other sets, and supplies the sum of absolute value of difference to the continuity direction derivation unit 404 as correlation information.
Based on the correlation information supplied from the error estimating unit 403, the continuity direction derivation unit 404 detects the data continuity angle based on the reference axis in the input image, corresponding to the lost continuity of the light signals of the actual world 1, and outputs data continuity information indicating an angle. For example, based on the correlation information supplied from the error estimating unit 403, the continuity direction derivation unit 404 detects an angle corresponding to the pixel set with the greatest correlation as the data continuity angle, and outputs data continuity information indicating the angle corresponding to the pixel set with the greatest correlation that has been detected.
The following description will be made regarding detection of data continuity angle in the range of 0 degrees through 90 degrees (the so-called first quadrant).
FIG. 53 is a block diagram illustrating a more detailed configuration of the data continuity detecting unit 101 shown in FIG. 49.
The data selecting unit 402 includes pixel selecting unit 411-1 through pixel selecting unit 411-L. The error estimating unit 403 includes estimated error calculating unit 412-1 through estimated error calculating unit 412-L. The continuity direction derivation unit 404 includes a smallest error angle selecting unit 413.
First, description will be made regarding the processing of the pixel selecting unit 411-1 through pixel selecting unit 411-L in the event that the data continuity angle indicated by the activity information is a value of any from 45 degrees to 135 degrees.
The pixel selecting unit 411-1 through pixel selecting unit 411-L set straight lines of mutually differing predetermined angles which pass through the pixel of interest, with the axis indicating the spatial direction X as the reference axis. The pixel selecting unit 411-1 through pixel selecting unit 411-L select, of the pixels belonging to a vertical row of pixels to which the pixel of interest belongs, a predetermined number of pixels above the pixel of interest, and predetermined number of pixels below the pixel of interest, and the pixel of interest, as a set.
For example, as shown in FIG. 54, the pixel selecting unit 411-1 through pixel selecting unit 411-L select 9 pixels centered on the pixel of interest, as a set of pixels, from the pixels belonging to a vertical row of pixels to which the pixel of interest belongs.
In FIG. 54, one grid-shaped square (one grid) represents one pixel. In FIG. 54, the circle shown at the center represents the pixel of interest.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a vertical row of pixels to the left of the vertical row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. In FIG. 54, the circle to the lower left of the pixel of interest represents an example of a selected pixel. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the vertical row of pixels to the left of the vertical row of pixels to which the pixel of interest belongs, a predetermined number of pixels above the selected pixel, a predetermined number of pixels below the selected pixel, and the selected pixel, as a set of pixels.
For example, as shown in FIG. 54, the pixel selecting unit 411-1 through pixel selecting unit 411-L select 9 pixels centered on the pixel at the position closest to the straight line, from the pixels belonging to the vertical row of pixels to the left of the vertical row of pixels to which the pixel of interest belongs, as a set of pixels.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a vertical row of pixels second left from the vertical row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. In FIG. 54, the circle to the far left represents an example of the selected pixel. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, as a set of pixels, from the pixels belonging to the vertical row of pixels second left from the vertical row of pixels to which the pixel of interest belongs, a predetermined number of pixels above the selected pixel, a predetermined number of pixels below the selected pixel, and the selected pixel.
For example, as shown in FIG. 54, the pixel selecting unit 411-1 through pixel selecting unit 411-L select 9 pixels centered on the pixel at the position closest to the straight line, from the pixels belonging to the vertical row of pixels second left from the vertical row of pixels to which the pixel of interest belongs, as a set of pixels.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a vertical row of pixels to the right of the vertical row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. In FIG. 54, the circle to the upper right of the pixel of interest represents an example of a selected pixel. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the vertical row of pixels to the right of the vertical row of pixels to which the pixel of interest belongs, a predetermined number of pixels above the selected pixel, a predetermined number of pixels below the selected pixel, and the selected pixel, as a set of pixels.
For example, as shown in FIG. 54, the pixel selecting unit 411-1 through pixel selecting unit 411-L select 9 pixels centered on the pixel at the position closest to the straight line, from the pixels belonging to the vertical row of pixels to the right of the vertical row of pixels to which the pixel of interest belongs, as a set of pixels.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a vertical row of pixels second right from the vertical row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. In FIG. 54, the circle to the far right represents an example of the selected pixel. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the vertical row of pixels second right from the vertical row of pixels to which the pixel of interest belongs, a predetermined number of pixels above the selected pixel, a predetermined number of pixels below the selected pixel, and the selected pixel, as a set of pixels.
For example, as shown in FIG. 54, the pixel selecting unit 411-1 through pixel selecting unit 411-L select 9 pixels centered on the pixel at the position closest to the straight line, from the pixels belonging to the vertical row of pixels second right from the vertical row of pixels to which the pixel of interest belongs, as a set of pixels.
Thus, the pixel selecting unit 411-1 through pixel selecting unit 411-L each select five sets of pixels.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select pixel sets for (lines set to) mutually different angles. For example, the pixel selecting unit 411-1 selects sets of pixels regarding 45 degrees, the pixel selecting unit 411-2 selects sets of pixels regarding 47.5 degrees, and the pixel selecting unit 411-3 selects sets of pixels regarding 50 degrees. The pixel selecting unit 411-1 through pixel selecting unit 411-L select sets of pixels regarding angles every 2.5 degrees, from 52.5 degrees through 135 degrees.
Note that the number of pixel sets may be an optional number, such as 3 or 7, for example, and does not restrict the present invention. Also, the number of pixels selected as one set may be an optional number, such as 5 or 13, for example, and does not restrict the present invention.
Note that the pixel selecting unit 411-1 through pixel selecting unit 411-L may be arranged to select pixel sets from pixels within a predetermined range in the vertical direction. For example, the pixel selecting unit 411-1 through pixel selecting unit 411-L can select pixel sets from 121 pixels in the vertical direction (60 pixels upward from the pixel of interest, and 60 pixels downward). In this case, the data continuity detecting unit 101 can detect the angle of data continuity up to 88.09 degrees as to the axis representing the spatial direction X.
The pixel selecting unit 411-1 supplies the selected set of pixels to the estimated error calculating unit 412-1, and the pixel selecting unit 411-2 supplies the selected set of pixels to the estimated error calculating unit 412-2. In the same way, each pixel selecting unit 411-3 through pixel selecting unit 411-L supplies the selected set of pixels to each estimated error calculating unit 412-3 through estimated error calculating unit 412-L.
The estimated error calculating unit 412-1 through estimated error calculating unit 412-L detect the correlation of the pixels values of the pixels at positions in the multiple sets, supplied from each of the pixel selecting unit 411-1 through pixel selecting unit 411-L. For example, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L calculates, as a value indicating the correlation, the sum of absolute values of difference between the pixel values of the pixels of the set containing the pixel of interest, and the pixel values of the pixels at corresponding positions in other sets, supplied from one of the pixel selecting unit 411-1 through pixel selecting unit 411-L.
More specifically, based on the pixel values of the pixels of the set containing the pixel of interest and the pixel values of the pixels of the set made up of pixels belonging to one vertical row of pixels to the left side of the pixel of interest supplied from one of the pixel selecting unit 411-1 through pixel selecting unit 411-L, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L calculates the difference of the pixel values of the topmost pixel, then calculates the difference of the pixel values of the second pixel from the top, and so on to calculate the absolute values of difference of the pixel values in order from the top pixel, and further calculates the sum of absolute values of the calculated differences. Based on the pixel values of the pixels of the set containing the pixel of interest and the pixel values of the pixels of the set made up of pixels belonging to one vertical row of pixels two to the left from the pixel of interest supplied from one of the pixel selecting unit 411-1 through pixel selecting unit 411-L, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L calculates the absolute values of difference of the pixel values in order from the top pixel, and calculates the sum of absolute values of the calculated differences.
Then, based on the pixel values of the pixels of the set containing the pixel of interest and the pixel values of the pixels of the set made up of pixels belonging to one vertical row of pixels to the right side of the pixel of interest supplied from one of the pixel selecting unit 411-1 through pixel selecting unit 411-L, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L calculates the difference of the pixel values of the topmost pixel, then calculates the difference of the pixel values of the second pixel from the top, and so on to calculate the absolute values of difference of the pixel values in order from the top pixel, and further calculates the sum of absolute values of the calculated differences. Based on the pixel values of the pixels of the set containing the pixel of interest and the pixel values of the pixels of the set made up of pixels belonging to one vertical row of pixels two to the right from the pixel of interest supplied from one of the pixel selecting unit 411-1 through pixel selecting unit 411-L, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L calculates the absolute values of difference of the pixel values in order from the top pixel, and calculates the sum of absolute values of the calculated differences.
The estimated error calculating unit 412-1 through estimated error calculating unit 412-L add all of the sums of absolute values of difference of the pixel values thus calculated, thereby calculating the aggregate of absolute values of difference of the pixel values.
The estimated error calculating unit 412-1 through estimated error calculating unit 412-L supply information indicating the detected correlation to the smallest error angle selecting unit 413. For example, the estimated error calculating unit 412-1 through estimated error calculating unit 412-L supply the aggregate of absolute values of difference of the pixel values calculated, to the smallest error angle selecting unit 413.
Note that the estimated error calculating unit 412-1 through estimated error calculating unit 412-L are not restricted to the sum of absolute values of difference of pixel values, and can also calculate other values as correlation values as well, such as the sum of squared differences of pixel values, or correlation coefficients based on pixel values, and so forth.
The smallest error angle selecting unit 413 detects the data continuity angle based on the reference axis in the input image which corresponds to the continuity of the image which is the lost actual world 1 light signals, based on the correlation detected by the estimated error calculating unit 412-1 through estimated error calculating unit 412-L with regard to mutually different angles. That is to say, based on the correlation detected by the estimated error calculating unit 412-1 through estimated error calculating unit 412-L with regard to mutually different angles, the smallest error angle selecting unit 413 selects the greatest correlation, and takes the angle regarding which the selected correlation was detected as the data continuity angle based on the reference axis, thereby detecting the data continuity angle based on the reference axis in the input image.
For example, of the aggregates of absolute values of difference of the pixel values supplied from the estimated error calculating unit 412-1 through estimated error calculating unit 412-L, the smallest error angle selecting unit 413 selects the smallest aggregate. With regard to the pixel set of which the selected aggregate was calculated, the smallest error angle selecting unit 413 makes reference to a pixel belonging to the one vertical row of pixels two to the left from the pixel of interest and at the closest pixel position to the straight line, and to a pixel belonging to the one vertical row of pixels two to the right from the pixel of interest and at the closest pixel position to the straight line.
As shown in FIG. 54, the smallest error angle selecting unit 413 obtains the distance S in the vertical direction of the position of the pixels to reference from the position of the pixel of interest. As shown in FIG. 55, the smallest error angle selecting unit 413 detects the angle θ of data continuity based on the axis indicating the spatial direction X which is the reference axis in the input image which is image data, that corresponds to the lost actual world 1 light signals continuity, from Expression (37).




  
    
      
        θ
        =
        
          
            tan
            
              -
              1
            
          
          ⁢
          
            S
            2
          
        
      
    
    
      
        (
        37
        )
      
    
  




Next, description will be made regarding the processing of the pixel selecting unit 411-1 through pixel selecting unit 411-L in the event that the data continuity angle indicated by the activity information is a value of any from 0 degrees to 45 degrees and 135 degrees to 180 degrees.
The pixel selecting unit 411-1 through pixel selecting unit 411-L set straight lines of predetermined angles which pass through the pixel of interest, with the axis indicating the spatial direction X as the reference axis, and select, of the pixels belonging to a horizontal row of pixels to which the pixel of interest belongs, a predetermined number of pixels to the left of the pixel of interest, and predetermined number of pixels to the right of the pixel of interest, and the pixel of interest, as a pixel set.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a horizontal row of pixels above the horizontal row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the horizontal row of pixels above the horizontal row of pixels to which the pixel of interest belongs, a predetermined number of pixels to the left of the selected pixel, a predetermined number of pixels to the right of the selected pixel, and the selected pixel, as a pixel set.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a horizontal row of pixels two above the horizontal row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the horizontal row of pixels two above the horizontal row of pixels to which the pixel of interest belongs, a predetermined number of pixels to the left of the selected pixel, a predetermined number of pixels to the right of the selected pixel, and the selected pixel, as a pixel set.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a horizontal row of pixels below the horizontal row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the horizontal row of pixels below the horizontal row of pixels to which the pixel of interest belongs, a predetermined number of pixels to the left of the selected pixel, a predetermined number of pixels to the right of the selected pixel, and the selected pixel, as a pixel set.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select, from pixels belonging to a horizontal row of pixels two below the horizontal row of pixels to which the pixel of interest belongs, a pixel at the position closest to the straight line set for each. The pixel selecting unit 411-1 through pixel selecting unit 411-L then select, from the pixels belonging to the horizontal row of pixels two below the horizontal row of pixels to which the pixel of interest belongs, a predetermined number of pixels to the left of the selected pixel, a predetermined number of pixels to the right of the selected pixel, and the selected pixel, as a pixel set.
Thus, the pixel selecting unit 411-1 through pixel selecting unit 411-L each select five sets of pixels.
The pixel selecting unit 411-1 through pixel selecting unit 411-L select pixel sets for mutually different angles. For example, the pixel selecting unit 411-1 selects sets of pixels regarding 0 degrees, the pixel selecting unit 411-2 selects sets of pixels regarding 2.5 degrees, and the pixel selecting unit 411-3 selects sets of pixels regarding 5 degrees. The pixel selecting unit 411-1 through pixel selecting unit 411-L select sets of pixels regarding angles every 2.5 degrees, from 7.5 degrees through 45 degrees and from 135 degrees through 180 degrees.
The pixel selecting unit 411-1 supplies the selected set of pixels to the estimated error calculating unit 412-1, and the pixel selecting unit 411-2 supplies the selected set of pixels to the estimated error calculating unit 412-2. In the same way, each pixel selecting unit 411-3 through pixel selecting unit 411-L supplies the selected set of pixels to each estimated error calculating unit 412-3 through estimated error calculating unit 412-L.
The estimated error calculating unit 412-1 through estimated error calculating unit 412-L detect the correlation of the pixels values of the pixels at positions in the multiple sets, supplied from each of the pixel selecting unit 411-1 through pixel selecting unit 411-L. The estimated error calculating unit 412-1 through estimated error calculating unit 412-L supply information indicating the detected correlation to the smallest error angle selecting unit 413.
The smallest error angle selecting unit 413 detects the data continuity angle based on the reference axis in the input image which corresponds to the continuity of the image which is the lost actual world 1 light signals, based on the correlation detected by the estimated error calculating unit 412-1 through estimated error calculating unit 412-L.
Next, data continuity detection processing with the data continuity detecting unit 101 of which the configuration is shown in FIG. 49, corresponding to the processing in step S101, will be described with reference to the flowchart in FIG. 56.
In step S401, the activity detecting unit 401 and the data selecting unit 402 select the pixel of interest which is a pixel of interest from the input image. The activity detecting unit 401 and the data selecting unit 402 select the same pixel of interest. For example, the activity detecting unit 401 and the data selecting unit 402 select the pixel of interest from the input image in raster scan order.
In step S402, the activity detecting unit 401 detects activity with regard to the pixel of interest. For example, the activity detecting unit 401 detects activity based on the difference of pixel values of pixels aligned in the vertical direction of a block made up of a predetermined number of pixels centered on the pixel of interest, and the difference of pixel values of pixels aligned in the horizontal direction.
The activity detecting unit 401 detects activity in the spatial direction as to the pixel of interest, and supplies activity information indicating the detected results to the data selecting unit 402 and the continuity direction derivation unit 404.
In step S403, the data selecting unit 402 selects, from a row of pixels including the pixel of interest, a predetermined number of pixels centered on the pixel of interest, as a pixel set. For example, the data selecting unit 402 selects a predetermined number of pixels above or to the left of the pixel of interest, and a predetermined number of pixels below or to the right of the pixel of interest, which are pixels belonging to a vertical or horizontal row of pixels to which the pixel of interest belongs, and also the pixel of interest, as a pixel set.
In step S404, the data selecting unit 402 selects, as a pixel set, a predetermined number of pixels each from a predetermined number of pixel rows for each angle in a predetermined range based on the activity detected by the processing in step S402. For example, the data selecting unit 402 sets straight lines with angles of a predetermined range which pass through the pixel of interest, with the axis indicating the spatial direction X as the reference axis, selects a pixel which is one or two rows away from the pixel of interest in the horizontal direction or vertical direction and which is closest to the straight line, and selects a predetermined number of pixels above or to the left of the selected pixel, and a predetermined number of pixels below or to the right of the selected pixel, and the selected pixel closest to the line, as a pixel set. The data selecting unit 402 selects pixel sets for each angle.
The data selecting unit 402 supplies the selected pixel sets to the error estimating unit 403.
In step S405, the error estimating unit 403 calculates the correlation between the set of pixels centered on the pixel of interest, and the pixel sets selected for each angle. For example, the error estimating unit 403 calculates the sum of absolute values of difference of the pixel values of the pixels of the set including the pixel of interest and the pixel values of the pixels at corresponding positions in other sets, for each angle.
The angle of data continuity may be detected based on the correlation between pixel sets selected for each angle.
The error estimating unit 403 supplies the information indicating the calculated correlation to the continuity direction derivation unit 404.
In step S406, from position of the pixel set having the strongest correlation based on the correlation calculated in the processing in step S405, the continuity direction derivation unit 404 detects the data continuity angle based on the reference axis in the input image which is image data that corresponds to the lost actual world 1 light signal continuity. For example, the continuity direction derivation unit 404 selects the smallest aggregate of the aggregate of absolute values of difference of pixel values, and detects the data continuity angle θ from the position of the pixel set regarding which the selected aggregate has been calculated.
The continuity direction derivation unit 404 outputs data continuity information indicating the angle of the data continuity that has been detected.
In step S407, the data selecting unit 402 determines whether or not processing of all pixels has ended, and in the event that determination is made that processing of all pixels has not ended, the flow returns to step S401, a pixel of interest is selected from pixels not yet taken as the pixel of interest, and the above-described processing is repeated.
In the event that determination is made in step S407 that processing of all pixels has ended, the processing ends.
Thus, the data continuity detecting unit 101 can detect the data continuity angle based on the reference axis in the image data, corresponding to the lost actual world 1 light signal continuity.
Note that an arrangement may be made wherein the data continuity detecting unit 101 of which the configuration is shown in FIG. 49 detects activity in the spatial direction of the input image with regard to the pixel of interest which is a pixel of interest in the frame of interest which is a frame of interest, extracts multiple pixel sets made up of a predetermined number of pixels in one row in the vertical direction or one row in the horizontal direction from the frame of interest and from each of frames before or after time-wise the frame of interest, for each angle and movement vector based on the pixel of interest and the space-directional reference axis, according to the detected activity, detects the correlation of the extracted pixel sets, and detects the data continuity angle in the time direction and spatial direction in the input image, based on this correlation.
For example, as shown in FIG. 57, the data selecting unit 402 extracts multiple pixel sets made up of a predetermined number of pixels in one row in the vertical direction or one row in the horizontal direction from frame #n which is the frame of interest, frame #n−1, and frame #n+1, for each angle and movement vector based on the pixel of interest and the space-directional reference axis, according to the detected activity.
The frame #n−1 is a frame which is previous to the frame #n time-wise, and the frame #n+1 is a frame following the frame #n time-wise. That is to say, the frame #n−1, frame #n, and frame #n+1, are displayed in the order of frame #n−1, frame #n, and frame #n+1.
The error estimating unit 403 detects the correlation of pixel sets for each single angle and single movement vector, with regard to the multiple sets of the pixels that have been extracted. The continuity direction derivation unit 404 detects the data continuity angle in the temporal direction and spatial direction in the input image which corresponds to the lost actual world 1 light signal continuity, based on the correlation of pixel sets, and outputs the data continuity information indicating the angle.
Next, description will be made regarding another embodiment example of the actual world estimating unit 102 (FIG. 3) with reference to FIG. 58 through FIG. 88.
FIG. 58 is a diagram for describing the principle of this embodiment example.
As shown in FIG. 58, a signal (light intensity allocation) in the actual world 1, which is an image cast on the sensor 2, is represented with a predetermined function F. Note that hereafter, with the description of this embodiment example, the signal serving as an image in the actual world 1 is particularly referred to as a light signal, and the function F is particularly referred to as a light signal function F.
With this embodiment example, in the event that the light signal in the actual world 1 represented with the light signal function F has predetermined continuity, the actual world estimating unit 102 estimates the light signal function F by approximating the light signal function F with a predetermined function f using an input image (image data including continuity of data corresponding to continuity) from the sensor 2, and data continuity information (data continuity information corresponding to continuity of the input image data) from the data continuity detecting unit 101. Note that with the description of this embodiment example, the function f is particularly referred to as an approximation function f, hereafter.
In other words, with this embodiment example, the actual world estimating unit 102 approximates (describes) the image (light signal in the actual world 1) represented with the light signal function F using a model 161 (FIG. 4) represented with the approximation function f. Accordingly, hereafter, this embodiment example is referred to as a function approximating method.
Now, description will be made regarding the background wherein the present applicant has invented the function approximating method, prior to entering the specific description of the function approximating method.
FIG. 59 is a diagram for describing integration effects in the case in which the sensor 2 is treated as a CCD.
As shown in FIG. 59, multiple detecting elements 2-1 are disposed on the plane of the sensor 2.
With the example in FIG. 59, a direction in parallel with a predetermined side of the detecting elements 2-1 is taken as the X direction, which is one direction in the spatial direction, and the a direction orthogonal to the X direction is taken as the Y direction, which is another direction in the spatial direction. Also, the direction perpendicular to the X-Y plane is taken as the direction t serving as the temporal direction.
Also, with the example in FIG. 59, the spatial shape of each detecting element 2-1 of the sensor 2 is represented with a square of which one side is 1 in length. The shutter time (exposure time) of the sensor 2 is represented with 1.
Further, with the example in FIG. 59, the center of one detecting element 2-1 of the sensor 2 is taken as the origin (position x=0 in the X direction, and position y=0 in the Y direction) in the spatial direction (X direction and Y direction), and the intermediate point-in-time of the exposure time is taken as the origin (position t=0 in the t direction) in the temporal direction (t direction).
In this case, the detecting element 2-1 of which the center is in the origin (x=0, y=0) in the spatial direction subjects the light signal function F(x, y, t) to integration with a range between −0.5 and 0.5 in the X direction, range between −0.5 and 0.5 in the Y direction, and range between −0.5 and 0.5 in the t direction, and outputs the integral value thereof as a pixel value P.
That is to say, the pixel value P output from the detecting element 2-1 of which the center is in the origin in the spatial direction is represented with the following Expression (38).




  
    
      
        P
        =
        
          
            ∫
            
              -
              0.5
            
            
              +
              0.5
            
          
          ⁢
          
            
              ∫
              
                -
                0.5
              
              
                +
                0.5
              
            
            ⁢
            
              
                ∫
                
                  -
                  0.5
                
                
                  +
                  0.5
                
              
              ⁢
              
                
                  F
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                      ,
                      t
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
                ⁢
                
                  d
                  t
                
              
            
          
        
      
    
    
      
        (
        38
        )
      
    
  




The other detecting elements 2-1 also output the pixel value P shown in Expression (38) by taking the center of the subject detecting element 2-1 as the origin in the spatial direction in the same way.
FIG. 60 is a diagram for describing a specific example of the integration effects of the sensor 2.
In FIG. 60, the X direction and Y direction represent the X direction and Y direction of the sensor 2 (FIG. 59).
A portion 2301 of the light signal in the actual world 1 (hereafter, such a portion is referred to as a region) represents an example of a region having predetermined continuity.
Note that the region 2301 is a portion of the continuous light signal (continuous region). On the other hand, in FIG. 60, the region 2301 is shown as divided into 20 small regions (square regions) in reality. This is because of representing that the size of the region 2301 is equivalent to the size wherein the four detecting elements (pixels) of the sensor 2 in the X direction, and also the five detecting elements (pixels) of the sensor 2 in the Y direction are arrayed. That is to say, each of the 20 small regions (virtual regions) within the region 2301 is equivalent to one pixel.
Also, a white portion shown in the drawing within the region 2301 represents a light signal corresponding to a fine line. Accordingly, the region 2301 has continuity in the direction wherein a fine line continues. Hereafter, the region 2301 is referred to as the fine-line-including actual world region 2301.
In this case, when the fine-line-including actual world region 2301 (a portion of a light signal in the actual world 1) is detected by the sensor 2, region 2302 (hereafter, this is referred to as a fine-line-including data region 2302) of the input image (pixel values) is output from the sensor 2 by integration effects.
Note that each pixel of the fine-line-including data region 2302 is represented as an image in the drawing, but is data representing a predetermined value in reality. That is to say, the fine-line-including actual world region 2301 is changed (distorted) to the fine-line-including data region 2302, which is divided into 20 pixels (20 pixels in total of 4 pixels in the X direction and also 5 pixels in the Y direction) each having a predetermined pixel value by the integration effects of the sensor 2.
FIG. 61 is a diagram for describing another specific example (example different from FIG. 60) of the integration effects of the sensor 2.
In FIG. 61, the X direction and Y direction represent the X direction and Y direction of the sensor 2 (FIG. 59).
A portion (region) 2303 of the light signal in the actual world 1 represents another example (example different from the fine-line-including actual world region 2301 in FIG. 60) of a region having predetermined continuity.
Note that the region 2303 is a region having the same size as the fine-line-including actual world region 2301. That is to say, the region 2303 is also a portion of the continuous light signal in the actual world 1 (continuous region) as with the fine-line-including actual world region 2301 in reality, but is shown as divided into 20 small regions (square regions) equivalent to one pixel of the sensor 2 in FIG. 61.
Also, the region 2303 includes a first portion having predetermined first light intensity (value), and a second portion edge having predetermined second light intensity (value). Accordingly, the region 2303 has continuity in the direction wherein the edges continue. Hereafter, the region 2303 is referred to as the two-valued-edge-including actual world region 2303.
In this case, when the two-valued-edge-including actual world region 2303 (a portion of the light signal in the actual world 1) is detected by the sensor 2, a region 2304 (hereafter, referred to as two-valued-edge-including data region 2304) of the input image (pixel value) is output from the sensor 2 by integration effects.
Note that each pixel value of the two-valued-edge-including data region 2304 is represented as an image in the drawing as with the fine-line-including data region 2302, but is data representing a predetermined value in reality. That is to say, the two-valued-edge-including actual world region 2303 is changed (distorted) to the two-valued-edge-including data region 2304, which is divided into 20 pixels (20 pixels in total of 4 pixels in the X direction and also 5 pixels in the Y direction) each having a predetermined pixel value by the integration effects of the sensor 2.
Conventional image processing devices have regarded image data output from the sensor 2 such as the fine-line-including data region 2302, two-valued-edge-including data region 2304, and the like as the origin (basis), and also have subjected the image data to the subsequent image processing. That is to say, regardless of that the image data output from the sensor 2 had been changed (distorted) to data different from the light signal in the actual world 1 by integration effects, the conventional image processing devices have performed image processing on assumption that the data different from the light signal in the actual world 1 is correct.
As a result, the conventional image processing devices have provided a problem wherein based on the waveform (image data) of which the details in the actual world is distorted at the stage wherein the image data is output from the sensor 2, it is very difficult to restore the original details from the waveform.
Accordingly, with the function approximating method, in order to solve this problem, as described above (as shown in FIG. 58), the actual world estimating unit 102 estimates the light signal function F by approximating the light signal function F (light signal in the actual world 1) with the approximation function f based on the image data (input image) such as the fine-line-including data region 2302, and two-valued-edge-including data region 2304 output from the sensor 2.
Thus, at a later stage than the actual world estimating unit 102 (in this case, the image generating unit 103 in FIG. 3), the processing can be performed by taking the image data wherein integration effects are taken into consideration, i.e., image data that can be represented with the approximation function f as the origin.
Hereafter, description will be made independently regarding three specific methods (first through third function approximating methods), of such a function approximating method with reference to the drawings.
First, description will be made regarding the first function approximating method with reference to FIG. 62 through FIG. 76.
FIG. 62 is a diagram representing the fine-line-including actual world region 2301 shown in FIG. 60 described above again.
In FIG. 62, the X direction and Y direction represent the X direction and Y direction of the sensor 2 (FIG. 59).
The first function approximating method is a method for approximating a one-dimensional waveform (hereafter, such a waveform is referred to as an X cross-sectional waveform F(x)) wherein the light signal function F(x, y, t) corresponding to the fine-line-including actual world region 2301 such as shown in FIG. 62 is projected in the X direction (direction of an arrow 2311 in the drawing), with the approximation function f(x) serving as an n-dimensional (n is an arbitrary integer) polynomial, for example. Accordingly, hereafter, the first function approximating method is particularly referred to as a one-dimensional approximating method.
Note that with the one-dimensional approximating method, the X cross-sectional waveform F(x), which is to be approximated, is not restricted to a waveform corresponding to the fine-line-including actual world region 2301 in FIG. 62, of course. That is to say, as described later, with the one-dimensional approximating method, any waveform can be approximated as long as the X cross-sectional waveform F(x) corresponds to the light signals in the actual world 1 having continuity.
Also, the direction of the projection of the light signal function F(x, y, t) is not restricted to the X direction, or rather the Y direction or t direction may be employed. That is to say, with the one-dimensional approximating method, a function F(y) wherein the light signal function F(x, y, t) is projected in the Y direction may be approximated with a predetermined approximation function f(y), or a function F(t) wherein the light signal function F(x, y, t) is projected in the t direction may be approximated with a predetermined approximation function f (t).
More specifically, the one-dimensional approximating method is a method for approximating, for example, the X cross-sectional waveform F(x) with the approximation function f(x) serving as an n-dimensional polynomial such as shown in the following Expression (39).




  
    
      
        
          f
          ⁡
          
            (
            x
            )
          
        
        =
        
          
            
              w
              0
            
            +
            
              
                w
                1
              
              ⁢
              x
            
            +
            
              
                w
                2
              
              ⁢
              x
            
            +
            ...
            +
            
              
                w
                n
              
              ⁢
              
                x
                n
              
            
          
          =
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                x
                i
              
            
          
        
      
    
    
      
        (
        39
        )
      
    
  




That is to say, with the one-dimensional approximating method, the actual world estimating unit 102 estimates the X cross-sectional waveform F(x) by calculating the coefficient (features) wi of xi in Expression (39).
This calculation method of the features wi is not restricted to a particular method, for example, the following first through third methods may be employed.
That is to say, the first method is a method that has been employed so far.
On the other hand, the second method is a method that has been newly invented by the present applicant, which is a method that considers continuity in the spatial direction as to the first method.
However, as described later, with the first and second methods, the integration effects of the sensor 2 are not taken into consideration. Accordingly, an approximation function f(x) obtained by substituting the features wi calculated by the first method or the second method for the above Expression (39) is an approximation function regarding an input image, but strictly speaking, cannot be referred to as the approximation function of the X cross-sectional waveform F(x).
Consequently, the present applicant has invented the third method that calculates the features wi further in light of the integration effects of the sensor 2 as to the second method. An approximation function f(x) obtained by substituting the features wi calculated with this third method for the above Expression (39) can be referred to as the approximation function of the X cross-sectional waveform F(x) in that the integration effects of the sensor 2 are taken into consideration.
Thus, strictly speaking, the first method and the second method cannot be referred to as the one-dimensional approximating method, and the third method alone can be referred to as the one-dimensional approximating method.
In other words, as shown in FIG. 63, the second method is different from the one-dimensional approximating method. That is to say, FIG. 63 is a diagram for describing the principle of the embodiment corresponding to the second method.
As shown in FIG. 63, with the embodiment corresponding to the second method, in the event that the light signal in the actual world 1 represented with the light signal function F has predetermined continuity, the actual world estimating unit 102 does not approximate the X cross-sectional waveform F(x) with an input image (image data including continuity of data corresponding to continuity) from the sensor 2, and data continuity information (data continuity information corresponding to continuity of input image data) from the data continuity detecting unit 101, but approximates the input image from the sensor 2 with a predetermined approximation function f2 (x).
Thus, it is hard to say that the second method is a method having the same level as the third method in that approximation of the input image alone is performed without considering the integral effects of the sensor 2. However, the second method is a method superior to the conventional first method in that the second method takes continuity in the spatial direction into consideration.
Hereafter, description will be made independently regarding the details of the first method, second method, and third method in this order.
Note that hereafter, in the event that the respective approximation functions f (x) generated by the first method, second method, and third method are distinguished from that of the other method, they are particularly referred to as approximation function f1 (x), approximation function f2 (x) and approximation function f3 (x) respectively.
First, description will be made regarding the details of the first method.
With the first method, on condition that the approximation function f1 (x) shown in the above Expression (39) holds within the fine-line-including actual world region 2301 in FIG. 64, the following prediction equation (40) is defined.

P(x, y)=f1(x)+e  (40)

In Expression (40), x represents a pixel position relative as to the X direction from a pixel of interest. y represents a pixel position relative as to the Y direction from the pixel of interest. e represents a margin of error. Specifically, for example, as shown in FIG. 64, let us say that the pixel of interest is the second pixel in the X direction from the left, and also the third pixel in the Y direction from the bottom in the drawing, of the fine-line-including data region 2302 (data of which the fine-line-including actual world region 2301 (FIG. 62) is detected by the sensor 2, and output). Also, let us say that the center of the pixel of interest is the origin (0, 0), and a coordinates system (hereafter, referred to as a pixel-of-interest coordinates system) of which axes are an x axis and y axis respectively in parallel with the X direction and Y direction of the sensor 2 (FIG. 59) is set. In this case, the coordinates value (x, y) of the pixel-of-interest coordinates system represents a relative pixel position.
Also, in Expression (40), P (x, y) represents a pixel value in the relative pixel positions (x, y). Specifically, in this case, the P (x, y) within the fine-line-including data region 2302 is such as shown in FIG. 65.
FIG. 65 represents this pixel value P (x, y) in a graphic manner.
In FIG. 65, the respective vertical axes of the graphs represent pixel values, and the horizontal axes represent a relative position x in the X direction from the pixel of interest. Also, in the drawing, the dashed line in the first graph from the top represents an input pixel value P (x, −2), the broken triple-dashed line in the second graph from the top represents an input pixel value P (x, −1), the solid line in the third graph from the top represents an input pixel value P (x, 0), the broken line in the fourth graph from the top represents an input pixel value P (x, 1), and the broken double-dashed line in the fifth graph from the top (the first from the bottom) represents an input pixel value P (x, 2) respectively.
Upon the 20 input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) (however, x is any one integer value of −1 through 2) shown in FIG. 65 being substituted for the above Expression (40) respectively, 20 equations as shown in the following Expression (41) are generated. Note that each ek (k is any one of integer values 1 through 20) represents a margin of error.

P(−1, −2)=f1(−1)+e1 

P(0, −2)=f1(0)+e2 

P(1, −2)=f1(1)+e3 

P(2, −2)=f1(2)+e4 

P(−1, −1)=f1(−1)+e5 

P(0, −1)=f1(0)+e6 

P(1, −1)=f1(1)+e7 

P(2, −1)=f1(2)+e8 

P(−1, 0)=f1(−1)+e9 

P(0, 0)=f1(0)+e10 

P(1, 0)=f1(1)+e11 

P(2, 0)=f1(2)+e12 

P(−1, 1)=f1(−1)+e13 

P(0, 1)=f1(0)+e14 

P(1, 1)=f1(1)+e15 

P(2, 1)=f1(2)+e16 

P(−1, 2)=f1(−1)+e17 

P(0, 2)=f1(0)+e18 

P(1, 2)=f1(1)+e19 

P(2, 2)=f1(2)+e20  (41)

Expression (41) is made up of 20 equations, so in the event that the number of the features wi of the approximation function f1 (x) is less than 20, i.e., in the event that the approximation function f1 (x) is a polynomial having the number of dimensions less than 19, the features wi can be calculated using the least square method, for example. Note that the specific solution of the least square method will be described later.
For example, if we say that the number of dimensions of the approximation function f1 (x) is five, the approximation function f1 (x) calculated with the least square method using Expression (41) (the approximation function f1 (x) generated by the calculated features wi) becomes a curve shown in FIG. 66.
Note that in FIG. 66, the vertical axis represents pixel values, and the horizontal axis represents a relative position x from the pixel of interest.
That is to say, for example, if we supplement the respective 20 pixel values P (x, y) (the respective input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) shown in FIG. 65) making up the fine-line-including data region 2302 in FIG. 64 along the x axis without any modification (if we regard a relative position y in the Y direction as constant, and overlay the five graphs shown in FIG. 65), multiple lines (dashed line, broken triple-dashed line, solid line, broken line, and broken double-dashed line) in parallel with the x axis, such as shown in FIG. 66, are distributed.
However, in FIG. 66, the dashed line represents the input pixel value P (x, −2), the broken triple-dashed line represents the input pixel value P (x, −1), the solid line represents the input pixel value P (x, 0), the broken line represents the input pixel value P (x, 1), and the broken double-dashed line represents the input pixel value P (x, 2) respectively. Also, in the event of the same pixel value, lines more than 2 lines are overlaid in reality, but in FIG. 66, the lines are drawn so as to distinguish each line, and so as not to overlay each line.
The respective 20 input pixel values (P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2)) thus distributed, and a regression curve (the approximation function f1 (x) obtained by substituting the features wi calculated with the least square method for the above Expression (38)) so as to minimize the error of the value f1 (x) become a curve (approximation function f1 (x)) shown in FIG. 66.
Thus, the approximation function f1 (x) represents nothing but a curve connecting in the X direction the means of the pixel values (pixel values having the same relative position x in the X direction from the pixel of interest) P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) in the Y direction. That is to say, the approximation function f1 (x) is generated without considering continuity in the spatial direction included in the light signal.
For example, in this case, the fine-line-including actual world region 2301 (FIG. 62) is regarded as a subject to be approximated. This fine-line-including actual world region 2301 has continuity in the spatial direction, which is represented with a gradient GF, such as shown in FIG. 67. Note that in FIG. 67, the X direction and Y direction represent the X direction and Y direction of the sensor 2 (FIG. 59).
Accordingly, the data continuity detecting unit 101 (FIG. 58) can output an angle θ (angle θ generated between the direction of data continuity represented with a gradient Gf corresponding to the gradient GF, and the X direction) such as shown in FIG. 67 as data continuity information corresponding to the gradient GF as continuity in the spatial direction.
However, with the first method, the data continuity information output from the data continuity detecting unit 101 is not employed at all.
In other words, such as shown in FIG. 67, the direction of continuity in the spatial direction of the fine-line-including actual world region 2301 is a general angle θ direction. However, the first method is a method for calculating the features wi of the approximation function f1 (x) on assumption that the direction of continuity in the spatial direction of the fine-line-including actual world region 2301 is the Y direction (i.e., on assumption that the angle θ is 90°).
Consequently, the approximation function f1 (x) becomes a function of which the waveform gets dull, and the detail decreases than the original pixel value. In other words, though not shown in the drawing, with the approximation function f1 (x) generated with the first method, the waveform thereof becomes a waveform different from the actual X cross-sectional waveform F(x).
To this end, the present applicant has invented the second method for calculating the features wi by further taking continuity in the spatial direction into consideration (utilizing the angle θ) as to the first method.
That is to say, the second method is a method for calculating the features wi of the approximation function f2 (x) on assumption that the direction of continuity of the fine-line-including actual world region 2301 is a general angle θ direction.
Specifically, for example, the gradient Gf representing continuity of data corresponding to continuity in the spatial direction is represented with the following Expression (42).




  
    
      
        
          G
          f
        
        =
        
          
            tan
            ⁢
            
              
            
            ⁢
            θ
          
          =
          
            
              d
              y
            
            
              d
              x
            
          
        
      
    
    
      
        (
        42
        )
      
    
  




Note that in Expression (42), dx represents the amount of fine movement in the X direction such as shown in FIG. 67, dy represents the amount of fine movement in the Y direction as to the dx such as shown in FIG. 67.
In this case, if we define the shift amount Cx (y) as shown in the following Expression (43), with the second method, an equation corresponding to Expression (40) employed in the first method becomes such as the following Expression (44).




  
    
      
        
          
            C
            x
          
          ⁡
          
            (
            y
            )
          
        
        =
        
          y
          
            G
            f
          
        
      
    
    
      
        (
        43
        )
      
    
  
  
    
      
        
          P
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            
              f
              2
            
            ⁡
            
              (
              
                x
                -
                
                  
                    C
                    x
                  
                  ⁡
                  
                    (
                    y
                    )
                  
                
              
              )
            
          
          +
          e
        
      
    
    
      
        (
        44
        )
      
    
  




That is to say, Expression (40) employed in the first method represents that the position x in the X direction of the pixel center position (x, y) is the same value regarding the pixel value P (x, y) of any pixel positioned in the same position. In other words, Expression (40) represents that pixels having the same pixel value continue in the Y direction (exhibits continuity in the Y direction).
On the other hand, Expression (44) employed in the second method represents that the pixel value P (x, y) of a pixel of which the center position is (x, y) is not identical to the pixel value (approximate equivalent to f2 (x)) of a pixel positioned in a place distant from the pixel of interest (a pixel of which the center position is the origin (0, 0)) in the X direction by x, and is the same value as the pixel value (approximate equivalent to f2 (x+Cx (y)) of a pixel positioned in a place further distant from the pixel thereof in the X direction by the shift amount Cx (y) (pixel positioned in a place distant from the pixel of interest in the X direction by x+Cx (y)). In other words, Expression (44) represents that pixels having the same pixel value continue in the angle θ direction corresponding to the shift amount Cx (y) (exhibits continuity in the general angle θ direction).
Thus, the shift amount Cx (y) is the amount of correction considering continuity (in this case, continuity represented with the gradient GF in FIG. 67 (strictly speaking, continuity of data represented with the gradient Gf)) in the spatial direction, and Expression (44) is obtained by correcting Expression (40) with the shift amount Cx(y).
In this case, upon the 20 pixel values P (x, y) (however, x is any one integer value of −1 through 2, and y is any one integer value of −2 through 2) of the fine-line-including data region 2302 shown in FIG. 64 being substituted for the above Expression (44) respectively, 20 equations as shown in the following Expression (45) are generated.

P(−1, −2)=f2(−1−Cx(−2))+e1 

P(0, −2)=f2(0−Cx(−2))+e2 

P(1, −2)=f2(1−Cx(−2))+e3 

P(2, −2)=f2(2−Cx(−2))+e4 

P(−1, −1)=f2(−1−Cx(−1))+e5 

P(0, −1)=f2(0−Cx(−1))+e6 

P(1, −1)=f2(1−Cx(−1))+e7 

P(2, −1)=f2(2−Cx(−1))+e8 

P(−1, 0)=f2(−1)+e9 

P(0, 0)=f2(0)+e10 

P(1, 0)=f2(1)+e11 

P(2, 0)=f2(2)+e12 

P(−1, 1)=f2(−1−Cx(1))+e13 

P(0, 1)=f2(0−Cx(1))+e14 

P(1, 1)=f2(1−Cx(1))+e15 

P(2, 1)=f2(2−Cx(1))+e16 

P(−1, 2)=f2(−1−Cx(2))+e17 

P(0, 2)=f2(0−Cx(2))+e18 

P(1, 2)=f2(1−Cx(2))+e19 

P(2, 2)=f2(2−Cx(2))+e20  (45)

Expression (45) is made up of 20 equations, as with the above Expression (41). Accordingly, with the second method, as with the first method, in the event that the number of the features wi of the approximation function f2 (x) is less than 20, i.e., the approximation function f2 (x) is a polynomial having the number of dimensions less than 19, the features wi can be calculated with the least square method, for example. Note that the specific solution regarding the least square method will be described later.
For example, if we say that the number of dimensions of the approximation function f2 (x) is five as with the first method, with the second method, the features wi are calculated as follows.
That is to say, FIG. 68 represents the pixel value P (x, y) shown in the left side of Expression (45) in a graphic manner. The respective five graphs shown in FIG. 68 are basically the same as shown in FIG. 65.
As shown in FIG. 68, the maximal pixel values (pixel values corresponding to fine lines) are continuous in the direction of continuity of data represented with the gradient Gf.
Consequently, with the second method, if we supplement the respective input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) shown in FIG. 68, for example, along the x axis, we supplement the pixel values after the pixel values are changed in the states shown in FIG. 69 instead of supplementing the pixel values without any modification as with the first method (let us assume that y is constant, and the five graphs are overlaid in the states shown in FIG. 68).
That is to say, FIG. 69 represents a state wherein the respective input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) shown in FIG. 68 are shifted by the shift amount Cx (y) shown in the above Expression (43). In other words, FIG. 69 represents a state wherein the five graphs shown in FIG. 68 are moved as if the gradient GF representing the actual direction of continuity of data were regarded as a gradient GF′ (in the drawing, a straight line made up of a dashed line were regarded as a straight line made up of a solid line).
In the states in FIG. 69, if we supplement the respective input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2), for example, along the x axis (in the states shown in FIG. 69, if we overlay the five graphs), multiple lines (dashed line, broken triple-dashed line, solid line, broken line, and broken double-dashed line) in parallel with the x axis, such as shown in FIG. 70, are distributed.
Note that in FIG. 70, the vertical axis represents pixel values, and the horizontal axis represents a relative position x from the pixel of interest. Also, the dashed line represents the input pixel value P (x, −2), the broken triple-dashed line represents the input pixel value P (x, −1), the solid line represents the input pixel value P (x, 0), the broken line represents the input pixel value P (x, 1), and the broken double-dashed line represents the input pixel value P (x, 2) respectively. Further, in the event of the same pixel value, lines more than 2 lines are overlaid in reality, but in FIG. 70, the lines are drawn so as to distinguish each line, and so as not to overlay each line.
The respective 20 input pixel values P (x, y) (however, x is any one integer value of −1 through 2, and y is any one integer value of −2 through 2) thus distributed, and a regression curve (the approximation function f2 (x) obtained by substituting the features wi calculated with the least square method for the above Expression (38)) to minimize the error of the value f2 (x+Cx(y)) become a curve f2 (x) shown in the solid line in FIG. 70.
Thus, the approximation function f2 (x) generated with the second method represents a curve connecting in the X direction the means of the input pixel values P (x, y) in the angle θ direction (i.e., direction of continuity in the general spatial direction) output from the data continuity detecting unit 101 (FIG. 58).
On the other hand, as described above, the approximation function f1 (x) generated with the first method represents nothing but a curve connecting in the X direction the means of the input pixel values P (x, y) in the Y direction (i.e., the direction different from the continuity in the spatial direction).
Accordingly, as shown in FIG. 70, the approximation function f2 (x) generated with the second method becomes a function wherein the degree of dullness of the waveform thereof decreases, and also the degree of decrease of the detail as to the original pixel value decreases less than the approximation function f1 (x) generated with the first method. In other words, though not shown in the drawing, with the approximation function f2 (x) generated with the second method, the waveform thereof becomes a waveform closer to the actual X cross-sectional waveform F(x) than the approximation function f1 (x) generated with the first method.
However, as described above, the approximation function f2 (x) is a function considering continuity in the spatial direction, but is nothing but a function generated wherein the input image (input pixel value) is regarded as the origin (basis). That is to say, as shown in FIG. 63 described above, the approximation function f2 (x) is nothing but a function that approximated the input image different from the X cross-sectional waveform F(x), and it is hard to say that the approximation function f2 (x) is a function that approximated the X cross-sectional waveform F(x). In other words, the second method is a method for calculating the features wi on assumption that the above Expression (44) holds, but does not take the relation in Expression (38) described above into consideration (does not consider the integration effects of the sensor 2).
Consequently, the present applicant has invented the third method that calculates the features wi of the approximation function f3 (x) by further taking the integration effects of the sensor 2 into consideration as to the second method.
That is to say, the third method is a method that introduces the concept of a spatial mixture or time mixture. Now, considering both spatial mixture and time mixture will complicate the description, so only spatial mixture will be considered here of spatial mixture and time mixture, and time mixture will be ignored.
Description will be made regarding spatial mixture with reference to FIG. 71 prior to description of the third method.
In FIG. 71, a portion 2321 (hereafter, referred to as a region 2321) of a light signal in the actual world 1 represents a region having the same area as one detecting element (pixel) of the sensor 2.
Upon the sensor 2 detecting the region 2321, the sensor 2 outputs a value (one pixel value) 2322 obtained by the region 2321 being subjected to integration in the temporal and spatial directions (X direction, Y direction, and t direction). Note that the pixel value 2322 is represented as an image in the drawing, but is actually data representing a predetermined value.
The region 2321 in the actual world 1 is clearly classified into a light signal (white region in the drawing) corresponding to the foreground (the above fine line, for example), and a light signal (black region in the drawing) corresponding to the background.
On the other hand, the pixel value 2322 is a value obtained by the light signal in the actual world 1 corresponding to the foreground and the light signal in the actual world 1 corresponding to the background being subjected to integration. In other words, the pixel value 2322 is a value corresponding to a level wherein the light level corresponding to the foreground and the light level corresponding to the background are spatially mixed.
Thus, in the event that a portion corresponding to one pixel (detecting element of the sensor 2) of the light signals in the actual world 1 is not a portion where the light signals having the same level are spatially uniformly distributed, but a portion where the light signals having a different level such as a foreground and background are distributed, upon the region thereof being detected by the sensor 2, the region becomes one pixel value as if the different light levels were spatially mixed by the integration effects of the sensor 2 (integrated in the spatial direction). Thus, a region made up of pixels in which an image (light signals in the actual world 1) corresponding to a foreground, and an image (light signals in the actual world 1) corresponding to a background are subjected to spatial integration, that is, mixed as it were, which is spatial mixing, is referred to as a spatial mixed region here.
Accordingly, with the third method, the actual world estimating unit 102 (FIG. 58) estimates the X cross-sectional waveform F(x) representing the original region 2321 in the actual world 1 (of the light signals in the actual world 1, the portion 2321 corresponding to one pixel of the sensor 2) by approximating the X cross-sectional waveform F(x) with the approximation function f3 (x) serving as a one-dimensional polynomial such as shown in FIG. 72.
That is to say, FIG. 72 represents an example of the approximation function f3 (x) corresponding to the pixel value 2322 serving as a spatial mixed region (FIG. 71), i.e., the approximation function f3 (x) that approximates the X cross-sectional waveform F(x) corresponding to the solid line within the region 2331 in the actual world 1 (FIG. 71). In FIG. 72, the axis in the horizontal direction in the drawing represents an axis in parallel with the side from the upper left end xs to lower right end xe of the pixel corresponding to the pixel value 2322 (FIG. 71), which is taken as the x axis. The axis in the vertical direction in the drawing is taken as an axis representing pixel values.
In FIG. 72, the following Expression (46) is defined on condition that the result obtained by subjecting the approximation function f3 (x) to integration in a range (pixel width) from the xs to the xe is generally identical with the pixel values P (x, y) output from the sensor 2 (dependent on a margin of error e alone).




  
    
      
        
          
            
              P
              =
              
                
                  
                    ∫
                    
                      X
                      s
                    
                    
                      X
                      e
                    
                  
                  ⁢
                  
                    
                      
                        f
                        3
                      
                      ⁡
                      
                        (
                        x
                        )
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      d
                      x
                    
                  
                
                +
                e
              
            
          
        
        
          
            
              =
              
                
                  
                    ∫
                    
                      X
                      s
                    
                    
                      X
                      e
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          w
                          0
                        
                        +
                        
                          
                            w
                            1
                          
                          ⁢
                          x
                        
                        +
                        
                          
                            w
                            2
                          
                          ⁢
                          
                            x
                            2
                          
                        
                        +
                        ⋯
                        +
                        
                          
                            w
                            n
                          
                          ⁢
                          
                            x
                            n
                          
                        
                      
                      )
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      d
                      x
                    
                  
                
                +
                e
              
            
          
        
        
          
            
              =
              
                
                  
                    w
                    0
                  
                  ⁡
                  
                    (
                    
                      
                        x
                        e
                      
                      -
                      
                        x
                        s
                      
                    
                    )
                  
                
                +
                ⋯
                +
                
                  
                    w
                    
                      n
                      -
                      1
                    
                  
                  ⁢
                  
                    
                      
                        x
                        e
                        n
                      
                      -
                      
                        x
                        s
                        n
                      
                    
                    n
                  
                
                +
                
                  
                    w
                    n
                  
                  ⁢
                  
                    
                      
                        x
                        e
                        
                          n
                          +
                          1
                        
                      
                      -
                      
                        x
                        s
                        
                          n
                          +
                          1
                        
                      
                    
                    
                      n
                      +
                      1
                    
                  
                
                +
                e
              
            
          
        
      
    
    
      
        (
        46
        )
      
    
  




In this case, the features wi of the approximation function f3 (x) are calculated from the 20 pixel values P (x, y) (however, x is any one integer value of −1 through 2, and y is any one integer value of −2 through 2) of the fine-line-including data region 2302 shown in FIG. 67, so the pixel value P in Expression (46) becomes the pixel values P (x, y).
Also, as with the second method, it is necessary to take continuity in the spatial direction into consideration, and accordingly, each of the start position xs and end position xe in the integral range in Expression (46) is dependent upon the shift amount Cx (y). That is to say, each of the start position xs and end position xe of the integral range in Expression (46) is represented such as the following Expression (47).

xs=x−Cx(y)−0.5

xe=x−Cx(y)+0.5  (47)

In this case, upon each pixel value of the fine-line-including data region 2302 shown in FIG. 67, i.e., each of the input pixel values P (x, −2), P (x, −1), P (x, 0), P (x, 1), and P (x, 2) (however, x is any one integer value of −1 through 2) shown in FIG. 68 being substituted for the above Expression (46) (the integral range is the above Expression (47)), 20 equations shown in the following Expression (48) are generated.




  
    
      
        
          
            P
            ⁡
            
              (
              
                
                  -
                  1
                
                ,
                
                  -
                  2
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              1
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                ,
                
                  -
                  2
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              2
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                1
                ,
                
                  -
                  2
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              3
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                2
                ,
                
                  -
                  2
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        2
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              4
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                
                  -
                  1
                
                ,
                
                  -
                  1
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              5
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                ,
                
                  -
                  1
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              6
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                1
                ,
                
                  -
                  1
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              7
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                2
                ,
                
                  -
                  1
                
              
              )
            
          
          =
          
            
              
                ∫
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  -
                  0.5
                
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              8
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                
                  -
                  1
                
                ,
                0
              
              )
            
          
          =
          
            
              
                ∫
                
                  
                    -
                    1
                  
                  -
                  0.5
                
                
                  
                    -
                    1
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              9
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                ,
                0
              
              )
            
          
          =
          
            
              
                ∫
                
                  0
                  -
                  0.5
                
                
                  0
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              10
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                1
                ,
                0
              
              )
            
          
          =
          
            
              
                ∫
                
                  1
                  -
                  0.5
                
                
                  1
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              11
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                2
                ,
                0
              
              )
            
          
          =
          
            
              
                ∫
                
                  2
                  -
                  0.5
                
                
                  2
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              12
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                
                  -
                  1
                
                ,
                1
              
              )
            
          
          =
          
            
              
                ∫
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  -
                  0.5
                
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              13
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                ,
                1
              
              )
            
          
          =
          
            
              
                ∫
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  -
                  0.5
                
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              14
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                1
                ,
                1
              
              )
            
          
          =
          
            
              
                ∫
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  -
                  0.5
                
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁢
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              15
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                2
                ,
                1
              
              )
            
          
          =
          
            
              
                ∫
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  -
                  0.5
                
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      1
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              16
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                
                  -
                  1
                
                ,
                2
              
              )
            
          
          =
          
            
              
                ∫
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  -
                  0.5
                
                
                  
                    -
                    1
                  
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              17
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                ,
                2
              
              )
            
          
          =
          
            
              
                ∫
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  -
                  0.5
                
                
                  0
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              18
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                1
                ,
                2
              
              )
            
          
          =
          
            
              
                ∫
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  -
                  0.5
                
                
                  1
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              19
            
          
        
        ,
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                2
                ,
                2
              
              )
            
          
          =
          
            
              
                ∫
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  -
                  0.5
                
                
                  2
                  -
                  
                    
                      C
                      x
                    
                    ⁡
                    
                      (
                      2
                      )
                    
                  
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    f
                    3
                  
                  ⁢
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
              
            
            +
            
              e
              20
            
          
        
      
    
    
      
        (
        48
        )
      
    
  




Expression (48) is made up of 20 equations as with the above Expression (45). Accordingly, with the third method as with the second method, in the event that the number of the features wi of the approximation function f3 (x) is less than 20, i.e., in the event that the approximation function f3 (x) is a polynomial having the number of dimensions less than 19, for example, the features wi may be calculated with the least square method. Note that the specific solution of the least square method will be described later.
For example, if we say that the number of dimensions of the approximation function f3 (x) is five, the approximation function f3 (x) calculated with the least square method using Expression (48) (the approximation function f3 (x) generated with the calculated features wi) becomes a curve shown with the solid line in FIG. 73.
Note that in FIG. 73, the vertical axis represents pixel values, and the horizontal axis represents a relative position x from the pixel of interest.
As shown in FIG. 73, in the event that the approximation function f3 (x) (a curve shown with a solid line in the drawing) generated with the third method is compared with the approximation function f2 (x) (a curve shown with a dashed line in the drawing) generated with the second method, a pixel value at x=0 becomes great, and also the gradient of the curve creates a steep waveform. This is because details increase more than the input pixels, resulting in being unrelated to the resolution of the input pixels. That is to say, we can say that the approximation function f3 (x) approximates the X cross-sectional waveform F(x). Accordingly, though not shown in the drawing, the approximation function f3 (x) becomes a waveform closer to the X cross-sectional waveform F(x) than the approximation function f2 (x).
FIG. 74 represents an configuration example of the actual world estimating unit 102 employing such a one-dimensional approximating method.
In FIG. 74, the actual world estimating unit 102 estimates the X cross-sectional waveform F(x) by calculating the features wi using the above third method (least square method) for example, and generating the approximation function f(x) of the above Expression (39) using the calculated features wi.
As shown in FIG. 74, the actual world estimating unit 102 includes a conditions setting unit 2331, input image storage unit 2332, input pixel value acquiring unit 2333, integral component calculation unit 2334, normal equation generating unit 2335, and approximation function generating unit 2336.
The conditions setting unit 2331 sets a pixel range (hereafter, referred to as a tap range) used for estimating the X cross-sectional waveform F(x) corresponding to a pixel of interest, and the number of dimensions n of the approximation function f(x).
The input image storage unit 2332 temporarily stores an input image (pixel values) from the sensor 2.
The input pixel value acquiring unit 2333 acquires, of the input images stored in the input image storage unit 2332, an input image region corresponding to the tap range set by the conditions setting unit 2231, and supplies this to the normal equation generating unit 2335 as an input pixel value table. That is to say, the input pixel value table is a table in which the respective pixel values of pixels included in the input image region are described. Note that a specific example of the input pixel value table will be described later.
Now, the actual world estimating unit 102 calculates the features wi of the approximation function f(x) with the least square method using the above Expression (46) and Expression (47) here, but the above Expression (46) can be represented such as the following Expression (49).




  
    
      
        
          
            
              
                P
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              =
              
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    n
                  
                  ⁢
                  
                    
                      w
                      i
                    
                    ×
                    
                      
                        
                          
                            (
                            
                              x
                              -
                              
                                
                                  C
                                  x
                                
                                ⁡
                                
                                  (
                                  y
                                  )
                                
                              
                              +
                              0.5
                            
                            )
                          
                          
                            i
                            +
                            1
                          
                        
                        -
                        
                          
                            (
                            
                              x
                              -
                              
                                
                                  C
                                  x
                                
                                ⁡
                                
                                  (
                                  y
                                  )
                                
                              
                              -
                              0.5
                            
                            )
                          
                          
                            i
                            +
                            1
                          
                        
                      
                      
                        i
                        +
                        1
                      
                    
                  
                
                +
                e
              
            
          
        
        
          
            
              =
              
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    n
                  
                  ⁢
                  
                    
                      w
                      i
                    
                    ×
                    
                      
                        S
                        i
                      
                      ⁡
                      
                        (
                        
                          
                            x
                            s
                          
                          ,
                          
                            x
                            e
                          
                        
                        )
                      
                    
                  
                
                +
                e
              
            
          
        
      
    
    
      
        (
        49
        )
      
    
  




In Expression (49), Si (xs, xe) represents the integral components of the i-dimensional term. That is to say, the integral components Si (xs, xe) are shown in the following Expression (50).




  
    
      
        
          
            S
            i
          
          ⁡
          
            (
            
              
                x
                s
              
              ,
              
                x
                e
              
            
            )
          
        
        =
        
          
            
              x
              e
              
                i
                +
                1
              
            
            -
            
              x
              s
              
                i
                +
                1
              
            
          
          
            i
            +
            1
          
        
      
    
    
      
        (
        50
        )
      
    
  




The integral component calculation unit 2334 calculates the integral components Si (xs, xe).
Specifically, the integral components Si (xs, xe) (however, the value xs and value xe are values shown in the above Expression (46)) shown in Expression (50) may be calculated as long as the relative pixel positions (x, y), shift amount Cx (y), and i of the i-dimensional terms are known. Also, of these, the relative pixel positions (x, y) are determined by the pixel of interest and the tap range, the shift amount Cx(y) is determined by the angle θ (by the above Expression (41) and Expression (43)), and the range of i is determined by the number of dimensions n, respectively.
Accordingly, the integral component calculation unit 2334 calculates the integral components Si (xs, xe) based on the tap range and the number of dimensions set by the conditions setting unit 2331, and the angle θ of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated results to the normal equation generating unit 2335 as an integral component table.
The normal equation generating unit 2335 generates the above Expression (46), i.e., a normal equation in the case of obtaining the features wi of the right side of Expression (49) with the least square method using the input pixel value table supplied from the input pixel value acquiring unit 2333, and the integral component table supplied from the integral component calculation unit 2334, and supplies this to the approximation function generating unit 2336 as a normal equation table. Note that a specific example of a normal equation will be described later.
The approximation function generating unit 2336 calculates the respective features wi of the above Expression (49) (i.e., the respective coefficients wi of the approximation function f(x) serving as a one-dimensional polynomial) by solving a normal equation included in the normal equation table supplied from the normal equation generating unit 2335 using the matrix solution, and outputs these to the image generating unit 103.
Next, description will be made regarding the actual world estimating processing (processing in step S102 in FIG. 29) of the actual world estimating unit 102 (FIG. 74) which employs the one-dimensional approximating method with reference to the flowchart in FIG. 75.
For example, let us say that an input image, which is a one-frame input image output from the sensor 2, including the fine-line-including data region 2302 in FIG. 60 described above has been already stored in the input image storage unit 2332. Also, let us say that the data continuity detecting unit 101 has subjected, at the continuity detection processing in step S101 (FIG. 29), the fine-line-including data region 2302 to the processing thereof, and has already output the angle θ as data continuity information.
In this case, the conditions setting unit 2331 sets conditions (a tap range and the number of dimensions) in step S2301 in FIG. 75.
For example, let us say that a tap range 2351 shown in FIG. 76 is set, and 5 dimensions are set as the number of dimensions.
That is to say, FIG. 76 is a diagram for describing an example of a tap range. In FIG. 76, the X direction and Y direction are the X direction and Y direction of the sensor 2 (FIG. 59) respectively. Also, the tap range 2351 represents a pixel group made up of 20 pixels in total (20 squares in the drawing) of 4 pixels in the X direction, and also 5 pixels in the Y direction.
Further, as shown in FIG. 76, let us say that a pixel of interest is set at the second pixel from the left and also the third pixel from the bottom in the drawing, of the tap range 2351. Also, let us say that each pixel is denoted with a number l such as shown in FIG. 76 (l is any integer value of 0 through 19) according to the relative pixel positions (x, y) from the pixel of interest (a coordinate value of a pixel-of-interest coordinates system wherein the center (0, 0) of the pixel of interest is taken as the origin).
Now, description will return to FIG. 75, wherein in step S2302, the conditions setting unit 2331 sets a pixel of interest.
In step S2303, the input pixel value acquiring unit 2333 acquires an input pixel value based on the condition (tap range) set by the conditions setting unit 2331, and generates an input pixel value table. That is to say, in this case, the input pixel value acquiring unit 2333 acquires the fine-line-including data region 2302 (FIG. 64), and generates a table made up of 20 input pixel values P (l) as an input pixel value table.
Note that in this case, the relation between the input pixel values P (1) and the above input pixel values P (x, y) is a relation shown in the following Expression (51). However, in Expression (51), the left side represents the input pixel values P (1), and the right side represents the input pixel values P (x, y).

P(0)=P(0,0)

P(1)=P(−1,2)

P(2)=P(0,2)

P(3)=P(1,2)

P(4)=P(2, 2)

P(5)=P(−1,1)

P(6)=P(0,1)

P(7)=P(1,1)

P(8)=P(2,1)

P(9)=P(−1,0)

P(10)=P(1,0)

P(11)=P(2,0)

P(12)=P(−1, −1)

P(13)=P(0, −1)

P(14)=P(1, −1)

P(15)=P(2, −1)

P(16)=P(−1, −2)

P(17)=P(0, −2)

P(18)=P(1, −2)

P(19)=P(2, −2)  (51)

In step S2304, the integral component calculation unit 2334 calculates integral components based on the conditions (a tap range and the number of dimensions) set by the conditions setting unit 2331, and the data continuity information (angle θ) supplied from the data continuity detecting unit 101, and generates an integral component table.
In this case, as described above, the input pixel values are not P (x, y) but P (l), and are acquired as the value of a pixel number l, so the integral component calculation unit 2334 calculates the above integral components Si (xs, xe) in Expression (50) as a function of l such as the integral components Si (l) shown in the left side of the following Expression (52).

Si(l)=Si(xs,xe)  (52)

Specifically, in this case, the integral components Si (l) shown in the following Expression (53) are calculated.

Si(0)=Si(−0.5,0.5)

Si(1)=Si(−1.5−Cx(2), −0.5−Cx(2))

Si(2)=Si(−0.5−Cx(2), 0.5−Cx(2))

Si(3)=Si(0.5−Cx(2), 1.5−Cx(2))

Si(4)=Si(1.5−Cx(2), 2.5−Cx(2))

Si(5)=Si(−1.5−Cx(1), −0.5−Cx(1))

Si(6)=Si(−0.5−Cx(1), 0.5−Cx(1))

Si(7)=Si(0.5−Cx(1), 1.5−Cx(1))

Si(8)=Si(1.5−Cx(1), 2.5−Cx(1))

Si(9)=Si(−1.5, −0.5)

Si(10)=Si(0.5, 1.5)

Si(11)=Si(1.5, 2.5)

Si(12)=Si(−1.5−Cx(−1), −0.5−Cx(−1))

Si(13)=Si(−0.5−Cx(−1), 0.5−Cx(−1))

Si(14)=Si(0.5−Cx(−1), 1.5−Cx(−1))

Si(15)=Si(1.5−Cx(−1), 2.5−Cx(−1))

Si(16)=Si(−1.5−Cx(−2), −0.5−Cx(−2))

Si(17)=Si(−0.5−Cx(−2), 0.5−Cx(−2))

Si(18)=Si(0.5−Cx(−2), 1.5−Cx(−2))

Si(19)=Si(1.5−Cx(−2), 2.5−Cx(−2))  (53)

Note that in Expression (53), the left side represents the integral components Si (l), and the right side represents the integral components Si (xs, xe). That is to say, in this case, i is 0 through 5, and accordingly, the 120 Si (1) in total of the 20 S0 (l), 20 S1 (l), 20 S2 (l) 20 S3 (l), 20 S4 (l), and 20 S5 (l) are calculated.
More specifically, first the integral component calculation unit 2334 calculates each of the shift amounts Cx (−2), Cx (−1), Cx (1), and Cx (2) using the angle θ supplied from the data continuity detecting unit 101. Next, the integral component calculation unit 2334 calculates each of the 20 integral components Si (xs, xe) shown in the right side of Expression (52) regarding each of i=0 through 5 using the calculated shift amounts Cx(−2), Cx(−1), Cx(1) and Cx (2). That is to say, the 120 integral components Si (xs, xe) are calculated. Note that with this calculation of the integral components Si (xs, xe), the above Expression (50) is used. Subsequently, the integral component calculation unit 2334 converts each of the calculated 120 integral components Si (xs, xe) into the corresponding integral components Si(l) in accordance with Expression (53), and generates an integral component table including the converted 120 integral components Si (l).
Note that the sequence of the processing in step S2303 and the processing in step S2304 is not restricted to the example in FIG. 75, the processing in step S2304 may be executed first, or the processing in step S2303 and the processing in step S2304 may be executed simultaneously.
Next, in step S2305, the normal equation generating unit 2335 generates a normal equation table based on the input pixel value table generated by the input pixel value acquiring unit 2333 at the processing in step S2303, and the integral component table generated by the integral component calculation unit 2334 at the processing in step S2304.
Specifically, in this case, the features wi of the following Expression (54) corresponding to the above Expression (49) are calculated using the least square method. A normal equation corresponding to this is represented as the following Expression (55).




  
    
      
        
          P
          ⁡
          
            (
            l
            )
          
        
        =
        
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
                w
                i
              
              ×
              
                
                  S
                  i
                
                ⁡
                
                  (
                  l
                  )
                
              
            
          
          +
          e
        
      
    
    
      
        (
        54
        )
      
    
  
  
    
      
        
          
            (
            
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋰
                
                
                  ⋮
                
              
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    w
                    0
                  
                
              
              
                
                  
                    w
                    1
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    w
                    n
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        55
        )
      
    
  




Note that in Expression (55), L represents the maximum value of the pixel number l in the tap range. n represents the number of dimensions of the approximation function f(x) serving as a polynomial. Specifically, in this case, n=5, and L=19.
If we define each matrix of the normal equation shown in Expression (55) as the following Expressions (56) through (58), the normal equation is represented as the following Expression (59).




  
    
      
        
          S
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋰
              
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        56
        )
      
    
  
  
    
      
        
          W
          MAT
        
        =
        
          (
          
            
              
                
                  w
                  0
                
              
            
            
              
                
                  w
                  1
                
              
            
            
              
                ⋮
              
            
            
              
                
                  W
                  n
                
              
            
          
          )
        
      
    
    
      
        (
        57
        )
      
    
  
  
    
      
        
          P
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        58
        )
      
    
  
  
    
      
        
          
            S
            MAT
          
          ⁢
          
            W
            MAT
          
        
        =
        
          P
          MAT
        
      
    
    
      
        (
        59
        )
      
    
  




As shown in Expression (57), the respective components of the matrix WMAT are the features wi to be obtained. Accordingly, in Expression (59), if the matrix SMAT of the left side and the matrix PMAT of the right side are determined, the matrix WMAT (i.e., features wi) may be calculated with the matrix solution.
Specifically, as shown in Expression (56), the respective components of the matrix SMAT may be calculated as long as the above integral components Si (l) are known. The integral components Si (l) are included in the integral component table supplied from the integral component calculation unit 2334, so the normal equation generating unit 2335 can calculate each component of the matrix SMAT using the integral component table.
Also, as shown in Expression (58), the respective components of the matrix PMAT may be calculated as long as the integral components Si (l) and the input pixel values P (l) are known. The integral components Si (l) is the same as those included in the respective components of the matrix SMAT, also the input pixel values P (l) are included in the input pixel value table supplied from the input pixel value acquiring unit 2333, so the normal equation generating unit 2335 can calculate each component of the matrix PMAT using the integral component table and input pixel value table.
Thus, the normal equation generating unit 2335 calculates each component of the matrix SMAT and matrix PMAT, and outputs the calculated results (each component of the matrix SMAT and matrix PMAT) to the approximation function generating unit 2336 as a normal equation table.
Upon the normal equation table being output from the normal equation generating unit 2335, in step S2306, the approximation function generating unit 2336 calculates the features wi (i.e., the coefficients wi of the approximation function f(x) serving as a one-dimensional polynomial) serving as the respective components of the matrix WMAT in the above Expression (59) based on the normal equation table.
Specifically, the normal equation in the above Expression (59) can be transformed as the following Expression (60).




  
    
      
        
          W
          MAT
        
        =
        
          
            S
            MAT
            
              -
              1
            
          
          ⁢
          
            P
            MAT
          
        
      
    
    
      
        (
        60
        )
      
    
  




In Expression (60), the respective components of the matrix WMAT in the left side are the features wi to be obtained. The respective components regarding the matrix SMAT and matrix PMAT are included in the normal equation table supplied from the normal equation generating unit 2335. Accordingly, the approximation function generating unit 2336 calculates the matrix WMAT by calculating the matrix in the right side of Expression (60) using the normal equation table, and outputs the calculated results (features wi) to the image generating unit 103.
In step S2307, the approximation function generating unit 2336 determines regarding whether or not the processing of all the pixels has been completed.
In step S2307, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S2302, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S2302 through S2307 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S2307, in the event that determination is made that the processing of all the pixels has been completed), the estimating processing of the actual world 1 ends.
Note that the waveform of the approximation function f(x) generated with the coefficients (features) wi thus calculated becomes a waveform such as the approximation function f3(x) in FIG. 73 described above.
Thus, with the one-dimensional approximating method, the features of the approximation function f(x) serving as a one-dimensional polynomial are calculated under the assumption, for example, that a waveform having the same form as the one-dimensional X cross-sectional waveform F(x) is continuous in the direction of continuity. Accordingly, with the one-dimensional approximating method, the features of the approximation function f(x) can be calculated with less amount of calculation processing than other function approximating methods.
Next, description will be made regarding the second function approximating method with reference to FIG. 77 through FIG. 83.
That is to say, the second function approximating method is a method wherein the light signal in the actual world 1 having continuity in the spatial direction represented with the gradient GF such as shown in FIG. 77 for example is regarded as a waveform F(x, y) on the X-Y plane (on the plane level in the X direction serving as one direction of the spatial directions, and in the Y direction orthogonal to the X direction), and the waveform F(x, y) is approximated with the approximation function f(x, y) serving as a two-dimensional polynomial, thereby estimating the waveform F(x, y). Accordingly, hereafter, the second function approximating method is referred to as a two-dimensional polynomial approximating method.
Note that in FIG. 77, the horizontal direction represents the X direction serving as one direction of the spatial directions, the upper right direction represents the Y direction serving as the other direction of the spatial directions, and the vertical direction represents the level of light respectively. GF represents the gradient as continuity in the spatial direction.
Also, with description of the two-dimensional polynomial approximating method, let us say that the sensor 2 is a CCD made up of the multiple detecting elements 2-1 disposed on the plane thereof, such as shown in FIG. 78.
With the example in FIG. 78, the direction in parallel with a predetermined side of the detecting elements 2-1 is taken as the X direction serving as one direction of the spatial directions, and the direction orthogonal to the X direction is taken as the Y direction serving as the other direction of the spatial directions. The direction orthogonal to the X-Y plane is taken as the t direction serving as the temporal direction.
Also, with the example in FIG. 78, the spatial shape of the respective detecting elements 2-1 of the sensor 2 is taken as a square of which one side is 1 in length. The shutter time (exposure time) of the sensor 2 is taken as 1.
Further, with the example in FIG. 78, the center of one certain detecting element 2-1 of the sensor 2 is taken as the origin (the position in the X direction is x=0, and the position in the Y direction is y=0) in the spatial directions (X direction and Y direction), and also the intermediate point-in-time of the exposure time is taken as the origin (the position in the t direction is t=0) in the temporal direction (t direction).
In this case, the detecting element 2-1 of which the center is in the origin (x=0, y=0) in the spatial directions subjects the light signal function F(x, y, t) to integration with a range of −0.5 through 0.5 in the X direction, with a range of −0.5 through 0.5 in the Y direction, and with a range of −0.5 through 0.5 in the t direction, and outputs the integral value as the pixel value P.
That is to say, the pixel value P output from the detecting element 2-1 of which the center is in the origin in the spatial directions is represented with the following Expression (61).




  
    
      
        P
        =
        
          
            ∫
            
              -
              0.5
            
            
              +
              0.5
            
          
          ⁢
          
            
              ∫
              
                -
                0.5
              
              
                +
                0.5
              
            
            ⁢
            
              
                ∫
                
                  -
                  0.5
                
                
                  +
                  0.5
                
              
              ⁢
              
                
                  F
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                      ,
                      t
                    
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  y
                
                ⁢
                
                  
                
                ⁢
                
                  d
                  t
                
              
            
          
        
      
    
    
      
        (
        61
        )
      
    
  




Similarly, the other detecting elements 2-1 output the pixel value P shown in Expression (61) by taking the center of the detecting element 2-1 to be processed as the origin in the spatial directions.
Incidentally, as described above, the two-dimensional polynomial approximating method is a method wherein the light signal in the actual world 1 is handled as a waveform F(x, y) such as shown in FIG. 77 for example, and the two-dimensional waveform F(x, y) is approximated with the approximation function f(x, y) serving as a two-dimensional polynomial.
First, description will be made regarding a method representing such the approximation function f(x, y) with a two-dimensional polynomial.
As described above, the light signal in the actual world 1 is represented with the light signal function F(x, y, t) of which variables are the position on the three-dimensional space x, y, and z, and point-in-time t. This light signal function F(x, y, t), i.e., a one-dimensional waveform projected in the X direction at an arbitrary position y in the Y direction is referred to as an X cross-sectional waveform F(x), here.
When paying attention to this X cross-sectional waveform F(x), in the event that the signal in the actual world 1 has continuity in a certain direction in the spatial directions, it can be conceived that a waveform having the same form as the X cross-sectional waveform F(x) continues in the continuity direction. For example, with the example in FIG. 77, a waveform having the same form as the X cross-sectional waveform F(x) continues in the direction of the gradient GF. In other words, it can be said that the waveform F(x, y) is formed by a waveform having the same form as the X cross-sectional waveform F(x) continuing in the direction of the gradient GF.
Accordingly, the approximation function f(x, y) can be represented with a two-dimensional polynomial by considering that the waveform of the approximation function f(x, y) approximating the waveform F(x, y) is formed by a waveform having the same form as the approximation function f(x) approximating the X cross-sectional F (x) continuing.
Description will be made in more detail regarding the representing method of the approximation function f(x, y).
For example, let us say that the light signal in the actual world 1 such as shown in FIG. 77 described above, i.e., a light signal having continuity in the spatial direction represented with the gradient GF is detected by the sensor 2 (FIG. 78), and output as an input image (pixel value).
Further, let us say that as shown in FIG. 79, the data continuity detecting unit 101 (FIG. 3) subjects an input image region 2401 made up of 20 pixels (in the drawing, 20 squares represented with dashed line) in total of 4 pixels in the X direction and also 5 pixels in the Y direction, of this input image, to the processing thereof, and outputs an angle θ (angle θ generated between the direction of data continuity represented with the gradient Gf corresponding to the gradient GF, and the X direction) as one of the data continuity information.
Note that with the input image region 2401, the horizontal direction in the drawing represents the X direction serving as one direction in the spatial directions, and the vertical direction in the drawing represents the Y direction serving as the other direction of the spatial directions.
Also, in FIG. 79, an (x, y) coordinates system is set such that a pixel in the second pixel from the left, and also the third pixel from the bottom is taken as a pixel of interest, and the center of the pixel of interest is taken as the origin (0, 0). A relative distance (hereafter, referred to as a cross-sectional direction distance) in the X direction as to the straight line (straight line having the gradient Gf representing the direction of data continuity) having an angle θ passing through the origin (0, 0) is described as x′.
Further, in FIG. 79, the graph on the right side is a function wherein an X cross-sectional waveform F(x′) is approximated, which represents an approximation function f(x′) serving as an n-dimensional (n is an arbitrary integer) polynomial. Of the axes in the graph on the right side, the axis in the horizontal direction in the drawing represents a cross-sectional direction distance, and the axis in the vertical direction in the drawing represents pixel values.
In this case, the approximation function f(x′) shown in FIG. 79 is an n-dimensional polynomial, so is represented as the following Expression (62).




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ′
            
            )
          
        
        =
        
          
            
              w
              0
            
            +
            
              
                w
                1
              
              ⁢
              
                x
                ′
              
            
            +
            
              
                w
                2
              
              ⁢
              
                x
                ′
              
            
            +
            ⋯
            +
            
              
                w
                n
              
              ⁢
              
                x
                
                  ′
                  ⁢
                  
                    
                  
                  ⁢
                  n
                
              
            
          
          =
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                x
                
                  ′
                  ⁢
                  
                    
                  
                  ⁢
                  i
                
              
            
          
        
      
    
    
      
        (
        62
        )
      
    
  




Also, since the angle θ is determined, the straight line having angle θ passing through the origin (0, 0) is uniquely determined, and a position x1 in the X direction of the straight line at an arbitrary position y in the Y direction is represented as the following Expression (63). However, in Expression (63), s represents cot θ(=1 ̃□□□θ).

xl=s×y  (63)

That is to say, as shown in FIG. 79, a point on the straight line corresponding to continuity of data represented with the gradient Gf is represented with a coordinate value (x1, y).
The cross-sectional direction distance x′ is represented as the following Expression (64) using Expression (63).

x′=x−xl=x−s×y  (64)

Accordingly, the approximation function f(x, y) at an arbitrary position (x, y) within the input image region 2401 is represented as the following Expression (65) using Expression (62) and Expression (64).




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
              
                w
                i
              
              ⁡
              
                (
                
                  x
                  -
                  
                    s
                    ×
                    y
                  
                
                )
              
            
            i
          
        
      
    
    
      
        (
        65
        )
      
    
  




Note that in Expression (65), wi represents coefficients of the approximation function f(x, y). Note that the coefficients wi of the approximation function f including the approximation function f(x, y) can be evaluated as the features of the approximation function f. Accordingly, the coefficients wi of the approximation function f are also referred to as the features wi of the approximation function f.
Thus, the approximation function f(x, y) having a two-dimensional waveform can be represented as the polynomial of Expression (65) as long as the angle θ is known.
Accordingly, if the actual world estimating unit 102 can calculate the features wi of Expression (65), the actual world estimating unit 102 can estimate the waveform F(x, y) such as shown in FIG. 77.
Consequently, hereafter, description will be made regarding a method for calculating the features wi of Expression (65).
That is to say, upon the approximation function f(x, y) represented with Expression (65) being subjected to integration with an integral range (integral range in the spatial direction) corresponding to a pixel (the detecting element 2-1 of the sensor 2 (FIG. 78)), the integral value becomes the estimated value regarding the pixel value of the pixel. It is the following Expression (66) that this is represented with an equation. Note that with the two-dimensional polynomial approximating method, the temporal direction t is regarded as a constant value, so Expression (66) is taken as an equation of which variables are the positions x and y in the spatial directions (X direction and Y direction).




  
    
      
        
          P
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            
              ∫
              
                y
                -
                0.5
              
              
                y
                +
                0.5
              
            
            ⁢
            
              
                ∫
                
                  x
                  -
                  0.5
                
                
                  x
                  +
                  0.5
                
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  n
                
                ⁢
                
                  
                    
                      w
                      i
                    
                    ⁡
                    
                      (
                      
                        x
                        -
                        
                          s
                          ×
                          y
                        
                      
                      )
                    
                  
                  i
                
              
            
          
          +
          e
        
      
    
    
      
        (
        66
        )
      
    
  




In Expression (66), P (x, y) represents the pixel value of a pixel of which the center position is in a position (x, y) (relative position (x, y) from the pixel of interest) of an input image from the sensor 2. Also, e represents a margin of error.
Thus, with the two-dimensional polynomial approximating method, the relation between the input pixel value P (x, y) and the approximation function f(x, y) serving as a two-dimensional polynomial can be represented with Expression (66), and accordingly, the actual world estimating unit 102 can estimate the two-dimensional function F(x, y) (waveform F(x, y) wherein the light signal in the actual world 1 having continuity in the spatial direction represented with the gradient GF (FIG. 77) is represented focusing attention on the spatial direction) by calculating the features wi with, for example, the least square method or the like using Expression (66) (by generating the approximation function f(x, y) by substituting the calculated features wi for Expression (64)).
FIG. 80 represents a configuration example of the actual world estimating unit 102 employing such a two-dimensional polynomial approximating method.
As shown in FIG. 80, the actual world estimating unit 102 includes a conditions setting unit 2421, input image storage unit 2422, input pixel value acquiring unit 2423, integral component calculation unit 2424, normal equation generating unit 2425, and approximation function generating unit 2426.
The conditions setting unit 2421 sets a pixel range (tap range) used for estimating the function F(x, y) corresponding to a pixel of interest, and the number of dimensions n of the approximation function f(x, y).
The input image storage unit 2422 temporarily stores an input image (pixel values) from the sensor 2.
The input pixel value acquiring unit 2423 acquires, of the input images stored in the input image storage unit 2422, an input image region corresponding to the tap range set by the conditions setting unit 2421, and supplies this to the normal equation generating unit 2425 as an input pixel value table. That is to say, the input pixel value table is a table in which the respective pixel values of pixels included in the input image region are described. Note that a specific example of the input pixel value table will be described later.
Incidentally, as described above, the actual world estimating unit 102 employing the two-dimensional approximating method calculates the features wi of the approximation function f(x, y) represented with the above Expression (65) by solving the above Expression (66) using the least square method.
Expression (66) can be represented as the following Expression (71) by using the following Expression (70) obtained by the following Expressions (67) through (69).




  
    
      
        
          ∫
          
            
              x
              i
            
            ⁢
            
              d
              x
            
          
        
        =
        
          
            x
            
              i
              +
              1
            
          
          
            i
            +
            1
          
        
      
    
    
      
        (
        67
        )
      
    
  
  
    
      
        
          ∫
          
            
              
                (
                
                  x
                  -
                  
                    s
                    ×
                    y
                  
                
                )
              
              i
            
            ⁢
            
              d
              x
            
          
        
        =
        
          
            
              (
              
                x
                -
                
                  s
                  ×
                  y
                
              
              )
            
            
              i
              +
              1
            
          
          
            (
            
              i
              +
              1
            
            )
          
        
      
    
    
      
        (
        68
        )
      
    
  
  
    
      
        
          ∫
          
            
              
                (
                
                  x
                  -
                  
                    s
                    ×
                    y
                  
                
                )
              
              i
            
            ⁢
            
              d
              y
            
          
        
        =
        
          
            
              (
              
                x
                -
                
                  s
                  ×
                  y
                
              
              )
            
            
              i
              +
              1
            
          
          
            s
            ⁡
            
              (
              
                i
                +
                1
              
              )
            
          
        
      
    
    
      
        (
        69
        )
      
    
  
  
    
      
        
          
            ∫
            
              y
              -
              0.5
            
            
              y
              +
              0.5
            
          
          ⁢
          
            
              ∫
              
                x
                -
                0.5
              
              
                x
                +
                0.5
              
            
            ⁢
            
              
                
                  (
                  
                    x
                    -
                    
                      s
                      ×
                      y
                    
                  
                  )
                
                i
              
              ⁢
              
                d
                x
              
              ⁢
              
                d
                y
              
            
          
        
        =
        
          
            
              ∫
              
                y
                -
                0.5
              
              
                y
                +
                0.5
              
            
            ⁢
            
              
                
                  [
                  
                    
                      
                        (
                        
                          x
                          -
                          
                            s
                            ×
                            y
                          
                        
                        )
                      
                      
                        i
                        +
                        1
                      
                    
                    
                      (
                      
                        i
                        +
                        1
                      
                      )
                    
                  
                  ]
                
                
                  x
                  -
                  0.5
                
                
                  x
                  +
                  0.5
                
              
              ⁢
              
                d
                y
              
            
          
          ⁢
          
            
          
          =
          
            
              
                ∫
                
                  y
                  -
                  0.5
                
                
                  y
                  +
                  0.5
                
              
              ⁢
              
                
                  
                    
                      
                        (
                        
                          x
                          +
                          0.5
                          -
                          
                            s
                            ×
                            y
                          
                        
                        )
                      
                      
                        i
                        +
                        1
                      
                    
                    -
                    
                      
                        (
                        
                          x
                          -
                          0.5
                          -
                          
                            s
                            ×
                            y
                          
                        
                        )
                      
                      
                        i
                        +
                        1
                      
                    
                  
                  
                    i
                    +
                    1
                  
                
                ⁢
                
                  d
                  y
                
              
            
            =
            
              
                
                  
                    [
                    
                      
                        
                          (
                          
                            x
                            +
                            0.5
                            -
                            
                              s
                              ×
                              y
                            
                          
                          )
                        
                        
                          i
                          +
                          2
                        
                      
                      
                        
                          s
                          ⁡
                          
                            (
                            
                              i
                              +
                              1
                            
                            )
                          
                        
                        ⁢
                        
                          (
                          
                            i
                            +
                            2
                          
                          )
                        
                      
                    
                    ]
                  
                  
                    y
                    -
                    0.5
                  
                  
                    y
                    +
                    0.5
                  
                
                -
                
                  
                    [
                    
                      
                        
                          (
                          
                            x
                            -
                            0.5
                            -
                            
                              s
                              ×
                              y
                            
                          
                          )
                        
                        
                          i
                          +
                          2
                        
                      
                      
                        
                          s
                          ⁡
                          
                            (
                            
                              i
                              +
                              1
                            
                            )
                          
                        
                        ⁢
                        
                          (
                          
                            i
                            +
                            2
                          
                          )
                        
                      
                    
                    ]
                  
                  
                    y
                    -
                    0.5
                  
                  
                    y
                    +
                    0.5
                  
                
              
              =
              
                
                  
                    
                      
                        
                          
                            (
                            
                              x
                              +
                              0.5
                              -
                              
                                s
                                ×
                                y
                              
                              +
                              
                                0.5
                                ⁢
                                
                                  
                                
                                ⁢
                                s
                              
                            
                            )
                          
                          
                            i
                            +
                            2
                          
                        
                        -
                        
                          
                            (
                            
                              x
                              +
                              0.5
                              -
                              
                                s
                                ×
                                y
                              
                              -
                              
                                0.5
                                ⁢
                                s
                              
                            
                            )
                          
                          
                            i
                            +
                            2
                          
                        
                        -
                      
                    
                  
                  
                    
                      
                        
                          
                            (
                            
                              x
                              -
                              0.5
                              -
                              
                                s
                                ×
                                y
                              
                              +
                              
                                0.5
                                ⁢
                                s
                              
                            
                            )
                          
                          
                            i
                            +
                            2
                          
                        
                        +
                        
                          
                            (
                            
                              x
                              -
                              0.5
                              -
                              
                                s
                                ×
                                y
                              
                              -
                              
                                0.5
                                ⁢
                                s
                              
                            
                            )
                          
                          
                            i
                            +
                            2
                          
                        
                      
                    
                  
                
                
                  
                    s
                    ⁡
                    
                      (
                      
                        i
                        +
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    (
                    
                      i
                      +
                      2
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        (
        70
        )
      
    
  
  
    
      
        
          
            
              
                P
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  n
                
                ⁢
                
                  
                    
                      w
                      i
                    
                    
                      
                        s
                        ⁡
                        
                          (
                          
                            i
                            +
                            1
                          
                          )
                        
                      
                      ⁢
                      
                        (
                        
                          i
                          +
                          2
                        
                        )
                      
                    
                  
                  ⁢
                  
                    {
                    
                      
                        
                          (
                          
                            x
                            +
                            0.5
                            -
                            
                              s
                              ×
                              y
                            
                            +
                            
                              0.5
                              ⁢
                              s
                            
                          
                          )
                        
                        
                          i
                          +
                          2
                        
                      
                      -
                    
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    (
                    
                      x
                      +
                      0.5
                      -
                      
                        s
                        ×
                        y
                      
                      -
                      
                        0.5
                        ⁢
                        s
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                -
                
                  
                    (
                    
                      x
                      -
                      0.5
                      -
                      
                        s
                        ×
                        y
                      
                      +
                      
                        0.5
                        ⁢
                        s
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                +
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    (
                    
                      x
                      -
                      0.5
                      -
                      
                        s
                        ×
                        y
                      
                      -
                      
                        0.5
                        ⁢
                        s
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                }
              
              +
              e
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    n
                  
                  ⁢
                  
                    
                      w
                      i
                    
                    ⁢
                    
                      
                        s
                        i
                      
                      ⁡
                      
                        (
                        
                          
                            x
                            -
                            0.5
                          
                          ,
                          
                            x
                            +
                            0.5
                          
                          ,
                          
                            y
                            -
                            0.5
                          
                          ,
                          
                            y
                            +
                            0.5
                          
                        
                        )
                      
                    
                  
                
                +
                e
              
            
          
        
      
    
    
      
        (
        71
        )
      
    
  




In Expression (71), Si (x−0.5, x+0.5, y−0.5, y+0.5) represents the integral components of i-dimensional terms. That is to say, the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) are as shown in the following Expression (72).




  
    
      
        
          
            s
            i
          
          ⁡
          
            (
            
              
                x
                -
                0.5
              
              ,
              
                x
                +
                0.5
              
              ,
              
                y
                -
                0.5
              
              ,
              
                y
                +
                0.5
              
            
            )
          
        
        =
        
          
            
              
                
                  
                    
                      (
                      
                        x
                        +
                        0.5
                        -
                        
                          s
                          ×
                          y
                        
                        +
                        
                          0.5
                          ⁢
                          
                            
                          
                          ⁢
                          s
                        
                      
                      )
                    
                    
                      i
                      +
                      2
                    
                  
                  -
                  
                    
                      (
                      
                        x
                        +
                        0.5
                        -
                        
                          s
                          ×
                          y
                        
                        -
                        
                          0.5
                          ⁢
                          s
                        
                      
                      )
                    
                    
                      i
                      +
                      2
                    
                  
                  -
                
              
            
            
              
                
                  
                    
                      (
                      
                        x
                        -
                        0.5
                        -
                        
                          s
                          ×
                          y
                        
                        +
                        
                          0.5
                          ⁢
                          s
                        
                      
                      )
                    
                    
                      i
                      +
                      2
                    
                  
                  +
                  
                    
                      (
                      
                        x
                        -
                        0.5
                        -
                        
                          s
                          ×
                          y
                        
                        -
                        
                          0.5
                          ⁢
                          s
                        
                      
                      )
                    
                    
                      i
                      +
                      2
                    
                  
                
              
            
          
          
            
              s
              ⁡
              
                (
                
                  i
                  +
                  1
                
                )
              
            
            ⁢
            
              (
              
                i
                +
                2
              
              )
            
          
        
      
    
    
      
        (
        72
        )
      
    
  




The integral component calculation unit 2424 calculates the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5).
Specifically, the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) shown in Expression (72) can be calculated as long as the relative pixel positions (x, y), the variable s and i of i-dimensional terms in the above Expression (65) are known. Of these, the relative pixel positions (x, y) are determined with a pixel of interest, and a tap range, the variable s is cot θ, which is determined with the angle θ, and the range of i is determined with the number of dimensions n respectively.
Accordingly, the integral component calculation unit 2424 calculates the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) based on the tap range and the number of dimensions set by the conditions setting unit 2421, and the angle θ of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated results to the normal equation generating unit 2425 as an integral component table.
The normal equation generating unit 2425 generates a normal equation in the case of obtaining the above Expression (66), i.e., Expression (71) by the least square method using the input pixel value table supplied from the input pixel value acquiring unit 2423, and the integral component table supplied from the integral component calculation unit 2424, and outputs this to the approximation function generating unit 2426 as a normal equation table. Note that a specific example of a normal equation will be described later.
The approximation function generating unit 2426 calculates the respective features wi of the above Expression (66) (i.e., the coefficients wi of the approximation function f(x, y) serving as a two-dimensional polynomial) by solving the normal equation included in the normal equation table supplied from the normal equation generating unit 2425 using the matrix solution, and output these to the image generating unit 103.
Next, description will be made regarding the actual world estimating processing (processing in step S102 in FIG. 29) to which the two-dimensional polynomial approximating method is applied, with reference to the flowchart in FIG. 81.
For example, let us say that the light signal in the actual world 1 having continuity in the spatial direction represented with the gradient GF has been detected by the sensor 2 (FIG. 78), and has been stored in the input image storage unit 2422 as an input image corresponding to one frame. Also, let us say that the data continuity detecting unit 101 has subjected the region 2401 shown in FIG. 79 described above of the input image to processing in the continuity detecting processing in step S101 (FIG. 29), and has output the angle θ as data continuity information.
In this case, in step S2401, the conditions setting unit 2421 sets conditions (a tap range and the number of dimensions).
For example, let us say that a tap range 2441 shown in FIG. 82 has been set, and also 5 has been set as the number of dimensions.
FIG. 82 is a diagram for describing an example of a tap range. In FIG. 82, the X direction and Y direction represent the X direction and Y direction of the sensor 2 (FIG. 78). Also, the tap range 2441 represents a pixel group made up of 20 pixels (20 squares in the drawing) in total of 4 pixels in the X direction and also 5 pixels in the Y direction.
Further, as shown in FIG. 82, let us say that a pixel of interest has been set to a pixel, which is the second pixel from the left and also the third pixel from the bottom in the drawing, of the tap range 2441. Also, let us say that each pixel is denoted with a number l such as shown in FIG. 82 (l is any integer value of 0 through 19) according to the relative pixel positions (x, y) from the pixel of interest (a coordinate value of a pixel-of-interest coordinates system wherein the center (0, 0) of the pixel of interest is taken as the origin).
Now, description will return to FIG. 81, wherein in step S2402, the conditions setting unit 2421 sets a pixel of interest.
In step S2403, the input pixel value acquiring unit 2423 acquires an input pixel value based on the condition (tap range) set by the conditions setting unit 2421, and generates an input pixel value table. That is to say, in this case, the input pixel value acquiring unit 2423 acquires the input image region 2401 (FIG. 79), generates a table made up of 20 input pixel values P (l) as an input pixel value table.
Note that in this case, the relation between the input pixel values P (l) and the above input pixel values P (x, y) is a relation shown in the following Expression (73). However, in Expression (73), the left side represents the input pixel values P (l), and the right side represents the input pixel values P (x, y).

P(0)=P(0,0)

P(1)=P(−1,2)

P(2)=P(0,2)

P(3)=P(1,2)

P(4)=P(2,2)

P(5)=P(−1,1)

P(6)=P(0,1)

P(7)=P(1,1)

P(8)=P(2,1)

P(9)=P(−1,0)

P(10)=P(1,0)

P(11)=P(2,0)

P(12)=P(−1, −1)

P(13)=P(0, −1)

P(14)=P(1, −1)

P(15)=P(2, −1)

P(16)=P(−1, −2)

P(17)=P(0, −2)

P(18)=P(1, −2)

P(19)=P(2, −2)  (73)

In step S2404, the integral component calculation unit 2424 calculates integral components based on the conditions (a tap range and the number of dimensions) set by the conditions setting unit 2421, and the data continuity information (angle θ) supplied from the data continuity detecting unit 101, and generates an integral component table.
In this case, as described above, the input pixel values are not P (x, y) but P (l), and are acquired as the value of a pixel number l, so the integral component calculation unit 2424 calculates the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) in the above Expression (72) as a function of l such as the integral components Si (l) shown in the left side of the following Expression (74).

Si(l)=Si(x−0.5,x+0.5,y−0.5,y+0.5)  (74)

Specifically, in this case, the integral components Si (l) shown in the following Expression (75) are calculated.

Si(0)=Si(−0.5,0.5, −0.5,0.5)

Si(1)=Si(−1.5, −0.5,1.5,2.5)

Si(2)=Si(−0.5,0.5, 1.5,2.5)

Si(3)=Si(0.5,1.5,1.5,2.5)

Si(4)=Si(1.5, 2.5, 1.5, 2.5)

Si(5)=Si(−1.5, −0.5,0.5,1.5)

Si(6)=Si(−0.5,0.5,0.5,1.5)

Si(7)=Si(0.5, 1.5,0.5,1.5)

Si(8)=Si(1.5,2.5,0.5,1.5)

Si(9)=Si(−1.5, −0.5, −0.5, 0.5)

Si(10)=Si(0.5, 1.5, −0.5,0.5)

Si(11)=Si(1.5, 2.5, −0.5,0.5)

Si(12)=Si(−1.5, −0.5, −1.5, −0.5)

Si(13)=Si(−0.5,0.5, −1.5, −0.5)

Si(14)=Si(0.5, 1.5, −1.5, −0.5)

Si(15)=Si(1.5, 2.5, −1.5, −0.5)

Si(16)=Si(−1.5, −0.5, −2.5, −1.5)

Si(17)=Si(−0.5,0.5, −2.5, −1.5)

Si(18)=Si(0.5, 1.5, −2.5, −1.5)

Si(19)=Si(1.5, 2.5, −2.5, −1.5)  (75)

Note that in Expression (75), the left side represents the integral components Si (l), and the right side represents the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5). That is to say, in this case, i is 0 through 5, and accordingly, the 120 Si (l) in total of the 20 S0 (l), 20 Si (l), 20 S2 (l), 20 S3 (l), 20 S4 (l), and 20 S5 (l) are calculated.
More specifically, first the integral component calculation unit 2424 calculates cot θ corresponding to the angle θ supplied from the data continuity detecting unit 101, and takes the calculated result as a variable s. Next, the integral component calculation unit 2424 calculates each of the 20 integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) shown in the right side of Expression (74) regarding each of i=0 through 5 using the calculated variable s. That is to say, the 120 integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) are calculated. Note that with this calculation of the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5), the above Expression (72) is used. Subsequently, the integral component calculation unit 2424 converts each of the calculated 120 integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) into the corresponding integral components Si (l) in accordance with Expression (75), and generates an integral component table including the converted 120 integral components Si (l).
Note that the sequence of the processing in step S2403 and the processing in step S2404 is not restricted to the example in FIG. 81, the processing in step S2404 may be executed first, or the processing in step S2403 and the processing in step S2404 may be executed simultaneously.
Next, in step S2405, the normal equation generating unit 2425 generates a normal equation table based on the input pixel value table generated by the input pixel value acquiring unit 2423 at the processing in step S2403, and the integral component table generated by the integral component calculation unit 2424 at the processing in step S2404.
Specifically, in this case, the features wi are calculated with the least square method using the above Expression (71) (however, in Expression (70), the Si (l) into which the integral components Si (x−0.5, x+0.5, y−0.5, y+0.5) are converted using Expression (74) is used), so a normal equation corresponding to this is represented as the following Expression (76).




  
    
      
        
          
            (
            
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ...
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ...
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋰
                
                
                  ⋮
                
              
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ...
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    w
                    0
                  
                
              
              
                
                  
                    w
                    1
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    w
                    n
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        76
        )
      
    
  




Note that in Expression (76), L represents the maximum value of the pixel number l in the tap range. n represents the number of dimensions of the approximation function f(x) serving as a polynomial. Specifically, in this case, n=5, and L=19.
If we define each matrix of the normal equation shown in Expression (76) as the following Expressions (77) through (79), the normal equation is represented as the following Expression (80).




  
    
      
        
          S
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ...
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ...
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋰
              
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ...
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        77
        )
      
    
  
  
    
      
        
          W
          MAT
        
        =
        
          (
          
            
              
                
                  w
                  0
                
              
            
            
              
                
                  w
                  1
                
              
            
            
              
                ⋮
              
            
            
              
                
                  w
                  n
                
              
            
          
          )
        
      
    
    
      
        (
        78
        )
      
    
  
  
    
      
        
          P
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        79
        )
      
    
  
  
    
      
        
          
            S
            MAT
          
          ⁢
          
            W
            MAT
          
        
        =
        
          P
          MAT
        
      
    
    
      
        (
        80
        )
      
    
  




As shown in Expression (78), the respective components of the matrix WMAT are the features wi to be obtained. Accordingly, in Expression (80), if the matrix SMAT of the left side and the matrix PMAT of the right side are determined, the matrix WMAT may be calculated with the matrix solution.
Specifically, as shown in Expression (77), the respective components of the matrix SMAT may be calculated with the above integral components Si (l). That is to say, the integral components Si (l) are included in the integral component table supplied from the integral component calculation unit 2424, so the normal equation generating unit 2425 can calculate each component of the matrix SMAT using the integral component table.
Also, as shown in Expression (79), the respective components of the matrix PMAT may be calculated with the integral components Si (l) and the input pixel values P (l). That is to say, the integral components Si (l) is the same as those included in the respective components of the matrix SMAT, also the input pixel values P (l) are included in the input pixel value table supplied from the input pixel value acquiring unit 2423, so the normal equation generating unit 2425 can calculate each component of the matrix PMAT using the integral component table and input pixel value table.
Thus, the normal equation generating unit 2425 calculates each component of the matrix SMAT and matrix PMAT, and outputs the calculated results (each component of the matrix SMAT and matrix PMAT) to the approximation function generating unit 2426 as a normal equation table.
Upon the normal equation table being output from the normal equation generating unit 2425, in step S2406, the approximation function generating unit 2426 calculates the features wi (i.e., the coefficients wi of the approximation function f(x, y) serving as a two-dimensional polynomial) serving as the respective components of the matrix WMAT in the above Expression (80) based on the normal equation table.
Specifically, the normal equation in the above Expression (80) can be transformed as the following Expression (81).




  
    
      
        
          W
          MAT
        
        =
        
          
            S
            MAT
            
              -
              1
            
          
          ⁢
          
            P
            MAT
          
        
      
    
    
      
        (
        81
        )
      
    
  




In Expression (81), the respective components of the matrix WMAT in the left side are the features wi to be obtained. The respective components regarding the matrix SMAT and matrix PMAT are included in the normal equation table supplied from the normal equation generating unit 2425. Accordingly, the approximation function generating unit 2426 calculates the matrix WMAT by calculating the matrix in the right side of Expression (81) using the normal equation table, and outputs the calculated results (features wi) to the image generating unit 103.
In step S2407, the approximation function generating unit 2426 determines regarding whether or not the processing of all the pixels has been completed.
In step S2407, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S2402, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S2402 through S2407 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S2407, in the event that determination is made that the processing of all the pixels has been completed), the estimating processing of the actual world 1 ends.
As description of the two-dimensional polynomial approximating method, an example for calculating the coefficients (features) wi of the approximation function f(x, y) corresponding to the spatial directions (X direction and Y direction) has been employed, but the two-dimensional polynomial approximating method can be applied to the temporal and spatial directions (X direction and t direction, or Y direction and t direction) as well.
That is to say, the above example is an example in the case of the light signal in the actual world 1 having continuity in the spatial direction represented with the gradient GF (FIG. 77), and accordingly, the equation including two-dimensional integration in the spatial directions (X direction and Y direction), such as shown in the above Expression (66). However, the concept regarding two-dimensional integration can be applied not only to the spatial direction but also to the temporal and spatial directions (X direction and t direction, or Y direction and t direction).
In other words, with the two-dimensional polynomial approximating method, even in the case in which the light signal function F(x, y, t), which needs to be estimated, has not only continuity in the spatial direction but also continuity in the temporal and spatial directions (however, X direction and t direction, or Y direction and t direction), this can be approximated with a two-dimensional approximation function f.
Specifically, for example, in the event that there is an object moving horizontally in the X direction at uniform velocity, the direction of movement of the object is represented with like a gradient VF in the X-t plane such as shown in FIG. 83. In other words, it can be said that the gradient VF represents the direction of continuity in the temporal and spatial directions in the X-t plane. Accordingly, the data continuity detecting unit 101 can output movement θ such as shown in FIG. 83 (strictly speaking, though not shown in the drawing, movement θ is an angle generated by the direction of data continuity represented with the gradient Vf corresponding to the gradient VF and the X direction in the spatial direction) as data continuity information corresponding to the gradient VF representing continuity in the temporal and spatial directions in the X-t plane as well as the above angle θ (data continuity information corresponding to continuity in the spatial directions represented with the gradient GF in the X-Y plane).
Accordingly, the actual world estimating unit 102 employing the two-dimensional polynomial approximating method can calculate the coefficients (features) wi of an approximation function f(x, t) in the same method as the above method by employing the movement θ instead of the angle θ. However, in this case, the equation to be employed is not the above Expression (66) but the following Expression (82).




  
    
      
        
          P
          ⁡
          
            (
            
              x
              ,
              t
            
            )
          
        
        =
        
          
            
              ∫
              
                t
                -
                0.5
              
              
                t
                +
                0.5
              
            
            ⁢
            
              
                ∫
                
                  x
                  -
                  0.5
                
                
                  x
                  +
                  0.5
                
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  n
                
                ⁢
                
                  
                    
                      
                        w
                        i
                      
                      ⁡
                      
                        (
                        
                          x
                          -
                          
                            s
                            ×
                            t
                          
                        
                        )
                      
                    
                    i
                  
                  ⁢
                  
                    d
                    x
                  
                  ⁢
                  
                    d
                    t
                  
                
              
            
          
          +
          e
        
      
    
    
      
        (
        82
        )
      
    
  




Note that in Expression (82), s is cot θ (however, θ is movement).
Also, an approximation function f(y, t) focusing attention on the spatial direction Y instead of the spatial direction X can be handled in the same way as the above approximation function f(x, t).
Thus, the two-dimensional polynomial approximating method takes not one-dimensional but two-dimensional integration effects into consideration, so can estimate the light signals in the actual world 1 more accurately than the one-dimensional approximating method.
Next, description will be made regarding the third function approximating method with reference to FIG. 84 through FIG. 88.
That is to say, the third function approximating method is a method for estimating the light signal function F(x, y, t) by approximating the light signal function F(x, y, t) with the approximation function f(x, y, t) focusing attention on that the light signal in the actual world 1 having continuity in a predetermined direction of the temporal and spatial directions is represented with the light signal function F(x, y, t), for example. Accordingly, hereafter, the third function approximating method is referred to as a three-dimensional function approximating method.
Also, with description of the three-dimensional function approximating method, let us say that the sensor 2 is a CCD made up of the multiple detecting elements 2-1 disposed on the plane thereof, such as shown in FIG. 84.
With the example in FIG. 84, the direction in parallel with a predetermined side of the detecting elements 2-1 is taken as the X direction serving as one direction of the spatial directions, and the direction orthogonal to the X direction is taken as the Y direction serving as the other direction of the spatial directions. The direction orthogonal to the X-Y plane is taken as the t direction serving as the temporal direction.
Also, with the example in FIG. 84, the spatial shape of the respective detecting elements 2-1 of the sensor 2 is taken as a square of which one side is 1 in length. The shutter time (exposure time) of the sensor 2 is taken as 1.
Further, with the example in FIG. 84, the center of one certain detecting element 2-1 of the sensor 2 is taken as the origin (the position in the X direction is x=0, and the position in the Y direction is y=0) in the spatial directions (X direction and Y direction), and also the intermediate point-in-time of the exposure time is taken as the origin (the position in the t direction is t=0) in the temporal direction (t direction).
In this case, the detecting element 2-1 of which the center is in the origin (x=0, y=0) in the spatial directions subjects the light signal function F(x, y, t) to integration with a range of −0.5 through 0.5 in the X direction, with a range of −0.5 through 0.5 in the Y direction, and with a range of −0.5 through 0.5 in the t direction, and outputs the integral value as the pixel value P.
That is to say, the pixel value P output from the detecting element 2-1 of which the center is in the origin in the spatial directions is represented with the following Expression (83).




  
    
      
        P
        =
        
          
            ∫
            
              -
              0.5
            
            
              +
              0.5
            
          
          ⁢
          
            
              ∫
              
                -
                0.5
              
              
                +
                0.5
              
            
            ⁢
            
              
                ∫
                
                  -
                  0.5
                
                
                  +
                  0.5
                
              
              ⁢
              
                
                  F
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                      ,
                      t
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
                ⁢
                
                  d
                  t
                
              
            
          
        
      
    
    
      
        (
        83
        )
      
    
  




Similarly, the other detecting elements 2-1 output the pixel value P shown in Expression (83) by taking the center of the detecting element 2-1 to be processed as the origin in the spatial directions.
Incidentally, as described above, with the three-dimensional function approximating method, the light signal function F(x, y, t) is approximated to the three-dimensional approximation function f(x, y, t).
Specifically, for example, the approximation function f(x, y, t) is taken as a function having N variables (features), a relational expression between the input pixel values P (x, y, t) corresponding to Expression (83) and the approximation function f(x, y, t) is defined. Thus, in the event that M input pixel values P (x, y, t) more than N are acquired, N variables (features) can be calculated from the defined relational expression. That is to say, the actual world estimating unit 102 can estimate the light signal function F(x, y, t) by acquiring M input pixel values P (x, y, t), and calculating N variables (features).
In this case, the actual world estimating unit 102 extracts (acquires) M input images P (x, y, t), of the entire input image by using continuity of data included in an input image (input pixel values) from the sensor 2 as a constraint (i.e., using data continuity information as to an input image to be output from the data continuity detecting unit 101). As a result, the approximation function f(x, y, t) is constrained by continuity of data.
For example, as shown in FIG. 85, in the event that the light signal function F(x, y, t) corresponding to an input image has continuity in the spatial direction represented with the gradient GF, the data continuity detecting unit 101 results in outputting the angle θ (the angle θ generated between the direction of continuity of data represented with the gradient Gf (not shown) corresponding to the gradient GF, and the X direction) as data continuity information as to the input image.
In this case, let us say that a one-dimensional waveform wherein the light signal function F(x, y, t) is projected in the X direction (such a waveform is referred to as an X cross-sectional waveform here) has the same form even in the event of projection in any position in the Y direction.
That is to say, let us say that there is an X cross-sectional waveform having the same form, which is a two-dimensional (spatial directional) waveform continuous in the direction of continuity (angle θ direction as to the X direction), and a three-dimensional waveform wherein such a two-dimensional waveform continues in the temporal direction t, is approximated with the approximation function f(x, y, t).
In other words, an X cross-sectional waveform, which is shifted by a position y in the Y direction from the center of the pixel of interest, becomes a waveform wherein the X cross-sectional waveform passing through the center of the pixel of interest is moved (shifted) by a predetermined amount (amount varies according to the angle θ) in the X direction. Note that hereafter, such an amount is referred to as a shift amount.
This shift amount can be calculated as follows.
That is to say, the gradient Vf (for example, gradient Vf representing the direction of data continuity corresponding to the gradient VF in FIG. 85) and angle θ are represented as the following Expression (84).




  
    
      
        
          G
          f
        
        =
        
          
            tan
            ⁢
            
              
            
            ⁢
            θ
          
          =
          
            
              d
              y
            
            
              d
              x
            
          
        
      
    
    
      
        (
        84
        )
      
    
  




Note that in Expression (84), dx represents the amount of fine movement in the X direction, and dy represents the amount of fine movement in the Y direction as to the dx.
Accordingly, if the shift amount as to the X direction is described as Cx (y), this is represented as the following Expression (85).




  
    
      
        
          
            C
            x
          
          ⁡
          
            (
            y
            )
          
        
        =
        
          y
          
            G
            f
          
        
      
    
    
      
        (
        85
        )
      
    
  




If the shift amount Cx (y) is thus defined, a relational expression between the input pixel values P (x, y, t) corresponding to Expression (83) and the approximation function f(x, y, t) is represented as the following Expression (86).




  
    
      
        
          P
          ⁡
          
            (
            
              x
              ,
              y
              ,
              t
              ,
            
            )
          
        
        =
        
          
            
              ∫
              
                t
                s
              
              
                t
                e
              
            
            ⁢
            
              
                ∫
                
                  y
                  s
                
                
                  y
                  e
                
              
              ⁢
              
                
                  ∫
                  
                    x
                    s
                  
                  
                    x
                    e
                  
                
                ⁢
                
                  
                    f
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                        ,
                        t
                        ,
                      
                      )
                    
                  
                  ⁢
                  
                    d
                    x
                  
                  ⁢
                  
                    d
                    y
                  
                  ⁢
                  
                    d
                    t
                  
                
              
            
          
          +
          e
        
      
    
    
      
        (
        86
        )
      
    
  




In Expression (86), e represents a margin of error. ts represents an integration start position in the t direction, and te represents an integration end position in the t direction. In the same way, ys represents an integration start position in the Y direction, and ye represents an integration end position in the Y direction. Also, xs represents an integration start position in the X direction, and xe represents an integration end position in the X direction. However, the respective specific integral ranges are as shown in the following Expression (87).

ts=t−0.5

te=t+0.5

ys=y−0.5

ye=y+0.5

xs=x−Cx(y)−0.5

xe=x−Cx(y)+0.5  (87)

As shown in Expression (87), it can be represented that an X cross-sectional waveform having the same form continues in the direction of continuity (angle θ direction as to the X direction) by shifting an integral range in the X direction as to a pixel positioned distant from the pixel of interest by (x, y) in the spatial direction by the shift amount Cx (Y).
Thus, with the three-dimensional approximating method, the relation between the pixel values P (x, y, t) and the three-dimensional approximation function f(x, y, t) can be represented with Expression (86) (Expression (87) for the integral range), and accordingly, the light signal function F(x, y, t) (for example, a light signal having continuity in the spatial direction represented with the gradient VF such as shown in FIG. 85) can be estimated by calculating the N features of the approximation function f(x, y, t), for example, with the least square method using Expression (86) and Expression (87).
Note that in the event that a light signal represented with the light signal function F(x, y, t) has continuity in the spatial direction represented with the gradient VF such as shown in FIG. 85, the light signal function F(x, y, t) may be approximated as follows.
That is to say, let us say that a one-dimensional waveform wherein the light signal function F(x, y, t) is projected in the Y direction (hereafter, such a waveform is referred to as a Y cross-sectional waveform) has the same form even in the event of projection in any position in the X direction.
In other words, let us say that there is a two-dimensional (spatial directional) waveform wherein a Y cross-sectional waveform having the same form continues in the direction of continuity (angle θ direction as to in the X direction), and a three-dimensional waveform wherein such a two-dimensional waveform continues in the temporal direction t is approximated with the approximation function f(x, y, t).
Accordingly, the Y cross-sectional waveform, which is shifted by x in the X direction from the center of the pixel of interest, becomes a waveform wherein the Y cross-sectional waveform passing through the center of the pixel of interest is moved by a predetermined shift amount (shift amount changing according to the angle θ) in the Y direction.
This shift amount can be calculated as follows.
That is to say, the gradient GF is represented as the above Expression (84), so if the shift amount as to the Y direction is described as Cy (x), this is represented as the following Expression (88).

Cy(x)=Gf×X  (88)

If the shift amount Cx(y) is thus defined, a relational expression between the input pixel values P (x, y, t) corresponding to Expression (83) and the approximation function f(x, y, t) is represented as the above Expression (86), as with when the shift amount Cx (y) is defined.
However, in this case, the respective specific integral ranges are as shown in the following Expression (89).

ts=t−0.5

te=t+0.5

ys=y−Cy(x)−0.5

ye=y−Cy(x)+0.5

xs=x−0.5

xe=x+0.5  (89)

As shown in Expression (89) (and the above Expression (86)), it can be represented that a Y cross-sectional waveform having the same form continues in the direction of continuity (angle θ direction as to the X direction) by shifting an integral range in the Y direction as to a pixel positioned distant from the pixel of interest by (x, y), by the shift amount Cx (y).
Thus, with the three-dimensional approximating method, the integral range of the right side of the above Expression (86) can be set to not only Expression (87) but also Expression (89), and accordingly, the light signal function F(x, y, t) (light signal in the actual world 1 having continuity in the spatial direction represented with the gradient GF) can be estimated by calculating the n features of the approximation function f(x, y, t) with, for example, the least square method or the like using Expression (86) in which Expression (89) is employed as an integral range.
Thus, Expression (87) and Expression (89), which represent an integral range, represent essentially the same with only a difference regarding whether perimeter pixels are shifted in the X direction (in the case of Expression (87)) or shifted in the Y direction (in the case of Expression (89)) in response to the direction of continuity.
However, in response to the direction of continuity (gradient GF), there is a difference regarding whether the light signal function F(x, y, t) is regarded as a group of X cross-sectional waveforms, or is regarded as a group of Y cross-sectional waveforms. That is to say, in the event that the direction of continuity is close to the Y direction, the light signal function F(x, y, t) is preferably regarded as a group of X cross-sectional waveforms. On the other hand, in the event that the direction of continuity is close to the X direction, the light signal function F(x, y, t) is preferably regarded as a group of Y cross-sectional waveforms.
Accordingly, it is preferable that the actual world estimating unit 102 prepares both Expression (87) and Expression (89) as an integral range, and selects any one of Expression (87) and Expression (89) as the integral range of the right side of the appropriate Expression (86) in response to the direction of continuity.
Description has been made regarding the three-dimensional approximation method in the case in which the light signal function F(x, y, t) has continuity (for example, continuity in the spatial direction represented with the gradient GF in FIG. 85) in the spatial directions (X direction and Y direction), but the three-dimensional approximation method can be applied to the case in which the light signal function F(x, y, t) has continuity (continuity represented with the gradient VF) in the temporal and spatial directions (X direction, Y direction, and t direction), as shown in FIG. 86.
That is to say, in FIG. 86, a light signal function corresponding to a frame #N−1 is taken as F (x, y, #N−1), a light signal function corresponding to a frame #N is taken as F (x, y, #N), and a light signal function corresponding to a frame #N+1 is taken as F (x, y, #N+1).
Note that in FIG. 86, the horizontal direction is taken as the X direction serving as one direction of the spatial directions, the upper right diagonal direction is taken as the Y direction serving as the other direction of the spatial directions, and also the vertical direction is taken as the t direction serving as the temporal direction in the drawing.
Also, the frame #N−1 is a frame temporally prior to the frame #N, the frame #N+1 is a frame temporally following the frame #N. That is to say, the frame #N−1, frame #N, and frame #N+1 are displayed in the sequence of the frame #N−1, frame #N, and frame #N+1.
With the example in FIG. 86, a cross-sectional light level along the direction shown with the gradient VF (upper right inner direction from lower left near side in the drawing) is regarded as generally constant. Accordingly, with the example in FIG. 86, it can be said that the light signal function F(x, y, t) has continuity in the temporal and spatial directions represented with the gradient VF.
In this case, in the event that a function C (x, y, t) representing continuity in the temporal and spatial directions is defined, and also the integral range of the above Expression (86) is defined with the defined function C (x, y, t), N features of the approximation function f(x, y, t) can be calculated as with the above Expression (87) and Expression (89).
The function C (x, y, t) is not restricted to a particular function as long as this is a function representing the direction of continuity. However, hereafter, let us say that linear continuity is employed, and Cx (t) and Cy (t) corresponding to the shift amount Cx (y) (Expression (85)) and shift amount Cy (x) (Expression (87)), which are functions representing continuity in the spatial direction described above, are defined as a function C (x, y, t) corresponding thereto as follows.
That is to say, if the gradient as continuity of data in the temporal and spatial directions corresponding to the gradient Gf representing continuity of data in the above spatial direction is taken as Vf, and if this gradient Vf is divided into the gradient in the X direction (hereafter, referred to as Vfx) and the gradient in the Y direction (hereafter, referred to as Vfy), the gradient Vfx is represented with the following Expression (90), and the gradient Vfy is represented with the following Expression (91), respectively.




  
    
      
        
          V
          fx
        
        =
        
          
            d
            x
          
          
            d
            t
          
        
      
    
    
      
        (
        90
        )
      
    
  
  
    
      
        
          V
          fy
        
        =
        
          
            d
            y
          
          
            d
            t
          
        
      
    
    
      
        (
        91
        )
      
    
  




In this case, the function Cx (t) is represented as the following Expression (92) using the gradient Vfx shown in Expression (90).

Cx(t)=Vfx×t  (92)

Similarly, the function Cy (t) is represented as the following Expression (93) using the gradient Vfy shown in Expression (91).

Cy(t)=Vfy×t  (93)

Thus, upon the function Cx(t) and function Cy(t), which represent continuity 2511 in the temporal and spatial directions, being defined, the integral range of Expression (86) is represented as the following Expression (94).

ts=t−0.5 

te=t+0.5

ys=y−Cy(t)−0.5

ye=y−Cy(t)+0.5

xs=x−Cx(t)−0.5

xe=x−Cx(t)+0.5  (94)

Thus, with the three-dimensional approximating method, the relation between the pixel values P (x, y, t) and the three-dimensional approximation function f(x, y, t) can be represented with Expression (86), and accordingly, the light signal function F(x, y, t) (light signal in the actual world 1 having continuity in a predetermined direction of the temporal and spatial directions) can be estimated by calculating the n+1 features of the approximation function f(x, y, t) with, for example, the least square method or the like using Expression (94) as the integral range of the right side of Expression (86).
FIG. 87 represents a configuration example of the actual world estimating unit 102 employing such a three-dimensional approximating method.
Note that the approximation function f(x, y, t) (in reality, the features (coefficients) thereof) calculated by the actual world estimating unit 102 employing the three-dimensional approximating method is not restricted to a particular function, but an n (n=N−1)-dimensional polynomial is employed in the following description.
As shown in FIG. 87, the actual world estimating unit 102 includes a conditions setting unit 2521, input image storage unit 2522, input pixel value acquiring unit 2523, integral component calculation unit 2524, normal equation generating unit 2525, and approximation function generating unit 2526.
The conditions setting unit 2521 sets a pixel range (tap range) used for estimating the light signal function F(x, y, t) corresponding to a pixel of interest, and the number of dimensions n of the approximation function f(x, y, t).
The input image storage unit 2522 temporarily stores an input image (pixel values) from the sensor 2.
The input pixel acquiring unit 2523 acquires, of the input images stored in the input image storage unit 2522, an input image region corresponding to the tap range set by the conditions setting unit 2521, and supplies this to the normal equation generating unit 2525 as an input pixel value table. That is to say, the input pixel value table is a table in which the respective pixel values of pixels included in the input image region are described.
Incidentally, as described above, the actual world estimating unit 102 employing the three-dimensional approximating method calculates the N features (in this case, coefficient of each dimension) of the approximation function f(x, y, t) with the least square method using the above Expression (86) (however, Expression (87), Expression (90), or Expression (94) for the integral range).
The right side of Expression (86) can be represented as the following Expression (95) by calculating the integration thereof.




  
    
      
        
          P
          ⁢
          
            (
            
              x
              ,
              y
              ,
              t
              ,
            
            )
          
        
        =
        
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                
                  S
                  i
                
                ⁡
                
                  (
                  
                    
                      x
                      s
                    
                    ,
                    
                      x
                      e
                    
                    ,
                    
                      y
                      s
                    
                    ,
                    
                      y
                      e
                    
                    ,
                    
                      t
                      s
                    
                    ,
                    
                      t
                      e
                    
                  
                  )
                
              
            
          
          +
          e
        
      
    
    
      
        (
        95
        )
      
    
  




In Expression (95), wi represents the coefficients (features) of the i-dimensional term, and also Si (xs, xe, ys, ye, ts, te) represents the integral components of the i-dimensional term. However, xs represents an integral range start position in the X direction, xe represents an integral range end position in the X direction, ys represents an integral range start position in the Y direction, ye represents an integral range end position in the Y direction, ts represents an integral range start position in the t direction, te represents an integral range end position in the t direction, respectively.
The integral component calculation unit 2524 calculates the integral components Si (xs, xe, ys, ye, ts, te).
That is to say, the integral component calculation unit 2524 calculates the integral components Si (xs, xe, ys, ye, ts, te) based on the tap range and the number of dimensions set by the conditions setting unit 2521, and the angle or movement (as the integral range, angle in the case of using the above Expression (87) or Expression (90), and movement in the case of using the above Expression (94)) of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated results to the normal equation generating unit 2525 as an integral component table.
The normal equation generating unit 2525 generates a normal equation in the case of obtaining the above Expression (95) with the least square method using the input pixel value table supplied from the input pixel value acquiring unit 2523, and the integral component table supplied from the integral component calculation unit 2524, and outputs this to the approximation function generating unit 2526 as a normal equation table. An example of a normal equation will be described later.
The approximation function generating unit 2526 calculates the respective features wi (in this case, the coefficients wi of the approximation function f(x, y, t) serving as a three-dimensional polynomial) by solving the normal equation included in the normal equation table supplied from the normal equation generating unit 2525 with the matrix solution, and output these to the image generating unit 103.
Next, description will be made regarding the actual world estimating processing (processing in step S102 in FIG. 29) to which the three-dimensional approximating method is applied, with reference to the flowchart in FIG. 88.
First, in step S2501, the conditions setting unit 2521 sets conditions (a tap range and the number of dimensions).
For example, let us say that a tap range made up of L pixels has been set. Also, let us say that a predetermined number l (l is any one of integer values 0 through L−1) is appended to each of the pixels.
Next, in step S2502, the conditions setting unit 2521 sets a pixel of interest.
In step S2503, the input pixel value acquiring unit 2523 acquires an input pixel value based on the condition (tap range) set by the conditions setting unit 2521, and generates an input pixel value table. In this case, a table made up of L input pixel values P (x, y, t) is generated. Here, let us say that each of the L input pixel values P (x, y, t) is described as P (l) serving as a function of the number l of the pixel thereof. That is to say, the input pixel value table becomes a table including L P (l).
In step S2504, the integral component calculation unit 2524 calculates integral components based on the conditions (a tap range and the number of dimensions) set by the conditions setting unit 2521, and the data continuity information (angle or movement) supplied from the data continuity detecting unit 101, and generates an integral component table.
However, in this case, as described above, the input pixel values are not P (x, y, t) but P (l), and are acquired as the value of a pixel number l, so the integral component calculation unit 2524 results in calculating the integral components Si (xs, xe, ys, ye, ts, te) in the above Expression (95) as a function of l such as the integral components Si (l). That is to say, the integral component table becomes a table including L×i Si (l).
Note that the sequence of the processing in step S2503 and the processing in step S2504 is not restricted to the example in FIG. 88, so the processing in step S2504 may be executed first, or the processing in step S2503 and the processing in step S2504 may be executed simultaneously.
Next, in step S2505, the normal equation generating unit 2525 generates a normal equation table based on the input pixel value table generated by the input pixel value acquiring unit 2523 at the processing in step S2503, and the integral component table generated by the integral component calculation unit 2524 at the processing in step S2504.
Specifically, in this case, the features wi of the following Expression (96) corresponding to the above Expression (95) are calculated using the least square method. A normal equation corresponding to this is represented as the following Expression (97).




  
    
      
        
          P
          ⁡
          
            (
            l
            )
          
        
        =
        
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                
                  S
                  i
                
                ⁡
                
                  (
                  l
                  )
                
              
            
          
          +
          e
        
      
    
    
      
        (
        96
        )
      
    
  
  
    
      
        
          
            (
            
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  
                    
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                        =
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                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
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                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
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                          0
                        
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                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
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                        l
                        =
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                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
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                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋰
                
                
                  ⋮
                
              
              
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          0
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
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                          1
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
                
                  ⋯
                
                
                  
                    
                      ∑
                      
                        l
                        =
                        0
                      
                      L
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                      ⁢
                      
                        
                          S
                          n
                        
                        ⁡
                        
                          (
                          l
                          )
                        
                      
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    W
                    0
                  
                
              
              
                
                  
                    W
                    1
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    W
                    n
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁢
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁢
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        97
        )
      
    
  




If we define each matrix of the normal equation shown in Expression (97) as the following Expressions (98) through (100), the normal equation is represented as the following Expression (101).




  
    
      
        
          S
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
              
                ⋰
              
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        1
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
              
                ⋯
              
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      
                        S
                        n
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        98
        )
      
    
  
  
    
      
        
          W
          MAT
        
        =
        
          (
          
            
              
                
                  W
                  0
                
              
            
            
              
                
                  W
                  1
                
              
            
            
              
                ⋮
              
            
            
              
                
                  W
                  n
                
              
            
          
          )
        
      
    
    
      
        (
        99
        )
      
    
  
  
    
      
        
          P
          MAT
        
        =
        
          (
          
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        0
                      
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        1
                      
                      ⁢
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
            
              
                ⋮
              
            
            
              
                
                  
                    ∑
                    
                      l
                      =
                      0
                    
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        S
                        n
                      
                      ⁢
                      
                        (
                        l
                        )
                      
                    
                    ⁢
                    
                      P
                      ⁡
                      
                        (
                        l
                        )
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        (
        100
        )
      
    
  
  
    
      
        
          
            S
            MAT
          
          ⁢
          
            W
            MAT
          
        
        =
        
          P
          MAT
        
      
    
    
      
        (
        101
        )
      
    
  




As shown in Expression (99), the respective components of the matrix WMAT are the features wi to be obtained. Accordingly, in Expression (101), if the matrix SMAT of the left side and the matrix PMAT of the right side are determined, the matrix WMAT (i.e., features wi) may be calculated with the matrix solution.
Specifically, as shown in Expression (98), the respective components of the matrix SMAT may be calculated as long as the above integral components Si (l) are known. The integral components Si (l) are included in the integral component table supplied from the integral component calculation unit 2524, so the normal equation generating unit 2525 can calculate each component of the matrix SMAT using the integral component table.
Also, as shown in Expression (100), the respective components of the matrix PMAT may be calculated as long as the integral components Si (l) and the input pixel values P (l) are known. The integral components Si (l) is the same as those included in the respective components of the matrix SMAT, also the input pixel values P (l) are included in the input pixel value table supplied from the input pixel value acquiring unit 2523, so the normal equation generating unit 2525 can calculate each component of the matrix PMAT using the integral component table and input pixel value table.
Thus, the normal equation generating unit 2525 calculates each component of the matrix SMAT and matrix PMAT, and outputs the calculated results (each component of the matrix SMAT and matrix PMAT) to the approximation function generating unit 2526 as a normal equation table.
Upon the normal equation table being output from the normal equation generating unit 2526, in step S2506, the approximation function generating unit 2526 calculates the features wi (i.e., the coefficients wi of the approximation function f(x, y, t)) serving as the respective components of the matrix WMAT in the above Expression (101) based on the normal equation table.
Specifically, the normal equation in the above Expression (101) can be transformed as the following Expression (102).




  
    
      
        
          W
          MAT
        
        =
        
          
            S
            MAT
            
              -
              1
            
          
          ⁢
          
            P
            MAT
          
        
      
    
    
      
        (
        102
        )
      
    
  




In Expression (102), the respective components of the matrix WMAT in the left side are the features wi to be obtained. The respective components regarding the matrix SMAT and matrix PMAT are included in the normal equation table supplied from the normal equation generating unit 2525. Accordingly, the approximation function generating unit 2526 calculates the matrix WMAT by calculating the matrix in the right side of Expression (102) using the normal equation table, and outputs the calculated results (features wi) to the image generating unit 103.
In step S2507, the approximation function generating unit 2526 determines regarding whether or not the processing of all the pixels has been completed.
In step S2507, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S2502, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S2502 through S2507 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S5407, in the event that determination is made that the processing of all the pixels has been completed), the estimating processing of the actual world 1 ends.
As described above, the three-dimensional approximating method takes three-dimensional integration effects in the temporal and spatial directions into consideration instead of one-dimensional or two-dimensional integration effects, and accordingly, can estimate the light signals in the actual world 1 more accurately than the one-dimensional approximating method and two-dimensional polynomial approximating method.
Next, description will be made regarding an embodiment of the image generating unit 103 (FIG. 3) with reference to FIG. 89 through FIG. 110.
FIG. 89 is a diagram for describing the principle of the present embodiment.
As shown in FIG. 89, the present embodiment is based on condition that the actual world estimating unit 102 employs a function approximating method. That is to say, let us say that the signals in the actual world 1 (distribution of light intensity) serving as an image cast in the sensor 2 are represented with a predetermined function F, it is an assumption for the actual world estimating unit 102 to estimate the function F by approximating the function F with a predetermined function f using the input image (pixel value P) output from the sensor 2 and the data continuity information output from the data continuity detecting unit 101.
Note that hereafter, with description of the present embodiment, the signals in the actual world 1 serving as an image are particularly referred to as light signals, and the function F is particularly referred to as a light signal function F. Also, the function f is particularly referred to as an approximation function f.
With the present embodiment, the image generating unit 103 integrates the approximation function f with a predetermined time-space range using the data continuity information output from the data continuity detecting unit 101, and the actual world estimating information (in the example in FIG. 89, the features of the approximation function f or approximation function f of which the features are identified) output from the actual world estimating unit 102 based on such an assumption, and outputs the integral value as an output pixel value M (output image). Note that with the present embodiment, an input pixel value is described as P, and an output pixel value is described as M in order to distinguish an input image pixel from an output image pixel.
In other words, upon the light signal function F being integrated once, the light signal function F becomes an input pixel value P, the light signal function F is estimated from the input pixel value P (approximated with the approximation function f), the estimated light signal function F(i.e., approximation function f) is integrated again, and an output pixel value M is generated. Accordingly, hereafter, integration of the approximation function f executed by the image generating unit 103 is referred to as reintegration. Also, the present embodiment is referred to as a reintegration method.
Note that as described later, with the reintegration method, the integral range of the approximation function f in the event that the output pixel value M is generated is not restricted to the integral range of the light signal function F in the event that the input pixel value P is generated (i.e., the vertical width and horizontal width of the detecting element of the sensor 2 for the spatial direction, the exposure time of the sensor 2 for the temporal direction), an arbitrary integral range may be employed.
For example, in the event that the output pixel value M is generated, varying the integral range in the spatial direction of the integral range of the approximation function f enables the pixel pitch of an output image according to the integral range thereof to be varied. That is to say, creation of spatial resolution is available.
In the same way, for example, in the event that the output pixel value M is generated, varying the integral range in the temporal direction of the integral range of the approximation function f enables creation of temporal resolution.
Hereafter, description will be made individually regarding three specific methods of such a reintegration method with reference to the drawings.
That is to say, three specific methods are reintegration methods corresponding to three specific methods of the function approximating method (the above three specific examples of the embodiment of the actual world estimating unit 102) respectively.
Specifically, the first method is a reintegration method corresponding to the above one-dimensional approximating method (one method of the function approximating method). Accordingly, with the first method, one-dimensional reintegration is performed, so hereafter, such a reintegration method is referred to as a one-dimensional reintegration method.
The second method is a reintegration method corresponding to the above two-dimensional polynomial approximating method (one method of the function approximating method). Accordingly, with the second method, two-dimensional reintegration is performed, so hereafter, such a reintegration method is referred to as a two-dimensional reintegration method.
The third method is a reintegration method corresponding to the above three-dimensional approximating method (one method of the function approximating method). Accordingly, with the third method, three-dimensional reintegration is performed, so hereafter, such a reintegration method is referred to as a three-dimensional reintegration method.
Hereafter, description will be made regarding each details of the one-dimensional reintegration method, two-dimensional reintegration method, and three-dimensional reintegration method in this order.
First, the one-dimensional reintegration method will be described.
With the one-dimensional reintegration method, it is assumed that the approximation function f(x) is generated using the one-dimensional approximating method.
That is to say, it is an assumption that a one-dimensional waveform (with description of the reintegration method, a waveform projected in the X direction of such a waveform is referred to as an X cross-sectional waveform F(x)) wherein the light signal function F(x, y, t) of which variables are positions x, y, and z on the three-dimensional space, and a point-in-time t is projected in a predetermined direction (for example, X direction) of the X direction, Y direction, and Z direction serving as the spatial direction, and t direction serving as the temporal direction, is approximated with the approximation function f(x) serving as an n-dimensional (n is an arbitrary integer) polynomial.
In this case, with the one-dimensional reintegration method, the output pixel value M is calculated such as the following Expression (103).




  
    
      
        M
        =
        
          
            G
            e
          
          ×
          
            
              ∫
              
                x
                s
              
              
                x
                e
              
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
        
      
    
    
      
        (
        103
        )
      
    
  




Note that in Expression (103), xs represents an integration start position, xe represents an integration end position. Also, Ge represents a predetermined gain.
Specifically, for example, let us say that the actual world estimating unit 102 has already generated the approximation function f(x) (the approximation function f(x) of the X cross-sectional waveform F(x)) such as shown in FIG. 90 with a pixel 3101 (pixel 3101 corresponding to a predetermined detecting element of the sensor 2) such as shown in FIG. 90 as a pixel of interest.
Note that with the example in FIG. 90, the pixel value (input pixel value) of the pixel 3101 is taken as P, and the shape of the pixel 3101 is taken as a square of which one side is 1 in length. Also, of the spatial directions, the direction in parallel with one side of the pixel 3101 (horizontal direction in the drawing) is taken as the X direction, and the direction orthogonal to the X direction (vertical direction in the drawing) is taken as the Y direction.
Also, on the lower side in FIG. 90, the coordinates system (hereafter, referred to as a pixel-of-interest coordinates system) in the spatial directions (X direction and Y direction) of which the center of the pixel 3101 is taken as the origin, and the pixel 3101 in the coordinates system are shown.
Further, on the upward direction in FIG. 90, a graph representing the approximation function f(x) at y=0 (y is a coordinate value in the Y direction in the pixel-of-interest coordinates system shown on the lower side in the drawing) is shown. In this graph, the axis in parallel with the horizontal direction in the drawing is the same axis as the x axis in the X direction in the pixel-of-interest coordinates system shown on the lower side in the drawing (the origin is also the same), and also the axis in parallel with the vertical direction in the drawing is taken as an axis representing pixel values.
In this case, the relation of the following Expression (104) holds between the approximation function f(x) and the pixel value P of the pixel 3101.




  
    
      
        P
        =
        
          
            
              ∫
              
                -
                0.5
              
              0.5
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
          +
          e
        
      
    
    
      
        (
        104
        )
      
    
  




Also, as shown in FIG. 90, let us say that the pixel 3101 has continuity of data in the spatial direction represented with the gradient Gf. Further, let us say that the data continuity detecting unit 101 (FIG. 89) has already output the angle θ such as shown in FIG. 90 as data continuity information corresponding to continuity of data represented with the gradient Gf.
In this case, for example, with the one-dimensional reintegration method, as shown in FIG. 91, four pixels 3111 through 3114 can be newly created in a range of −0.5 through 0.5 in the X direction, and also in a range of −0.5 through 0.5 in the Y direction (in the range where the pixel 3101 in FIG. 90 is positioned).
Note that on the lower side in FIG. 91, the same pixel-of-interest coordinates system as that in FIG. 90, and the pixels 3111 through 3114 in the pixel-of-interest coordinates system thereof are shown. Also, on the upper side in FIG. 91, the same graph (graph representing the approximation function f(x) at y=0) as that in FIG. 90 is shown.
Specifically, as shown in FIG. 91, with the one-dimensional reintegration method, calculation of the pixel value M (1) of the pixel 3111 using the following Expression (105), calculation of the pixel value M (2) of the pixel 3112 using the following Expression (106), calculation of the pixel value M (3) of the pixel 3113 using the following Expression (107), and calculation of the pixel value M (4) of the pixel 3114 using the following Expression (108) are available respectively.




  
    
      
        
          M
          ⁡
          
            (
            1
            )
          
        
        =
        
          2
          ×
          
            
              ∫
              
                x
                
                  s
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              
                x
                
                  e
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
        
      
    
    
      
        (
        105
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            2
            )
          
        
        =
        
          2
          ×
          
            
              ∫
              
                x
                
                  s
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
              
                x
                
                  e
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
        
      
    
    
      
        (
        106
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            3
            )
          
        
        =
        
          2
          ×
          
            
              ∫
              
                x
                
                  s
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
              
              
                x
                
                  e
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
              
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
        
      
    
    
      
        (
        107
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            4
            )
          
        
        =
        
          2
          ×
          
            
              ∫
              
                x
                
                  s
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
              
              
                x
                
                  e
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
              
            
            ⁢
            
              
                f
                ⁡
                
                  (
                  x
                  )
                
              
              ⁢
              
                
              
              ⁢
              
                d
                x
              
            
          
        
      
    
    
      
        (
        108
        )
      
    
  




Note that xs1 in Expression (105), xs2 in Expression (106), xs3 in Expression (107), and xs4 in Expression (108) each represent the integration start position of the corresponding expression. Also, xe1 in Expression (105), xe2 in Expression (106), xe3 in Expression (107), and xe4 in Expression (108) each represent the integration end position of the corresponding expression.
The integral range in the right side of each of Expression (105) through Expression (108) becomes the pixel width (length in the X direction) of each of the pixel 3111 through pixel 3114. That is to say, each of xe1−xs1, xe2−xs2, xe3−xs3, and xe4−xs4 becomes 0.5.
However, in this case, it can be conceived that a one-dimensional waveform having the same form as that in the approximation function f(x) at y=0 continues not in the Y direction but in the direction of data continuity represented with the gradient Gf (i.e., angle θ direction) (in fact, a waveform having the same form as the X cross-sectional waveform F(x) at y=0 continues in the direction of continuity). That is to say, in the case in which a pixel value f (0) in the origin (0, 0) in the pixel-of-interest coordinates system in FIG. 91 (center of the pixel 3101 in FIG. 90) is taken as a pixel value f1, the direction where the pixel value f1 continues is not the Y direction but the direction of data continuity represented with the gradient Gf (angle θ direction).
In other words, in the case of conceiving the waveform of the approximation function f(x) in a predetermined position y in the Y direction (however, y is a numeric value other than zero), the position corresponding to the pixel value f1 is not a position (0, y) but a position (Cx (y), y) obtained by moving in the X direction from the position (0, y) by a predetermined amount (here, let us say that such an amount is also referred to as a shift amount. Also, a shift amount is an amount depending on the position y in the Y direction, so let us say that this shift amount is described as Cx (y)).
Accordingly, as the integral range of the right side of each of the above Expression (105) through Expression (108), the integral range needs to be set in light of the position y in the Y direction where the center of the pixel value M (l) to be obtained (however, l is any integer value of 1 through 4) exists, i.e., the shift amount Cx (Y).
Specifically, for example, the position y in the Y direction where the centers of the pixel 3111 and pixel 3112 exist is not y=0 but y=0.25.
Accordingly, the waveform of the approximation function f(x) at y=0.25 is equivalent to a waveform obtained by moving the waveform of the approximation function f(x) at y=0 by the shift amount Cx (0.25) in the X direction.
In other words, in the above Expression (105), if we say that the pixel value M (l) as to the pixel 3111 is obtained by integrating the approximation function f(x) at y=0 with a predetermined integral range (from the start position xs1 to the end position xe1), the integral range thereof becomes not a range from the start position xs1=−0.5 to the end position xe1=0 (a range itself where the pixel 3111 occupies in the X direction) but the range shown in FIG. 91, i.e., from the start position xs1=−0.5+Cx (0.25) to the end position xe1=0+Cx (0.25) (a range where the pixel 3111 occupies in the X direction in the event that the pixel 3111 is tentatively moved by the shift amount Cx (0.25)).
Similarly, in the above Expression (106), if we say that the pixel value M (2) as to the pixel 3112 is obtained by integrating the approximation function f(x) at y=0 with a predetermined integral range (from the start position xs2 to the end position xe2), the integral range thereof becomes not a range from the start position xs2=0 to the end position xe2=0.5 (a range itself where the pixel 3112 occupies in the X direction) but the range shown in FIG. 91, i.e., from the start position xs2=0+Cx (0.25) to the end position xe1=0.5+Cx(0.25) (a range where the pixel 3112 occupies in the X direction in the event that the pixel 3112 is tentatively moved by the shift amount Cx (0.25)).
Also, for example, the position y in the Y direction where the centers of the pixel 3113 and pixel 3114 exist is not y=0 but y=−0.25.
Accordingly, the waveform of the approximation function f(x) at y=−0.25 is equivalent to a waveform obtained by moving the waveform of the approximation function f(x) at y=0 by the shift amount Cx (−0.25) in the X direction.
In other words, in the above Expression (107), if we say that the pixel value M (3) as to the pixel 3113 is obtained by integrating the approximation function f(x) at y=0 with a predetermined integral range (from the start position xs3 to the end position xe3), the integral range thereof becomes not a range from the start position xs3=−0.5 to the end position Xe3=0 (a range itself where the pixel 3113 occupies in the X direction) but the range shown in FIG. 91, i.e., from the start position xe3=−0.5+Cx(−0.25) to the end position xe3=0+Cx(−0.25) (a range where the pixel 3113 occupies in the X direction in the event that the pixel 3113 is tentatively moved by the shift amount Cx (−0.25)).
Similarly, in the above Expression (108), if we say that the pixel value M (4) as to the pixel 3114 is obtained by integrating the approximation function f(x) at y=0 with a predetermined integral range (from the start position xs4 to the end position xe4), the integral range thereof becomes not a range from the start position xs4=0 to the end position xe4=0.5 (a range itself where the pixel 3114 occupies in the X direction) but the range shown in FIG. 91, i.e., from the start position Xs4=0+Cx (−0.25) to the end position xe1=0.5+Cx(−0.25) (a range where the pixel 3114 occupies in the X direction in the event that the pixel 3114 is tentatively moved by the shift amount Cx(−0.25)).
Accordingly, the image generating unit 102 (FIG. 89) calculates the above Expression (105) through Expression (108) by substituting the corresponding integral range of the above integral ranges for each of these expressions, and outputs the calculated results of these as the output pixel values M (1) through M (4).
Thus, the image generating unit 102 can create four pixels having higher spatial resolution than that of the output pixel 3101, i.e., the pixel 3111 through pixel 3114 (FIG. 91) by employing the one-dimensional reintegration method as a pixel at the output pixel 3101 (FIG. 90) from the sensor 2 (FIG. 89). Further, though not shown in the drawing, as described above, the image generating unit 102 can create a pixel having an arbitrary powered spatial resolution as to the output pixel 3101 without deterioration by appropriately changing an integral range, in addition to the pixel 3111 through pixel 3114.
FIG. 92 represents a configuration example of the image generating unit 103 employing such a one-dimensional reintegration method.
As shown in FIG. 92, the image generating unit 103 shown in this example includes a conditions setting unit 3121, features storage unit 3122, integral component calculation unit 3123, and output pixel value calculation unit 3124.
The conditions setting unit 3121 sets the number of dimensions n of the approximation function f(x) based on the actual world estimating information (the features of the approximation function f(x) in the example in FIG. 92) supplied from the actual world estimating unit 102.
The conditions setting unit 3121 also sets an integral range in the case of reintegrating the approximation function f(x) (in the case of calculating an output pixel value). Note that an integral range set by the conditions setting unit 3121 does not need to be the width of a pixel. For example, the approximation function f(x) is integrated in the spatial direction (X direction), and accordingly, a specific integral range can be determined as long as the relative size (power of spatial resolution) of an output pixel (pixel to be calculated by the image generating unit 103) as to the spatial size of each pixel of an input image from the sensor 2 (FIG. 89) is known. Accordingly, the conditions setting unit 3121 can set, for example, a spatial resolution power as an integral range.
The features storage unit 3122 temporally stores the features of the approximation function f(x) sequentially supplied from the actual world estimating unit 102. Subsequently, upon the features storage unit 3122 storing all of the features of the approximation function f(x), the features storage unit 3122 generates a features table including all of the features of the approximation function f(x), and supplies this to the output pixel value calculation unit 3124.
Incidentally, as described above, the image generating unit 103 calculates the output pixel value M using the above Expression (103), but the approximation function f(x) included in the right side of the above Expression (103) is represented as the following Expression (109) specifically.




  
    
      
        
          f
          ⁡
          
            (
            x
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ×
            
              x
              i
            
            ⁢
            
              d
              x
            
          
        
      
    
    
      
        (
        109
        )
      
    
  




Note that in Expression (109), wi represents the features of the approximation function f(x) supplied from the actual world estimating unit 102.
Accordingly, upon the approximation function f(x) of Expression (109) being substituted for the approximation function f(x) of the right side of the above Expression (103) so as to expand (calculate) the right side of Expression (103), the output pixel value M is represented as the following Expression (110).




  
    
      
        
          
            
              M
              =
              
              ⁢
              
                
                  G
                  e
                
                ×
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    n
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      w
                      i
                    
                    ×
                    
                      
                        
                          x
                          e
                          
                            i
                            +
                            1
                          
                        
                        -
                        
                          x
                          s
                          
                            i
                            +
                            1
                          
                        
                      
                      
                        i
                        +
                        1
                      
                    
                  
                
              
            
          
        
        
          
            
              =
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  n
                
                ⁢
                
                  
                
                ⁢
                
                  
                    w
                    i
                  
                  ×
                  
                    
                      k
                      i
                    
                    ⁡
                    
                      (
                      
                        
                          x
                          s
                        
                        ,
                        
                          x
                          e
                        
                      
                      )
                    
                  
                
              
            
          
        
      
    
    
      
        (
        110
        )
      
    
  




In Expression (110), Ki (xs, xe) represent the integral components of the i-dimensional term. That is to say, the integral components Ki (xs, xe) are such as shown in the following Expression (111).




  
    
      
        
          
            k
            i
          
          ⁡
          
            (
            
              
                x
                s
              
              ,
              
                x
                e
              
            
            )
          
        
        =
        
          
            G
            e
          
          ×
          
            
              
                x
                e
                
                  i
                  +
                  1
                
              
              -
              
                x
                s
                
                  i
                  +
                  1
                
              
            
            
              i
              +
              1
            
          
        
      
    
    
      
        (
        111
        )
      
    
  




The integral component calculation unit 3123 calculates the integral components Ki (xs, xe).
Specifically, as shown in Expression (111), the integral components Ki(xs, xe) can be calculated as long as the start position xs and end position xe of an integral range, gain Ge, and i of the i-dimensional term are known.
Of these, the gain Ge is determined with the spatial resolution power (integral range) set by the conditions setting unit 3121.
The range of i is determined with the number of dimensions n set by the conditions setting unit 3121.
Also, each of the start position xs and end position xe of an integral range is determined with the center pixel position (x, y) and pixel width of an output pixel to be generated from now, and the shift amount Cx (y) representing the direction of data continuity. Note that (x, y) represents the relative position from the center position of a pixel of interest when the actual world estimating unit 102 generates the approximation function f(x).
Further, each of the center pixel position (x, y) and pixel width of an output pixel to be generated from now is determined with the spatial resolution power (integral range) set by the conditions setting unit 3121.
Also, with the shift amount Cx(y), and the angle θ supplied from the data continuity detecting unit 101, the relation such as the following Expression (112) and Expression (113) holds, and accordingly, the shift amount Cx (y) is determined with the angle θ.




  
    
      
        
          G
          f
        
        =
        
          
            tan
            ⁢
            
              
            
            ⁢
            θ
          
          =
          
            
              d
              y
            
            
              d
              x
            
          
        
      
    
    
      
        (
        112
        )
      
    
  
  
    
      
        
          
            C
            x
          
          ⁡
          
            (
            y
            )
          
        
        =
        
          y
          
            G
            f
          
        
      
    
    
      
        (
        113
        )
      
    
  




Note that in Expression (112), Gf represents a gradient representing the direction of data continuity, θ represents an angle (angle generated between the X direction serving as one direction of the spatial directions and the direction of data continuity represented with a gradient Gf) of one of the data continuity information output from the data continuity detecting unit 101 (FIG. 89). Also, dx represents the amount of fine movement in the X direction, and dy represents the amount of fine movement in the Y direction (spatial direction perpendicular to the X direction) as to the dx.
Accordingly, the integral component calculation unit 3123 calculates the integral components Ki (xs, xe) based on the number of dimensions and spatial resolution power (integral range) set by the conditions setting unit 3121, and the angle θ of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated results to the output pixel value calculation unit 3124 as an integral component table.
The output pixel value calculation unit 3124 calculates the right side of the above Expression (110) using the features table supplied from the features storage unit 3122 and the integral component table supplied from the integral component calculation unit 3123, and outputs the calculation result as an output pixel value M.
Next, description will be made regarding image generating processing (processing in step S103 in FIG. 29) by the image generating unit 103 (FIG. 92) employing the one-dimensional reintegration method with reference to the flowchart in FIG. 93.
For example, now, let us say that the actual world estimating unit 102 has already generated the approximation function f(x) such as shown in FIG. 90 while taking the pixel 3101 such as shown in FIG. 90 described above as a pixel of interest at the processing in step S102 in FIG. 29 described above.
Also, let us say that the data continuity detecting unit 101 has already output the angle θ such as shown in FIG. 90 as data continuity information at the processing in step S101 in FIG. 29 described above.
In this case, the conditions setting unit 3121 sets conditions (the number of dimensions and an integral range) at step S3101 in FIG. 93.
For example, now, let us say that 5 has been set as the number of dimensions, and also a spatial quadruple density (spatial resolution power to cause the pitch width of a pixel to become half power in the upper/lower/left/right sides) has been set as an integral range.
That is to say, in this case, consequently, it has been set that the four pixel 3111 through pixel 3114 are created newly in a range of −0.5 through 0.5 in the X direction, and also a range of −0.5 through 0.5 in the Y direction (in the range of the pixel 3101 in FIG. 90), such as shown in FIG. 91.
In step S3102, the features storage unit 3122 acquires the features of the approximation function f(x) supplied from the actual world estimating unit 102, and generates a features table. In this case, coefficients w0 through w5 of the approximation function f(x) serving as a five-dimensional polynomial are supplied from the actual world estimating unit 102, and accordingly, (w0, w1, w2, w3, w4, w5) is generated as a features table.
In step S3103, the integral component calculation unit 3123 calculates integral components based on the conditions (the number of dimensions and integral range) set by the conditions setting unit 3121, and the data continuity information (angle θ) supplied from the data continuity detecting unit 101, and generates an integral component table.
Specifically, for example, if we say that the respective pixels 3111 through 3114, which are to be generated from now, are appended with numbers (hereafter, such a number is referred to as a mode number) 1 through 4, the integral component calculation unit 3123 calculates the integral components Ki (xs, xe) of the above Expression (111) as a function of l (however, l represents a mode number) such as integral components Ki (l) shown in the left side of the following Expression (114).

Ki(1)=Ki(xs,xe)  (114)

Specifically, in this case, the integral components Ki (l) shown in the following Expression (115) are calculated.

ki(1)=ki(−0.5−Cx(−0.25), 0−Cx(−0.25))

ki(2)=ki(0−Cx(−0.25), 0.5−Cx(−0.25))

ki(3)=ki(−0.5−Cx(0.25), 0−Cx(0.25))

ki(4)=ki(0−Cx(0.25), 0.5−Cx(0.25))  (115)

Note that in Expression (115), the left side represents the integral components Ki (l), and the right side represents the integral components Ki (xs, xe). That is to say, in this case, l is any one of 1 through 4, and also i is any one of 0 through 5, and accordingly, 24 Ki (l) in total of 6 Ki (1), 6 Ki (2), 6 Ki (3), and 6 Ki (4) are calculated.
More specifically, first, the integral component calculation unit 3123 calculates each of the shift amounts Cx (−0.25) and Cx (0.25) from the above Expression (112) and Expression (113) using the angle θ supplied from the data continuity detecting unit 101.
Next, the integral component calculation unit 3123 calculates the integral components Ki (xs, xe) of each right side of the four expressions in Expression (115) regarding i=0 through 5 using the calculated shift amounts Cx (−0.25) and Cx (0.25). Note that with this calculation of the integral components Ki (xs, xe), the above Expression (111) is employed.
Subsequently, the integral component calculation unit 3123 converts each of the 24 integral components Ki (xs, xe) calculated into the corresponding integral components Ki(1) in accordance with Expression (115), and generates an integral component table including the 24 integral components Ki (l) converted (i.e., 6 Ki (1), 6 Ki (2), 6 Ki (3), and 6 Ki (4)).
Note that the sequence of the processing in step S3102 and the processing in step S3103 is not restricted to the example in FIG. 93, the processing in step S3103 may be executed first, or the processing in step S3102 and the processing in step S3103 may be executed simultaneously.
Next, in step S3104, the output pixel value calculation unit 3124 calculates the output pixel values M (1) through M (4) respectively based on the features table generated by the features storage unit 3122 at the processing in step S3102, and the integral component table generated by the integral component calculation unit 3123 at the processing in step S3103.
Specifically, in this case, the output pixel value calculation unit 3124 calculates each of the pixel value M (1) of the pixel 3111 (pixel of mode number 1), the pixel value M (2) of the pixel 3112 (pixel of mode number 2), the pixel value M (3) of the pixel 3113 (pixel of mode number 3), and the pixel value M (4) of the pixel 3114 (pixel of mode number 4) by calculating the right sides of the following Expression (116) through Expression (119) corresponding to the above Expression (110).




  
    
      
        
          M
          ⁡
          
            (
            1
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            5
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                k
                i
              
              ⁡
              
                (
                1
                )
              
            
          
        
      
    
    
      
        (
        116
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            2
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            5
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                k
                i
              
              ⁡
              
                (
                2
                )
              
            
          
        
      
    
    
      
        (
        117
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            3
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            5
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                k
                i
              
              ⁡
              
                (
                3
                )
              
            
          
        
      
    
    
      
        (
        118
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            4
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            5
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ⁢
            
              
                k
                i
              
              ⁡
              
                (
                4
                )
              
            
          
        
      
    
    
      
        (
        119
        )
      
    
  




In step S3105, the output pixel value calculation unit 3124 determines regarding whether or not the processing of all the pixels has been completed.
In step S3105, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S3102, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S3102 through S3104 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S3105, in the event that determination is made that the processing of all the pixels has been completed), the output pixel value calculation unit 3124 outputs the image in step S3106. Then, the image generating processing ends.
Next, description will be made regarding the differences between the output image obtained by employing the one-dimensional reintegration method and the output image obtained by employing another method (conventional classification adaptation processing) regarding a predetermined input image with reference to FIG. 94 through FIG. 101.
FIG. 94 is a diagram illustrating the original image of the input image, and FIG. 95 illustrates image data corresponding to the original image in FIG. 94. In FIG. 95, the axis in the vertical direction in the drawing represents pixel values, and the axis in the lower right direction in the drawing represents the X direction serving as one direction of the spatial directions of the image, and the axis in the upper right direction in the drawing represents the Y direction serving as the other direction of the spatial directions of the image. Note that the respective axes in later-described FIG. 97, FIG. 99, and FIG. 101 corresponds to the axes in FIG. 95.
FIG. 96 is a diagram illustrating an example of an input image. The input image illustrated in FIG. 96 is an image generated by taking the mean of the pixel values of the pixels belonged to a block made up of 2×2 pixels shown in FIG. 94 as the pixel value of one pixel. That is to say, the input image is an image obtained by integrating the image shown in FIG. 94 in the spatial direction, which imitates the integration property of a sensor. Also, FIG. 97 illustrates image data corresponding to the input image in FIG. 96.
The original image illustrated in FIG. 94 includes a fine-line image inclined almost 5° clockwise from the vertical direction. Similarly, the input image illustrated in FIG. 96 includes a fine-line image inclined almost 5° clockwise from the vertical direction.
FIG. 98 is a diagram illustrating an image (hereafter, the image illustrated in FIG. 98 is referred to as a conventional image) obtained by subjecting the input image illustrated in FIG. 96 to conventional class classification adaptation processing. Also, FIG. 99 illustrates image data corresponding to the conventional image.
Note that the class classification adaptation processing is made up of classification processing and adaptation processing, data is classified based on the property thereof by the class classification processing, and is subjected to the adaptation processing for each class, as described above. With the adaptation processing, for example, a low-quality or standard-quality image is subjected to mapping using a predetermined tap coefficient so as to be converted into a high-quality image.
FIG. 100 is a diagram illustrating a reintegration image (hereafter, the image illustrated in FIG. 100 is referred to as an image) obtained by applying the one-dimensional reintegration method, to the input image illustrated in FIG. 96. Also, FIG. 101 illustrates image data corresponding to the reintegration image.
It can be understood that upon the conventional image in FIG. 98 being compared with the reintegration image in FIG. 100, a fine-line image is different from that in the original image in FIG. 94 in the conventional image, but on the other hand, the fine-line image is almost the same as that in the original image in FIG. 94 in the reintegration image.
This difference is caused by a difference wherein the conventional class classification adaptation processing is a method for performing processing on the basis (origin) of the input image in FIG. 96, but on the other hand, the one-dimensional reintegration method is a method for estimating the original image in FIG. 94 (generating the approximation function f(x) corresponding to the original image) in light of continuity of a fine line, and performing processing (performing reintegration so as to calculate pixel values) on the basis (origin) of the original image estimated.
Thus, with the one-dimensional reintegration method, an output image (pixel values) is generated by integrating the approximation function f(x) in an arbitrary range on the basis (origin) of the approximation function f(x) (the approximation function f(x) of the X cross-sectional waveform F(x) in the actual world) serving as the one-dimensional polynomial generated with the one-dimensional approximating method.
Accordingly, with the one-dimensional reintegration method, it becomes possible to output an image more similar to the original image (the light signal in the actual world 1 which is to be cast in the sensor 2) in comparison with the conventional other methods.
Also, with the one-dimensional reintegration method, as described above, the integral range is arbitrary, and accordingly, it becomes possible to create resolution (temporal resolution or spatial resolution) different from the resolution of an input image by varying the integral range. That is to say, it becomes possible to generate an image having arbitrary powered resolution as well as an integer value as to the resolution of the input image.
Further, the one-dimensional reintegration method enables calculation of an output image (pixel values) with less calculation processing amount than other reintegration methods.
Next, description will be made regarding a two-dimensional reintegration method with reference to FIG. 102 through FIG. 108.
The two-dimensional reintegration method is based on condition that the approximation function f(x, y) has been generated with the two-dimensional polynomial approximating method.
That is to say, for example, it is an assumption that the image function F(x, y, t) representing the light signal in the actual world 1 (FIG. 89) having continuity in the spatial direction represented with the gradient GF has been approximated with a waveform projected in the spatial directions (X direction and Y direction), i.e., the waveform F(x, y) on the X-Y plane has been approximated with the approximation function f(x, y) serving as a n-dimensional (n is an arbitrary integer) polynomial, such as shown in FIG. 102.
In FIG. 102, the horizontal direction represents the X direction serving as one direction in the spatial directions, the upper right direction represents the Y direction serving as the other direction in the spatial directions, and the vertical direction represents light levels, respectively in the drawing. GF represents gradient as continuity in the spatial directions.
Note that with the example in FIG. 102, the direction of continuity is taken as the spatial directions (X direction and Y direction), so the projection function of a light signal to be approximated is taken as the function F(x, y), but as described later, the function F(x, t) or function F(y, t) may be a target of approximation according to the direction of continuity.
In the case of the example in FIG. 102, with the two-dimensional reintegration method, the output pixel value M is calculated as the following Expression (120).




  
    
      
        M
        =
        
          
            G
            e
          
          ×
          
            
              ∫
              
                y
                s
              
              
                y
                e
              
            
            ⁢
            
              
                ∫
                
                  x
                  s
                
                
                  x
                  e
                
              
              ⁢
              
                
                  f
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
              
            
          
        
      
    
    
      
        (
        120
        )
      
    
  




Note that in Expression (120), ys represents an integration start position in the Y direction, and Ye represents an integration end position in the Y direction. Similarly, xs represents an integration start position in the X direction, and xe represents an integration end position in the X direction. Also, Ge represents a predetermined gain.
In Expression (120), an integral range can be set arbitrarily, and accordingly, with the two-dimensional reintegration method, it becomes possible to create pixels having an arbitrary powered spatial resolution as to the original pixels (the pixels of an input image from the sensor 2 (FIG. 89)) without deterioration by appropriately changing this integral range.
FIG. 103 represents a configuration example of the image generating unit 103 employing the two-dimensional reintegration method.
As shown in FIG. 103, the image generating unit 103 in this example includes a conditions setting unit 3201, features storage unit 3202, integral component calculation unit 3203, and output pixel value calculation unit 3204.
The conditions setting unit 3201 sets the number of dimensions n of the approximation function f(x, y) based on the actual world estimating information (with the example in FIG. 103, the features of the approximation function f(x, y)) supplied from the actual world estimating unit 102.
The conditions setting unit 3201 also sets an integral range in the case of reintegrating the approximation function f(x, y) (in the case of calculating an output pixel value). Note that an integral range set by the conditions setting unit 3201 does not need to be the vertical width or the horizontal width of a pixel. For example, the approximation function f(x, y) is integrated in the spatial directions (X direction and Y direction), and accordingly, a specific integral range can be determined as long as the relative size (power of spatial resolution) of an output pixel (pixel to be generated from now by the image generating unit 103) as to the spatial size of each pixel of an input image from the sensor 2 is known. Accordingly, the conditions setting unit 3201 can set, for example, a spatial resolution power as an integral range.
The features storage unit 3202 temporally stores the features of the approximation function f(x, y) sequentially supplied from the actual world estimating unit 102. Subsequently, upon the features storage unit 3202 storing all of the features of the approximation function f(x, y), the features storage unit 3202 generates a features table including all of the features of the approximation function f(x, y), and supplies this to the output pixel value calculation unit 3204.
Now, description will be made regarding the details of the approximation function f(x, y).
For example, now, let us say that the light signals (light signals represented with the wave F (x, y)) in the actual world 1 (FIG. 89) having continuity in the spatial directions represented with the gradient GF shown in FIG. 102 described above have been detected by the sensor 2 (FIG. 89), and have been output as an input image (pixel values).
Further, for example, let us say that the data continuity detecting unit 101 (FIG. 3) has subjected a region 3221 of an input image made up of 20 pixels in total (20 squares represented with a dashed line in the drawing) of 4 pixels in the X direction and also 5 pixels in the Y direction of this input image to the processing thereof, and has output an angle θ (angle θ generated between the direction of data continuity represented with the gradient Gf corresponding to the gradient GF and the X direction) as one of data continuity information, as shown in FIG. 104.
Note that as viewed from the actual world estimating unit 102, the data continuity detecting unit 101 should simply output the angle θ at a pixel of interest, and accordingly, the processing region of the data continuity detecting unit 101 is not restricted to the above region 3221 in the input image.
Also, with the region 3221 in the input image, the horizontal direction in the drawing represents the X direction serving as one direction of the spatial directions, and the vertical direction in the drawing represents the Y direction serving the other direction of the spatial directions.
Further, in FIG. 104, a pixel, which is the second pixel from the left, and also the third pixel from the bottom, is taken as a pixel of interest, and an (x, y) coordinates system is set so as to take the center of the pixel of interest as the origin (0, 0). A relative distance (hereafter, referred to as a cross-sectional direction distance) in the X direction as to a straight line (straight line of the gradient Gf representing the direction of data continuity) having an angle θ passing through the origin (0, 0) is taken as x′.
Further, in FIG. 104, the graph on the right side represents the approximation function f(x′) serving as a n-dimensional (n is an arbitrary integer) polynomial, which is a function approximating a one-dimensional waveform (hereafter, referred to as an X cross-sectional waveform F(x′)) wherein the image function F(x, y, t) of which variables are positions x, y, and z on the three-dimensional space, and point-in-time t is projected in the X direction at an arbitrary position y in the Y direction. Of the axes in the graph on the right side, the axis in the horizontal direction in the drawing represents a cross-sectional direction distance, and the axis in the vertical direction in the drawing represents pixel values.
In this case, the approximation function f(x′) shown in FIG. 104 is a n-dimensional polynomial, so is represented as the following Expression (121).




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ′
            
            )
          
        
        =
        
          
            
              w
              0
            
            +
            
              
                w
                1
              
              ⁢
              
                x
                ′
              
            
            +
            
              
                w
                2
              
              ⁢
              
                x
                ′
              
            
            +
            ...
            +
            
              
                w
                n
              
              ⁢
              
                x
                
                  ′
                  ⁢
                  
                    
                  
                  ⁢
                  n
                
              
            
          
          =
          
            
              ∑
              
                i
                =
                0
              
              n
            
            ⁢
            
              
            
            ⁢
            
              
                w
                i
              
              ⁢
              
                x
                
                  ′
                  ⁢
                  
                    
                  
                  ⁢
                  i
                
              
            
          
        
      
    
    
      
        (
        121
        )
      
    
  




Also, since the angle θ is determined, the straight line having angle θ passing through the origin (0, 0) is uniquely determined, and a position x1 in the X direction of the straight line at an arbitrary position y in the Y direction is represented as the following Expression (122). However, in Expression (122), s represents cot θ.

x1=s×y  (122)

That is to say, as shown in FIG. 104, a point on the straight line corresponding to continuity of data represented with the gradient Gf is represented with a coordinate value (x1, y).
The cross-sectional direction distance x′ is represented as the following Expression (123) using Expression (122).

x′=x−x1=x−s×y  (123)

Accordingly, the approximation function f(x, y) at an arbitrary position (x, y) within the input image region 3221 is represented as the following Expression (124) using Expression (121) and Expression (123).




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ⁡
            
              (
              
                x
                -
                
                  s
                  ×
                  y
                
              
              )
            
          
        
      
    
    
      
        (
        124
        )
      
    
  




Note that in Expression (124), wi represents the features of the approximation function f(x, y).
Now, description will return to FIG. 103, wherein the features wi included in Expression (124) are supplied from the actual world estimating unit 102, and stored in the features storage unit 3202. Upon the features storage unit 3202 storing all of the features wi represented with Expression (124), the features storage unit 3202 generates a features table including all of the features wi, and supplies this to the output pixel value calculation unit 3204.
Also, upon the right side of the above Expression (120) being expanded (calculated) by substituting the approximation function f(x, y) of Expression (124) for the approximation function f(x, y) in the right side of Expression (120), the output pixel value M is represented as the following Expression (125).




  
    
      
        
          
            
              M
              =
              
                
                  G
                  e
                
                ×
                
                  -
                  
                    
                      ∑
                      
                        i
                        =
                        0
                      
                      n
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        w
                        i
                      
                      ×
                      
                        
                          
                            
                              
                                {
                                
                                  
                                    
                                      (
                                      
                                        
                                          x
                                          e
                                        
                                        -
                                        
                                          s
                                          ×
                                          
                                            y
                                            e
                                          
                                        
                                      
                                      )
                                    
                                    
                                      i
                                      +
                                      2
                                    
                                  
                                  -
                                  
                                    
                                      (
                                      
                                        
                                          x
                                          e
                                        
                                        -
                                        
                                          s
                                          ×
                                          
                                            y
                                            s
                                          
                                        
                                      
                                      )
                                    
                                    
                                      i
                                      +
                                      2
                                    
                                  
                                  -
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    
                                      (
                                      
                                        
                                          x
                                          s
                                        
                                        -
                                        
                                          s
                                          ×
                                          
                                            y
                                            e
                                          
                                        
                                      
                                      )
                                    
                                    
                                      i
                                      +
                                      2
                                    
                                  
                                  +
                                  
                                    
                                      (
                                      
                                        
                                          x
                                          s
                                        
                                        -
                                        
                                          s
                                          ×
                                          
                                            y
                                            s
                                          
                                        
                                      
                                      )
                                    
                                    
                                      i
                                      +
                                      2
                                    
                                  
                                
                                }
                              
                            
                          
                        
                        
                          
                            s
                            ⁡
                            
                              (
                              
                                i
                                +
                                1
                              
                              )
                            
                          
                          ⁢
                          
                            (
                            
                              i
                              +
                              2
                            
                            )
                          
                        
                      
                    
                  
                
              
            
          
        
        
          
            
              =
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  n
                
                ⁢
                
                  
                
                ⁢
                
                  
                    w
                    i
                  
                  ×
                  
                    
                      k
                      i
                    
                    ⁡
                    
                      (
                      
                        
                          x
                          s
                        
                        ,
                        
                          x
                          e
                        
                        ,
                        
                          y
                          s
                        
                        ,
                        
                          y
                          e
                        
                      
                      )
                    
                  
                
              
            
          
        
      
    
    
      
        (
        125
        )
      
    
  




In Expression (125), Ki (xs, xe, ys, ye) represent the integral components of the i-dimensional term. That is to say, the integral components Ki (xs, xe, ys, ye) are such as shown in the following Expression (126).




  
    
      
        
          
            k
            i
          
          ⁡
          
            (
            
              
                x
                s
              
              ,
              
                x
                e
              
              ,
              
                y
                s
              
              ,
              
                y
                e
              
            
            )
          
        
        =
        
          
            G
            e
          
          ×
          
            
              {
              
                
                  
                    (
                    
                      
                        x
                        e
                      
                      -
                      
                        s
                        ×
                        
                          y
                          e
                        
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                -
                
                  
                    (
                    
                      
                        x
                        e
                      
                      -
                      
                        s
                        ×
                        
                          y
                          s
                        
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                -
                
                  
                    (
                    
                      
                        x
                        s
                      
                      -
                      
                        s
                        ×
                        
                          y
                          e
                        
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
                +
                
                  
                    (
                    
                      
                        x
                        s
                      
                      -
                      
                        s
                        ×
                        
                          y
                          s
                        
                      
                    
                    )
                  
                  
                    i
                    +
                    2
                  
                
              
              }
            
            
              
                s
                ⁡
                
                  (
                  
                    i
                    +
                    1
                  
                  )
                
              
              ⁢
              
                (
                
                  i
                  +
                  2
                
                )
              
            
          
        
      
    
    
      
        (
        126
        )
      
    
  




The integral component calculation unit 3203 calculates the integral components Ki (xs, xe, Ys, ye).
Specifically, as shown in Expression (125) and Expression (126), the integral components Ki (xs, xe, ys, ye) can be calculated as long as the start position xs in the X direction and end position xe in the X direction of an integral range, the start position Ys in the Y direction and end position ye in the Y direction of an integral range, variable s, gain Ge, and i of the i-dimensional term are known.
Of these, the gain Ge is determined with the spatial resolution power (integral range) set by the conditions setting unit 3201.
The range of i is determined with the number of dimensions n set by the conditions setting unit 3201.
A variable s is, as described above, cot θ, so is determined with the angle θ output from the data continuity detecting unit 101.
Also, each of the start position xs in the X direction and end position xe in the X direction of an integral range, and the start position ys in the Y direction and end position ye in the Y direction of an integral range is determined with the center pixel position (x, y) and pixel width of an output pixel to be generated from now. Note that (x, y) represents a relative position from the center position of the pixel of interest when the actual world estimating unit 102 generates the approximation function f(x).
Further, each of the center pixel position (x, y) and pixel width of an output pixel to be generated from now is determined with the spatial resolution power (integral range) set by the conditions setting unit 3201.
Accordingly, the integral component calculation unit 3203 calculates integral components Ki (xs, xe, ys, ye) based on the number of dimensions and the spatial resolution power (integral range) set by the conditions setting unit 3201, and the angle θ of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated result to the output pixel value calculation unit 3204 as an integral component table.
The output pixel value calculation unit 3204 calculates the right side of the above Expression (125) using the features table supplied from the features storage unit 3202, and the integral component table supplied from the integral component calculation unit 3203, and outputs the calculated result to the outside as the output pixel value M.
Next, description will be made regarding image generating processing (processing in step S103 in FIG. 29) by the image generating unit 103 (FIG. 104) employing the two-dimensional reintegration method with reference to the flowchart in FIG. 105.
For example, let us say that the light signals represented with the function F(x, y) shown in FIG. 102 have been cast in the sensor 2 so as to become an input image, and the actual world estimating unit 102 has already generated the approximation function f(x, y) for approximating the function F(x, y) with one pixel 3231 such as shown in FIG. 106 as a pixel of interest at the processing in step S102 in FIG. 29 described above.
Note that in FIG. 106, the pixel value (input pixel value) of the pixel 3231 is taken as P, and the shape of the pixel 3231 is taken as a square of which one side is 1 in length. Also, of the spatial directions, the direction in parallel with one side of the pixel 3231 is taken as the X direction, and the direction orthogonal to the X direction is taken as the Y direction. Further, a coordinates system (hereafter, referred to as a pixel-of-interest coordinates system) in the spatial directions (X direction and Y direction) of which the origin is the center of the pixel 3231 is set.
Also, let us say that in FIG. 106, the data continuity detecting unit 101, which takes the pixel 3231 as a pixel of interest, has already output the angle θ as data continuity information corresponding to continuity of data represented with the gradient Gf at the processing in step S101 in FIG. 29 described above.
Description will return to FIG. 105, and in this case, the conditions setting unit 3201 sets conditions (the number of dimensions and an integral range) at step S3201.
For example, now, let us say that 5 has been set as the number of dimensions, and also spatial quadruple density (spatial resolution power to cause the pitch width of a pixel to become half power in the upper/lower/left/right sides) has been set as an integral range.
That is to say, in this case, it has been set that the four pixel 3241 through pixel 3244 are created newly in a range of −0.5 through 0.5 in the X direction, and also a range of −0.5 through 0.5 in the Y direction (in the range of the pixel 3231 in FIG. 106), such as shown in FIG. 107. Note that in FIG. 107 as well, the same pixel-of-interest coordinates system as that in FIG. 106 is shown.
Also, in FIG. 107, M (1) represents the pixel value of the pixel 3241 to be generated from now, M (2) represents the pixel value of the pixel 3242 to be generated from now, M (3) represents the pixel value of the pixel 3243 to be generated from now, and M (4) represents the pixel value of the pixel 3244 to be generated from now.
Description will return to FIG. 105, in step S3202, the features storage unit 3202 acquires the features of the approximation function f(x, y) supplied from the actual world estimating unit 102, and generates a features table. In this case, the coefficients w0 through w5 of the approximation function f(x) serving as a 5-dimensional polynomial are supplied from the actual world estimating unit 102, and accordingly, (w0, w1, w2, w3, w4, w5) is generated as a features table.
In step S3203, the integral component calculation unit 3203 calculates integral components based on the conditions (the number of dimensions and an integral range) set by the conditions setting unit 3201, and the data continuity information (angle θ) supplied from the data continuity detecting unit 101, and generates an integral component table.
Specifically, for example, let us say that numbers (hereafter, such a number is referred to as a mode number) 1 through 4 are respectively appended to the pixel 3241 through pixel 3244 to be generated from now, the integral component calculation unit 3203 calculates the integral components Ki (xs, xe, ys, ye) of the above Expression (125) as a function of l (however, l represents a mode number) such as the integral components Ki (l) shown in the left side of the following Expression (127).

Ki(l)=Ki(xs,xe,ys,ye)  (127)

Specifically, in this case, the integral components Ki (l) shown in the following Expression (128) are calculated.

ki(1)=ki(−0.5,0,0,0.5)

ki(2)=ki(0,0.5,0,0.5)

ki(3)=ki(−0.5,0, −0.5, 0)

ki(4)=ki(0,0.5, −0.5,0)  (128)

Note that in Expression (128), the left side represents the integral components Ki (l), and the right side represents the integral components Ki (xs, xe, ys, ye). That is to say, in this case, l is any one of 1 thorough 4, and also i is any one of 0 through 5, and accordingly, 24 Ki (l) in total of 6 Ki (1), 6 Ki (2), 6 Ki (3), and 6 Ki (4) are calculated.
More specifically, first, the integral component calculation unit 3203 calculates the variable s (s=cot θ) of the above Expression (122) using the angle θ supplied from the data continuity detecting unit 101.
Next, the integral component calculation unit 3203 calculates the integral components Ki (xs, xe, ys, ye) of each right side of the four expressions in Expression (128) regarding i=0 through 5 using the calculated variable s. Note that with this calculation of the integral components Ki (xs, xe, ys, ye), the above Expression (125) is employed.
Subsequently, the integral component calculation unit 3203 converts each of the 24 integral components Ki (xs, xe, ys, ye) calculated into the corresponding integral components Ki (l) in accordance with Expression (128), and generates an integral component table including the 24 integral components Ki (l) converted (i.e., 6 Ki (1), 6 Ki (2), 6 Ki (3), and 6 Ki (4)).
Note that the sequence of the processing in step S3202 and the processing in step S3203 is not restricted to the example in FIG. 105, the processing in step S3203 may be executed first, or the processing in step S3202 and the processing in step S3203 may be executed simultaneously.
Next, in step S3204, the output pixel value calculation unit 3204 calculates the output pixel values M (1) through M (4) respectively based on the features table generated by the features storage unit 3202 at the processing in step S3202, and the integral component table generated by the integral component calculation unit 3203 at the processing in step S3203.
Specifically, in this case, the output pixel value calculation unit 3204 calculates each of the pixel value M (1) of the pixel 3241 (pixel of mode number 1), the pixel value M (2) of the pixel 3242 (pixel of mode number 2), the pixel value M (3) of the pixel 3243 (pixel of mode number 3), and the pixel value M (4) of the pixel 3244 (pixel of mode number 4) shown in FIG. 107 by calculating the right sides of the following Expression (129) through Expression (132) corresponding to the above Expression (125).




  
    
      
        
          M
          ⁡
          
            (
            1
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ×
            
              
                k
                i
              
              ⁡
              
                (
                1
                )
              
            
          
        
      
    
    
      
        (
        129
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            2
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ×
            
              
                k
                i
              
              ⁡
              
                (
                2
                )
              
            
          
        
      
    
    
      
        (
        130
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            3
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ×
            
              
                k
                i
              
              ⁡
              
                (
                3
                )
              
            
          
        
      
    
    
      
        (
        131
        )
      
    
  
  
    
      
        
          M
          ⁡
          
            (
            4
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
          
          ⁢
          
            
              w
              i
            
            ×
            
              
                k
                i
              
              ⁡
              
                (
                4
                )
              
            
          
        
      
    
    
      
        (
        132
        )
      
    
  




However, in this case, each n of Expression (129) through Expression (132) becomes 5.
In step S3205, the output pixel value calculation unit 3204 determines regarding whether or not the processing of all the pixels has been completed.
In step S3205, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S3202, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S3202 through S3204 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S3205, in the event that determination is made that the processing of all the pixels has been completed), the output pixel value calculation unit 3204 outputs the image in step S3206. Then, the image generating processing ends.
Thus, four pixels having higher spatial resolution than the input pixel 3231, i.e., the pixel 3241 through pixel 3244 (FIG. 107) can be created by employing the two-dimensional reintegration method as a pixel at the pixel 3231 of the input image (FIG. 106) from the sensor 2 (FIG. 89). Further, though not shown in the drawing, as described above, the image generating unit 103 can create a pixel having an arbitrary powered spatial resolution as to the input pixel 3231 without deterioration by appropriately changing an integral range, in addition to the pixel 3241 through pixel 3244.
As described above, as description of the two-dimensional reintegration method, an example for subjecting the approximation function f(x, y) as to the spatial directions (X direction and Y direction) to two-dimensional integration has been employed, but the two-dimensional reintegration method can be applied to the time-space directions (X direction and t direction, or Y direction and t direction).
That is to say, the above example is an example in the case in which the light signals in the actual world 1 (FIG. 89) have continuity in the spatial directions represented with the gradient GF such as shown in FIG. 102, and accordingly, an expression including two-dimensional integration in the spatial directions (X direction and Y direction) such as shown in the above Expression (120) has been employed. However, the concept regarding two-dimensional integration can be applied not only to the spatial direction but also the time-space directions (X direction and t direction, or Y direction and t direction).
In other words, with the two-dimensional polynomial approximating method serving as an assumption of the two-dimensional reintegration method, it is possible to perform approximation using a two-dimensional approximation function f even in the case in which the image function F(x, y, t) representing the light signals has continuity in the time-space directions (however, X direction and t direction, or Y direction and t direction) as well as continuity in the spatial directions.
Specifically, for example, in the event that there is an object moving horizontally in the X direction at uniform velocity, the direction of movement of the object is represented with like a gradient VF in the X-t plane such as shown in FIG. 108. In other words, it can be said that the gradient VF represents the direction of continuity in the time-space directions in the X-t plane. Accordingly, the data continuity detecting unit 101 (FIG. 89) can output movement θ such as shown in FIG. 108 (strictly speaking, though not shown in the drawing, movement θ is an angle generated by the direction of data continuity represented with the gradient Vf corresponding to the gradient VF and the X direction in the spatial direction) as data continuity information corresponding to the gradient VF representing continuity in the time-space directions in the X-t plane as well as the above angle θ (data continuity information corresponding to the gradient GF representing continuity in the spatial directions in the X-Y plane).
Also, the actual world estimating unit 102 (FIG. 89) employing the two-dimensional polynomial approximating method can calculate the coefficients (features) wi of an approximation function f(x, t) with the same method as the above method by employing the movement θ instead of the angle θ described above. However, in this case, the equation to be employed is not the above Expression (124) but the following Expression (133).




  
    
      
        
          f
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
              w
              i
            
            ⁡
            
              (
              
                x
                -
                
                  s
                  ×
                  t
                
              
              )
            
          
        
      
    
    
      
        (
        133
        )
      
    
  




Note that in Expression (133), s is cot θ (however, θ is movement).
Accordingly, the image generating unit 103 (FIG. 89) employing the two-dimensional reintegration method can calculate the pixel value M by substituting the f (x, t) of the above Expression (133) for the right side of the following Expression (134), and calculating this.




  
    
      
        M
        =
        
          
            G
            e
          
          ×
          
            
              ∫
              
                t
                s
              
              
                t
                e
              
            
            ⁢
            
              
                ∫
                
                  x
                  s
                
                
                  x
                  e
                
              
              ⁢
              
                
                  f
                  ⁡
                  
                    (
                    
                      x
                      ,
                      t
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  t
                
              
            
          
        
      
    
    
      
        (
        134
        )
      
    
  




Note that in Expression (134), ts represents an integration start position in the t direction, and te represents an integration end position in the t direction. Similarly, xs represents an integration start position in the X direction, and xe represents an integration end position in the X direction. Ge represents a predetermined gain.
Alternately, an approximation function f(y, t) focusing attention on the spatial direction Y instead of the spatial direction X can be handled as the same way as the above approximation function f(x, t).
Incidentally, in Expression (133), it becomes possible to obtain data not integrated in the temporal direction, i.e., data without movement blurring by regarding the t direction as constant, i.e., by performing integration while ignoring integration in the t direction. In other words, this method may be regarded as one of two-dimensional reintegration methods in that reintegration is performed on condition that one certain dimension of the two-dimensional approximation function f is constant, or in fact, may be regarded as one of one-dimensional reintegration methods in that one-dimensional reintegration in the X direction is performed.
Also, in Expression (134), an integral range may be set arbitrarily, and accordingly, with the two-dimensional reintegration method, it becomes possible to create a pixel having an arbitrary powered resolution as to the original pixel (pixel of an input image from the sensor 2 (FIG. 89)) without deterioration by appropriately changing this integral range.
That is to say, with the two-dimensional reintegration method, it becomes possible to create temporal resolution by appropriately changing an integral range in the temporal direction t. Also, it becomes possible to create spatial resolution by appropriately changing an integral range in the spatial direction X (or spatial direction Y). Further, it becomes possible to create both temporal resolution and spatial resolution by appropriately changing each integral range in the temporal direction t and in the spatial direction X.
Note that as described above, creation of any one of temporal resolution and spatial resolution may be performed even with the one-dimensional reintegration method, but creation of both temporal resolution and spatial resolution cannot be performed with the one-dimensional reintegration method in theory, which becomes possible only by performing two-dimensional or more reintegration. That is to say, creation of both temporal resolution and spatial resolution becomes possible only by employing the two-dimensional reintegration method and a later-described three-dimensional reintegration method.
Also, the two-dimensional reintegration method takes not one-dimensional but two-dimensional integration effects into consideration, and accordingly, an image more similar to the light signal in the actual world 1 (FIG. 89) may be created.
Next, description will be made regarding a three-dimensional reintegration method with reference to FIG. 109 and FIG. 110.
With the three-dimensional reintegration method, the approximation function f(x, y, t) has been created using the three-dimensional approximating method, which is an assumption.
In this case, with the three-dimensional reintegration method, the output pixel value M is calculated as the following Expression (135).




  
    
      
        M
        =
        
          
            G
            e
          
          ×
          
            
              ∫
              
                t
                s
              
              
                t
                e
              
            
            ⁢
            
              
                ∫
                
                  y
                  s
                
                
                  y
                  e
                
              
              ⁢
              
                
                  ∫
                  
                    x
                    s
                  
                  
                    x
                    e
                  
                
                ⁢
                
                  
                    f
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                        ,
                        t
                      
                      )
                    
                  
                  ⁢
                  
                    d
                    x
                  
                  ⁢
                  
                    d
                    y
                  
                  ⁢
                  
                    d
                    t
                  
                
              
            
          
        
      
    
    
      
        (
        135
        )
      
    
  




Note that in Expression (135), ts represents an integration start position in the t direction, and te represents an integration end position in the t direction. Similarly, ys represents an integration start position in the Y direction, and ye represents an integration end position in the Y direction. Also, xs represents an integration start position in the X direction, and xe represents an integration end position in the X direction. Ge represents a predetermined gain.
Also, in Expression (135), an integral range may be set arbitrarily, and accordingly, with the three-dimensional reintegration method, it becomes possible to create a pixel having an arbitrary powered time-space resolution as to the original pixel (pixel of an input image from the sensor 2 (FIG. 89)) without deterioration by appropriately changing this integral range. That is to say, upon the integral range in the spatial direction being reduced, a pixel pitch can be reduced without restraint. On the other hand, upon the integral range in the spatial direction being enlarged, a pixel pitch can be enlarged without restraint. Also, upon the integral range in the temporal direction being reduced, temporal resolution can be created based on an actual waveform.
FIG. 109 represents a configuration example of the image generating unit 103 employing the three-dimensional reintegration method.
As shown in FIG. 109, this example of the image generating unit 103 includes a conditions setting unit 3301, features storage unit 3302, integral component calculation unit 3303, and output pixel value calculation unit 3304.
The conditions setting unit 3301 sets the number of dimensions n of the approximation function f(x, y, t) based on the actual world estimating information (with the example in FIG. 109, features of the approximation function f(x, y, t)) supplied from the actual world estimating unit 102.
The conditions setting unit 3301 sets an integral range in the case of reintegrating the approximation function f(x, y, t) (in the case of calculating output pixel values). Note that an integral range set by the conditions setting unit 3301 needs not to be the width (vertical width and horizontal width) of a pixel or shutter time itself. For example, it becomes possible to determine a specific integral range in the spatial direction as long as the relative size (spatial resolution power) of an output pixel (pixel to be generated from now by the image generating unit 103) as to the spatial size of each pixel of an input image from the sensor 2 (FIG. 89) is known. Similarly, it becomes possible to determine a specific integral range in the temporal direction as long as the relative time (temporal resolution power) of an output pixel value as to the shutter time of the sensor 2 (FIG. 89) is known. Accordingly, the conditions setting unit 3301 can set, for example, a spatial resolution power and temporal resolution power as an integral range.
The features storage unit 3302 temporally stores the features of the approximation function f(x, y, t) sequentially supplied from the actual world estimating unit 102. Subsequently, upon the features storage unit 3302 storing all of the features of the approximation function f(x, y, t), the features storage unit 3302 generates a features table including all of the features of the approximation function f(x, y, t), and supplies this to the output pixel value calculation unit 3304.
Incidentally, upon the right side of the approximation function f(x, y) of the right side of the above Expression (135) being expanded (calculated), the output pixel value M is represented as the following Expression (136).




  
    
      
        M
        =
        
          
            ∑
            
              i
              =
              0
            
            n
          
          ⁢
          
            
              w
              i
            
            ×
            
              
                k
                i
              
              ⁡
              
                (
                
                  
                    x
                    s
                  
                  ,
                  
                    x
                    e
                  
                  ,
                  
                    y
                    s
                  
                  ,
                  
                    y
                    e
                  
                  ,
                  
                    t
                    s
                  
                  ,
                  
                    t
                    e
                  
                
                )
              
            
          
        
      
    
    
      
        (
        136
        )
      
    
  




In Expression (136), Ki (xs, xe, ys, ye, ts, te) represents the integral components of the i-dimensional term. However, xs represents an integration range start position in the X direction, xe represents an integration range end position in the X direction, ys represents an integration range start position in the Y direction, ye represents an integration range end position in the Y direction, ts represents an integration range start position in the t direction, and te represents an integration range end position in the t direction, respectively.
The integral component calculation unit 3303 calculates the integral components Ki (xs, xe, ys, ye, ts, te).
Specifically, the integral component calculation unit 3303 calculates the integral components Ki (xs, xe, ys, ye, ts, te) based on the number of dimensions and the integral range (spatial resolution power or temporal resolution power) set by the conditions setting unit 3301, and the angle θ or movement θ of the data continuity information output from the data continuity detecting unit 101, and supplies the calculated results to the output pixel value calculation unit 3304 as an integral component table.
The output pixel value calculation unit 3304 calculates the right side of the above Expression (136) using the features table supplied from the features storage unit 3302, and the integral component table supplied from the integral component calculation unit 3303, and outputs the calculated result to the outside as the output pixel value M.
Next, description will be made regarding image generating processing (processing in step S103 in FIG. 29) by the image generating unit 103 (FIG. 109) employing the three-dimensional reintegration method with reference to the flowchart in FIG. 110.
For example, let us say that the actual world estimating unit 102 (FIG. 89) has already generated an approximation function f(x, y, t) for approximating the light signals in the actual world 1 (FIG. 89) with a predetermined pixel of an input image as a pixel of interest at the processing in step S102 in FIG. 29 described above.
Also, let us say that the data continuity detecting unit 101 (FIG. 89) has already output the angle θ or movement θ as data continuity information with the same pixel as the actual world estimating unit 102 as a pixel of interest at the processing in step S101 in FIG. 29.
In this case, the conditions setting unit 3301 sets conditions (the number of dimensions and an integral range) at step S3301 in FIG. 110.
In step S3302, the features storage unit 3302 acquires the features wi of the approximation function f(x, y, t) supplied from the actual world estimating unit 102, and generates a features table.
In step S3303, the integral component calculation unit 3303 calculates integral components based on the conditions (the number of dimensions and an integral range) set by the conditions setting unit 3301, and the data continuity information (angle θ or movement θ) supplied from the data continuity detecting unit 101, and generates an integral component table.
Note that the sequence of the processing in step S3302 and the processing in step S3303 is not restricted to the example in FIG. 110, the processing in step S3303 may be executed first, or the processing in step S3302 and the processing in step S3303 may be executed simultaneously.
Next, in step S3304, the output pixel value calculation unit 3304 calculates each output pixel value based on the features table generated by the features storage unit 3302 at the processing in step S3302, and the integral component table generated by the integral component calculation unit 3303 at the processing in step S3303.
In step S3305, the output pixel value calculation unit 3304 determines regarding whether or not the processing of all the pixels has been completed.
In step S3305, in the event that determination is made that the processing of all the pixels has not been completed, the processing returns to step S3302, wherein the subsequent processing is repeatedly performed. That is to say, the pixels that have not become a pixel of interest are sequentially taken as a pixel of interest, and the processing in step S3302 through S3304 is repeatedly performed.
In the event that the processing of all the pixels has been completed (in step S3305, in the event that determination is made that the processing of all the pixels has been completed), the output pixel value calculation unit 3304 outputs the image in step S3306. Then, the image generating processing ends.
Thus, in the above Expression (135), an integral range may be set arbitrarily, and accordingly, with the three-dimensional reintegration method, it becomes possible to create a pixel having an arbitrary powered resolution as to the original pixel (pixel of an input image from the sensor 2 (FIG. 89)) without deterioration by appropriately changing this integral range.
That is to say, with the three-dimensional reintegration method, appropriately changing an integral range in the temporal direction enables temporal resolution to be created. Also, appropriately changing an integral range in the spatial direction enables spatial resolution to be created. Further, appropriately changing each integral range in the temporal direction and in the spatial direction enables both temporal resolution and spatial resolution to be created.
Specifically, with the three-dimensional reintegration method, approximation is not necessary when degenerating three dimension to two dimension or one dimension, thereby enabling high-precision processing. Also, movement in an oblique direction may be processed without degenerating to two dimension. Further, no degenerating to two dimension enables process at each dimension. For example, with the two-dimensional reintegration method, in the event of degenerating in the spatial directions (X direction and Y direction), process in the t direction serving as the temporal direction cannot be performed. On the other hand, with the thee-dimensional reintegration method, any process in the time-space directions may be performed.
Note that as described above, creation of any one of temporal resolution and spatial resolution may be performed even with the one-dimensional reintegration method, but creation of both temporal resolution and spatial resolution cannot be performed with the one-dimensional reintegration method in theory, which becomes possible only by performing two-dimensional or more reintegration. That is to say, creation of both temporal resolution and spatial resolution becomes possible only by employing the above two-dimensional reintegration method and the three-dimensional reintegration method.
Also, the three-dimensional reintegration method takes not one-dimensional and two-dimensional but three-dimensional integration effects into consideration, and accordingly, an image more similar to the light signal in the actual world 1 (FIG. 89) may be created.
Next, with the signal processing device 4 shown in FIG. 3, data continuity is detected at the data continuity detecting unit 101, and estimation of actual world 1 signal waveforms, i.e., for example, an approximation function approximating the X-cross-section waveform F(x), is obtained at the actual world estimating unit 102, based on the continuity.
Thus, waveform estimation of actual world 1 signals is performed at the signal processing device 4 based on continuity, so in the event that the continuity detected by the data continuity detecting unit 101 is incorrect or detection precision thereof is poor, the estimation precision of the waveform of the actual world 1 signals is also poor.
Also, the signal processing device 4 performs signal processing based on continuity which actual world 1 signals, which is an image in this case, for example, have, signal processing with better precision than signal processing with other signal processing devices can be performed for the parts of the actual world 1 signals where continuity exists, and consequently, an image closer to the image corresponding to the actual world 1 signals can be output.
However, the signal processing device 4 cannot perform signal processing for parts of the actual world 1 signals where no clear continuity exists at the same level of precision as four parts were continuity does exist, since the signal processing is being performed based on continuity, and consequently, an image including error with regard to the image corresponding to the actual world 1 signals is output.
Accordingly, in order to obtain an image closer to the image corresponding to the actual world 1 signals with the signal processing device 4, processing regions where signal processing with the signal processing device 4 is to be performed, precision of the continuity used with the signal processing device 4, and so forth, are issues.
Here, FIG. 111 illustrates the configuration example of another embodiment of the signal processing device 4.
In FIG. 111, the signal processing device 4 comprises a processing region setting unit 10001, a continuity setting unit 10002, an actual world estimating unit 10003, an image generating unit 10004, an image display unit 10005, and a user I/F (Interface) 10006.
With the signal processing device 4 of which the configuration is shown in FIG. 111, image data (input image) which is an example of the data 3, is input from the sensor 2 (FIG. 1), and the input image is supplied to the processing region setting unit 10001, the continuity setting unit 10002, the actual world estimating unit 10003, the image generating unit 10004, and the image display unit 10005.
The processing region setting unit 1001 sets the processing region for the input image, and supplies processing region information identifying the processing region to the continuity setting unit 10002, the actual world estimating unit 10003, and the image generating unit 10004.
The continuity setting unit 10002 recognizes the processing region in the input image from the processing region information supplied from the processing regions setting unit 10001, sets the continuity of the actual world 1 signals lost from the image data at that processing region, and supplies continuity information representing that continuity to the actual world estimating unit 10003 and the image generating unit 10004.
The actual world estimating unit 10003 is configured of a model generating unit 10011, equation generating unit 10012, and actual world waveform estimating unit 10013, and estimates the actual world 1 signals from the image data within the processing region, according to the continuity of the corresponding actual world 1 signals.
That is to say, the model generating unit 10011 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 10001, generates a function serving as a model which models the relation between the pixel values of the pixels within the processing region and the actual world 1 signals, according to the pixels making up the processing region and the continuity of the actual world 1 signals corresponding to the image data in the processing region, and supplies this to the equation generating unit 10012.
The question generating unit 10012 recognizes the processing region in the input image from the processing region information supplied from the processing regions setting unit 10001. Further, the equation generating unit 10012 substitutes the pixel values of each of the pixels making up the processing region into the function serving as a model that has been supplied from the model generating unit 10011, thereby generating an equation, which is supplied to the actual world waveform estimating unit 10013.
The actual world waveform estimating unit 10013 estimates the waveform of the actual world 1 signals, by computing the equation supplied from the equation generating unit 10012. That is to say, the actual world waveform estimating unit 10013 obtains an approximation function approximating the actual world 1 signals by solving the equation supplied from the equation generating unit 10012, and supplies the approximation function to the image generating unit 10004, as estimation results of the waveform of the actual world 1 signals. Note that approximation function approximating the actual world 1 signals include functions with constant function values, regardless of argument value.
The image generating unit 10004 generates signals closer approximating the actual world 1 signals, based on the approximation function representing the waveform of the actual world 1 signals estimated at the actual world estimating unit 10003, and the continuity information supplied from the continuity setting unit 10002. That is to say, the image generating unit 10004 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 10001, and generates image data closer approximating the image corresponding to the actual world 1 signals with regard to the processing region, based on the approximation function supplied from (the actual world waveform estimating unit 10013) of the actual world estimating unit 10003, and the continuity information supplied from the continuity setting unit 10002.
Further, the image generating unit 10004 synthesizes the input image and image data generated based on the approximation function (hereafter referred to as approximation image as appropriate), generates an image wherein the portion of the processing region of the input image has been substituted with the approximation image, and supplies the image as an output image to the image display unit 10005.
The image display unit 10005 is configured of a CRT (Cathode Ray Tube) or an LCD (Liquid Crystal Display), and displays input images, or output images supplied from the image generating unit 10004.
Note that the image display unit 10005 can be configured of single or multiple CRTs or LCDs. In the event of configuring the image display unit 10005 with a single CRT or LCD, an arrangement maybe made wherein the screen of the single CRT or LCD is divided into multiple screens, with input images displayed on one screen and output images displayed on another screen. Further, in the event of configuring the image display unit 10005 of multiple CRTs or LCDs, an arrangement may be made wherein input images are displayed on one CRT or LCD, and outputs images are displayed on another CRT or LCD.
Also, the image display unit 10005 performs display of various types in accordance with the output of the user I/F 10006. That is to say, the image display unit 10005 displays a cursor, for example, and in the event that the user operates the user I/F 10006 so as to move the cursor, the cursor is moved in accordance with the operations thereof. Also, in the event that the user operates the user I/F 10006 so as to select a predetermined range, the image display unit 10005 displays a frame surrounding the range selected on the screen in accordance with the operations thereof.
The user I/F 10006 is operated by the user, and in accordance with the user operations, supplies information relating to at least one of, for example, processing range, continuity, and real world signals, to the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10003.
That is to say, the user views an input image or output image displayed on the image display unit 10005, and operates the user I/F 10006 so as to provide input with regard to the input image or output image. The user I/F 10006 is operated by the user, and in accordance with the user operations, supplies information relating to processing range, continuity, or real world signals, to the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10003, as assisting information for assisting the processing of the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10003.
Upon assisting information being supplied from the user I/F 10006, the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10003 each perform setting of processing region, setting of continuity, or estimation of actual world 1 signals, based on the assisting information.
Note however, that the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10003, can each perform the setting of processing region, setting of continuity, or estimation of actual world 1 signals, even without using the assisting information, i.e., even without the user operating the user I/F 10006.
Specifically, with the processing region setting unit 10001, processing can be performed in the same way as with the data continuity detecting unit 101 shown in FIG. 3, as described with reference to FIG. 30 to FIG. 48, wherein a continuity region is detected from the input image, and a rectangular (oblong) region surrounding the continuity region is set as a processing region.
Also, with the continuity setting unit 10002, processing can be performed in the same way as with the data continuity detecting unit 101 shown in FIG. 3, as described with reference to FIG. 49 through FIG. 57, wherein data continuity is detected from the input image, and the continuity of the corresponding actual world 1 signals is set based on the continuity of that data, i.e., for example, the data continuity is set as continuity of the actual world 1 signals with no change.
Further, with the actual world estimating unit 10003, processing may be performed in the same way as with the actual world estimating unit 102 shown in FIG. 3, as described with reference to FIG. 58 through FIG. 88, where actual world 1 signals are estimated from the image data of the processing region set by the processing region setting unit 10001, corresponding to the continuity set by the continuity setting unit 10002. Note that while the data continuity has been used for estimating actual world 1 signals that the actual world estimating unit 102 in FIG. 3, an arrangement may be made wherein the continuity of corresponding actual world 1 signals is used instead of the data continuity for estimating actual world 1 signals.
Next, the processing of the signal processing device 4 shown in FIG. 111 will be described with reference to the flowchart in FIG. 112.
First, in step S10001, the signal processing device 4 performs pre-processing, and the flow proceeds to step S10002. That is to say, the signal processing device 4 supplies one frame or one field, for example, of the input image, supplied from the sensor 2 (FIG. 1) as data 3, to the processing region setting unit 10001, continuity setting unit 10002, actual world estimating unit 10003, image generating unit 10004, and image display unit 10005. Further, the signal processing unit 4 causes the image display unit 10005 to display the input image.
In step S10002, the user I/F 10006 determines whether or not there has been some sort of user input, by the user operating the user I/F 10006. In step S10002, in the event that determination is made that there is no user input, i.e., in the event that the user has made no operations, step S10003 through step S10005 are skipped, and the flow proceeds to step S10006.
Also, in the event that determination is made in step S10002 that there has been user input, i.e., in the event that the user has viewed the input image displayed on the image display unit 10005 and operated the user I/F 10006, thereby making user input indicating some sort of instruction or information, the flow proceeds to step S10003, where the user I/F 10006 determines whether or not the user input is ending instructions for instructing ending of the processing of the signal processing device 4.
In the event that determination is made in step S10003 that the user input is ending instructions, the signal processing device for ends processing.
Also, in the event that determination is made in step S10003 that the user input is not ending instructions, the flow proceeds to step S10004, where the user I/F 10006 determines whether or not the user input is assisting information. In the event that determination is made in step S10004 that the user input is not assisting information, the flow skips step S10005, and proceeds to step S10006.
Also, in the event that determination is made in step S10004 that the user input is assisting information, the flow proceeds to step S10005, where the user I/F 10006 supplies the assisting information to the processing region setting unit 10001, continuity setting unit 10002, or actual world estimating unit 10006, and the flow proceeds to step S10006.
In step S10006, the processing region setting unit 10001 sets the processing region based on the input image, and supplies the processing region information identifying the processing region to the continuity setting unit 10002, actual world estimating unit 10003, and image generating unit 10004, and the flow proceeds to step S10007. Now, in the event that assisting information has been supplied from the user I/F 10006 in that immediately-preceding step S10005, the processing region setting unit 10001 performs setting of the processing region using that assisting information.
In step S10007, the continuity setting unit 10002 recognizes the processing region in the input image, from the processing region information supplied from the processing region setting unit 10001. Further, the continuity setting unit 10002 sets continuity of the actual world 1 signals that has been lost in the image data of the processing region, and supplies continuity information indicating the continuity thereof to the actual world estimating unit 10003, and the flow proceeds to step S10008. Now, in the event that assisting information has been supplied from the user I/F 10006 in that immediately-preceding step S10005, the continuity setting unit 10002 performs setting of continuity using that assisting information.
In step S10008, the actual world estimating unit 10003 estimates actual world 1 signals regarding to the image data with in the processing region of the input image, according to the continuity of the corresponding actual world 1 signals.
That is to say, at the actual world estimating unit 10003, the model generating unit 10011 recognizes the processing region in the input image, from the processing region information supplied from the processing region setting unit 10001, and also recognizes continuity of the actual world 1 signals corresponding to the image data in the processing region, from the continuity information supplied from the continuity setting unit 10002. Further the model generating unit 10011 generates a function serving as a model modeling the relation between the pixel values of each of the pixels within the processing region and the actual world 1 signals, according to the pixels making up the processing region in the input image, and the continuity of actual world 1 signals corresponding to the image data of the processing region, and supplies this to the equation generating unit 10012.
The equation generating unit 10012 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 10001, and substitutes the pixel values of each of the pixels of the input image making up the processing region into the function serving as the model which is supplied from the model generating unit 10011, thereby generating an equation for obtaining an approximation function approximating the actual world 1 signals, which is supplied to the actual world waveform estimating unit 10013.
The actual world waveform estimating unit 10013 estimates the waveform of the actual world 1 signals by computing the equation supplied from the equation generating unit 10012. That is, the actual world waveform estimating unit 10013 obtains the approximation function serving as a model modeling the actual world 1 signals by solving the equation supplied from the equation generating unit 10012, and supplies the approximation function to the image generating unit 10004 as estimation results of the waveform of the actual world 1 signals.
Note that with the actual world estimating unit 10003, in the event that assisting information has been supplied from the user I/F 10006 in the immediately-preceding step S10005, at the model generating unit 10011 and equation generating unit 10012, processing is performed using that assisting information.
Following processing of step S10008, the flow proceeds to step S10009, where the image generating unit 10004 generates signals closer approximating the actual world 1 signals based on the approximation function approximating the waveform of the actual world 1 signals supplied from (the actual world waveform estimating unit 10013 of) the actual world estimating unit 10003. That is to say, the image generating unit 10004 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 10001, and with regard to this processing region, generates an approximation image which is image data closer approximating the image corresponding to the actual world 1 signals, based on the approximation function supplied from the actual world estimating unit 10003. Further the image generating unit 10004 generates, as an output image, an image wherein the portion of the processing region of the input image has been replaced with the approximation image, and supplies this to the image display 10005, and the flow proceeds from step S10009 to step S10010.
In step S10010, the image display unit 10005 displays the output image supplied from the image generating unit 10004 instead of the input image displayed in step S10001, or along with the input image, and the flow proceeds to step S10011.
In step S10011, the user I/F 10006 determines whether or not there has been user input of some sort by the user operating the user I/F 10006, in the same way as with step S10002, and in the event that determination is made that there has been no user input, i.e., in the event that the user has made no operations, the flow returns to step S10011, and awaits user input.
Also, in the event that determination is made in step S10011 that there has been user input, i.e., in the event that the user has viewed the input image or output image displayed on the image display unit 10005 and operated the user I/F 10006, thereby making some sort of user input indicating instruction or information, the flow proceeds to step S10012, where the user I/F 10006 determines whether or not the user input is ending instructions instructing ending of the processing of the signal processing device 4.
In the event that determination is made in step S10012 that the user input is ending instructions, the signal processing device 4 ends processing.
Also, in the event that determination is made in step S10012 that the user input is not ending instructions, the flow proceeds to step S10013, where the user I/F 10006 determines whether or not the user input is assisting information. In the event that determination is made in step S10013 that the user input is not assisting information, the flow returns to step S10011, and the same processing is repeated thereafter.
Also, in step S10013, in the event that determination is made that the user input is assisting information, the flow returns to step S10005, and as described above, the user I/F 10006 supplies the assisting information to the processing region setting unit 10001, the continuity setting unit 10002, or the actual world estimating unit 10006. The flow then proceeds from step S10005 to step S10006, and hereafter the same processing is repeated.
As described above, with the signal processing device 4 shown in FIG. 111, assisting information for assisting the processing region setting unit 10001, the continuity setting unit 10002, or the actual world estimating unit 10006, is supplied from the user I/F 10006 to the processing region setting unit 10001, the continuity setting unit 10002, or the actual world estimating unit 10003 and processing region setting, continuity setting, or actual world 1 signals estimation is performed at the processing region setting unit 10001, the continuity setting unit 10002, or the actual world estimating unit 10003 based on the assisting information from the user I/F 10006, thereby improving the processing precision of the processing region setting unit 10001, the continuity setting unit 10002, or the actual world estimating unit 10003, and enabling, for example, a high-quality output image meeting user preferences.
Next, various types of application examples of the signal processing device 4 shown in FIG. 111 will be described.
FIG. 113 illustrates a configuration example of an embodiment of an application example of the signal processing device 4 shown in FIG. 111.
In FIG. 113, the processing region setting unit 17001, the continuity setting unit 17002, the actual world estimating unit 17003, image generating unit 17004, image display unit 17005, and user I/F 17006, each correspond to the processing region setting unit 10001, the continuity setting unit 10002, the actual world estimating unit 10003, image generating unit 10004, image display unit 10005, and user I/F 10006 shown in FIG. 111, and basically perform the same processing as the processing region setting unit 10001, the continuity setting unit 10002, the actual world estimating unit 10003, image generating unit 10004, image display unit 10005, and user I/F 10006. Further; in FIG. 113, the actual world estimating unit 17003 comprises a model generating unit 17011, an equation generating unit 17012, and actual world waveform estimating unit 17013. The model generating unit 17011, equation generating unit 17012, and actual world waveform estimating unit 17013 correspond to each of the model generating unit 10011, equation generating unit 10012, and actual world waveform estimating unit 10013 in FIG. 111, and basically perform the same functions as each of the model generating unit 10011, equation generating unit 10012, and actual world waveform estimating unit 10013.
Note however, that in FIG. 113, the actual world estimating unit 17003 employs a spline function as an approximation function f.
Now, FIG. 113 illustrates one configuration example of the signal processing device 4 shown in FIG. 1, but in FIG. 1, for example, with the sensor 2 serving as an image sensor, the actual world 1 light signals are projected on multiple pixels each having time-space integration effects, i.e., the three-dimensional actual world 1 is projected with the sensor 2 serving as a two-dimensional image sensor, and according to the projection thereof, image data wherein part of the continuity of the actual world 1 light signal is missed is supplied to the signal processing device 4 from the sensor 2 as the data 3.
With the image data supplied to the signal processing device 4 from the sensor 2 as the data 3, part of the continuity of the actual world 1 light signal is missed, and some sort of distortion exists. The signal processing device 4 performs signal processing as to the image data having the distortion thereof.
FIG. 114 illustrates the type (category) of the signal processing performed as to the image data having distortion.
Examples of the types of the signal processing performed as to the image data having distortion are classified into “detection of distortion”, “removal of distortion”, “extraction of significant information”, and “signal processing considering distortion”.
Examples of processing included in “detection of distortion” include region identifying (extracting) processing for identifying a region having distortion from image data. Examples of processing included in “removal of distortion” include foreground background separating processing for separating image data into foreground and background in a state wherein both are not mixed, and movement blurring removal processing for removing movement blurring as distortion. Examples of processing included in “extraction of significant information” include processing for extracting movement vector serving as significant information from image data, and processing for estimating a mixture ratio described in FIG. 25. Examples of processing included in “signal processing considering distortion” include the above class classification adaptation processing, and frame double-speed processing for doubling a frame rate by inserting a frame between frames.
Of “detection of distortion”, “removal of distortion”, “extraction of significant information”, “signal processing considering distortion” shown in FIG. 114, the signal processing device 4 in FIG. 113 performs, for example, signal processing classified into “removal of distortion”. Here, let us say that of signal processing classified into “removal of distortion”, the signal processing device 4 in FIG. 113 performs processing for removing movement blurring, or the like, for example.
The signal processing device 4 in FIG. 113 can input the assisting information by the user operating the user I/F 17006. The processing region setting unit 17001, continuity setting unit 17002, and actual world estimating unit 17003 can perform, in the event that the assisting information is input by the user operating the user I/F 17006, processing based on the assisting information thereof. Further, in the event that the assisting information is not input (further, even in the event that the assisting information is input), the processing region setting unit 17001, continuity setting unit 17002, and actual world estimating unit 17003 can perform processing without the assisting information.
Now, first, description will be made regarding the processing of the signal processing device 4 shown in FIG. 113, in the event that the processing region setting unit 17001, continuity setting unit 17002, and actual world estimating unit 17003 perform processing without the assisting information.
FIG. 115 is a flowchart describing the processing of the signal processing device 4 shown in FIG. 113, in the event that the processing region setting unit 17001, continuity setting unit 17002, and actual world estimating unit 17003 perform processing without the assisting information.
With the signal processing device 4 in FIG. 113, the actual world is estimated based on continuity, and accordingly, processing for removing movement blurring which occurs due to temporal-direction mixing (temporal mixing) of the signals of objects, or the like, due to temporal integration effects of the sensor 2, is performed.
That is to say, in an input image obtained by a taking an image in the actual world 1 wherein an object such as an automobile or the like is moving, with the sensor 2 which is an image sensor, the object moves over time, so light signals of that object and light signals of portions other than that object are mixed (temporal mixing) due to temporal integration effects of the sensor 2, thereby causing so-called movement blurring at the boundary portions of the object and the like, for example.
With the signal processing device 4 in FIG. 113, a high-image-quality output image of which the movement blurring caused due to such time mixture is removed from the input image is generated, and consequently, an output image wherein the movement blurring is removed from the input image is obtained.
With the signal processing device 4 shown in FIG. 113, first, in step S17001, pre-processing is performed, and the flow proceeds to step S17002. That is to say, the signal processing device 4 supplies one frame or one field of input image for example, supplied from the sensor 2 (FIG. 1) as data 3, to the processing region setting unit 17001, continuity setting unit 17002, actual world estimating unit 17003, image generating unit 17004, and image display unit 17005. Further, the signal processing unit 4 displays an input image on the image display unit 17005.
Note here that an image with movement blurring due to temporal mixing, obtained by the taking a scene wherein an object such as the automobile moves in the horizontal direction at a constant speed with the sensor 2, is input to the signal processing device 4 as an input image.
In step S17002, the processing region setting unit 17001 sets the processing region and supplies processing region information representing the processing region to the continuity setting unit 17002, actual world estimating unit 17003, and image generating unit 17004, and the flow proceeds to step S17003.
Here, let us say that in step S17002, for example, a rectangular region surrounding a portion where movement blurring occurs due to an object moving in the horizontal direction in the input image is set to the processing region, for example.
In step S17003, the continuity setting unit 17002 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 17001. Further, the continuity setting unit 17002 sets the continuity of the actual world 1 signals lost in the processing region image data, and supplies continuity information representing the continuity for the processing region to the actual world estimating unit 17003, and the flow proceeds to step S17004.
Here, let us say that the actual world 1 image corresponding to the input image includes continuity wherein a certain shaped object is moving in the horizontal direction at a constant speed, and in step S17003, the movement amount in the horizontal direction of the object in the processing region is obtained as continuity information.
In step S17004, the actual world estimating unit 17003 estimates actual world 1 signals regarding to the image data with in the processing region of the input image, according to the continuity of the corresponding actual world 1 signals.
That is to say, at the actual world estimating unit 17003, the model generating unit 17011 recognizes the processing region in the input image, from the processing region information supplied from the processing region setting unit 17001, and also recognizes continuity (here, amount of movement) of the actual world 1 signals corresponding to the image data in the processing region, from the continuity information supplied from the continuity setting unit 17002. Further the model generating unit 17011 generates a function serving as a relation model modeling the relation between the pixel values of each of the pixels within the processing region and the actual world 1 signals, according to the pixels making up the processing region in the input image, and the continuity of actual world 1 signals corresponding to the image data of the processing region, and supplies this to the equation generating unit 17012.
The equation generating unit 17012 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 17001, and substitutes the pixel values of each of the pixels of the input image making up the processing region into the function serving as the model which is supplied from the model generating unit 17011, thereby generating an equation for obtaining an approximation function approximating the actual world 1 signals, which is supplied to the actual world waveform estimating unit 17013.
Note that here, a spline function is employed as an approximation function, for example.
The actual world waveform estimating unit 17013 estimates the waveform of the actual world 1 signals by computing the equation supplied from the equation generating unit 17012. That is, the actual world waveform estimating unit 17013 obtains the approximation function serving as a approximation model modeling the actual world 1 signals, and supplies the approximation function to the image generating unit 17004.
Following processing of step S17004, the flow proceeds to step S17005, where the image generating unit 17004 generates signals closer approximating the actual world 1 signals based on the approximation function supplied from (the actual world waveform estimating unit 17013 of) the actual world estimating unit 17003. That is to say, the image generating unit 17004 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 17001, and with regard to this processing region, generates an approximation image which is image data closer approximating the image corresponding to the actual world 1 signals, based on the approximation function supplied from the actual world estimating unit 17003. Further the image generating unit 17004 generates, as an output image, an image wherein the portion of the processing region of the input image has been replaced with the approximation image, and supplies this to the image display unit 17005, and the flow proceeds from step S17005 to step S17006.
In step S17006, the image display unit 17005 displays the output image supplied from the image generating unit 17004 instead of the input image displayed in step S17001, or along with the input image, and the processing ends.
Next, description will be made regarding spatial temporal integration effects in the event that the sensor 2 in FIG. 1 is an image sensor with reference to FIG. 116 and FIG. 117.
An image sensor images a subject (object) in the real world, and outputs the image data to be obtained as a result of imagining in increments of single frame (or field). That is to say, the light signals of the actual world 1 which is light reflected off of the subject of the actual world 1 are projected on the image sensor, but the image sensor outputs the projected results as the data 3.
For example, the image sensor outputs image data of 30 frames per second. In this case, the exposure time (shutter time) of the image sensor is conceptually a period equal to or less than 1/30 sec.
FIG. 116 is a diagram describing an example of a pixel array on the image sensor. In FIG. 116, A through I denote individual pixels. The pixels are placed on a plane corresponding to the image displayed by the image data. A single detecting element corresponding to a single pixel is placed on the image sensor. At the time of the image sensor taking images of the actual world 1 (light signals), the one detecting element outputs one pixel value corresponding to the one pixel making up the image data. For example, the position in the spatial direction X (X coordinate) of the detecting element corresponds to the horizontal position on the image displayed by the image data, and the position in the spatial direction Y (Y coordinate) of the detecting element corresponds to the vertical position on the image displayed by the image data.
Distribution of intensity of light of the actual world 1 has expanse in the three-dimensional spatial directions and the time direction, but the image sensor acquires light signals of the actual world 1 in two-dimensional spatial directions and the time direction, and generates data 3 representing the distribution of intensity of light in the two-dimensional spatial direction and the time direction.
As shown in FIG. 117, the detecting device which is a CCD for example, converts light cast onto the photoreception face (photoreception region) (detecting region) into electric charge during a period corresponding to the shutter time ts, and accumulates the converted charge. The light is information (signals) of the actual world 1 regarding which the intensity is determined by the three-dimensional spatial position and point-in-time. The distribution of intensity of light of the actual world 1 can be represented by a function F(x, y, z, t), wherein position x, y, z, in three-dimensional space, and point-in-time t, are variables.
The amount of charge accumulated in the detecting device which is a CCD is approximately proportionate to the intensity of the light cast onto the entire photoreception face having two-dimensional spatial expanse, and the amount of time that light is cast thereupon. The detecting device adds the charge converted from the light cast onto the entire photoreception face, to the charge already accumulated during a period corresponding to the shutter time. That is to say, the detecting device integrates the light cast onto the entire photoreception face having a two-dimensional spatial expanse, and accumulates a charge of an amount corresponding to the integrated light during a period corresponding to the shutter time ts. Accordingly, the detecting device (pixel) has an integration effect regarding space (photoreception face) and time (shutter time).
As described above, the detecting device outputs the pixel value corresponding to the accumulated electric charge as the data 3. Accordingly, the individual pixel values output from the image sensor are the results of integrating the portion of the light signals of the actual world 1 having time-space expanse with regard to the time direction of the shutter time and the spatial direction of the photoreception face of the detecting device.
The image data made up of such a pixel value, i.e., the image data serving as the data 3 to be output by the image sensor can be classified into three regions of a background region, foreground region, and mixed region, according to the properties thereof, for example.
For example, let us consider a case wherein as shown in FIG. 118, a certain background object, and a foreground object positioned closer to the image sensor than the background object are captured by the image sensor. Note that here, an object closer to the image sensor is defined as an foreground object, and an object away from the image sensor is defined as a background object.
In the event that either the foreground object or the background object is moving, the actual world 1 light signal projected on the image sensor changes over time. In FIG. 118, the background object is stationary, and the foreground object is moving in the horizontal direction (from left to right direction) at a constant speed.
In the event that the actual world 1 light signal projected on the image sensor changes over time, distortion is caused due to the above integration effects (temporal integration effects) of the image sensor. That is to say, in FIG. 118, the background object is stationary, and the foreground object is moving, so with the region of the acceptance surface of the image sensor, of the exposure time (e.g., 1/30 sec, 1/60 sec or the like), a region, which changes from a state wherein the light signal corresponding to one of the foreground object and the background object is projected to a state wherein the light signal corresponding to the other is projected, is created. In other words, some regions (pixels) of the image sensor are integrated wherein the light signal corresponding to one of the foreground object and the background object, and the light signal corresponding to the other are mixed. Such a region is defined as a mixed region. Also, of the regions of the image sensor, a portion obtained by removing the mixed region from the region where the foreground object is projected is defined as a foreground region, and also a portion obtained by removing the mixed region from the region where the background object is projected is defined as a background region.
FIG. 119 illustrates a foreground region, a background region, and a mixed region.
In FIG. 119, the upper side view illustrates image data obtained at the image sensor assuming that the horizontal direction is the horizontal direction (x direction) of the image sensor, and the vertical direction is the vertical direction (y direction) of the image sensor, and the lower side view illustrates an electric charge charged (accumulated) to the image sensor assuming that the horizontal direction is the horizontal direction (x direction), and the vertical direction is the time direction (t direction).
Upon the image sensor receiving the actual world 1 light signal corresponding to the stationary background object, and the foreground object moving in the horizontal direction, as described above, part of the reception surface of the image sensor becomes a state wherein only the light signal corresponding to the foreground object is projected at exposure time serving as finite time, other part of the region becomes a state wherein only the light signal corresponding to the background object is projected, and the residual region becomes a state wherein the light signal corresponding to one of the foreground object and the background object is projected to a state wherein the light signal corresponding to the other is projected.
Now, if we say that with the image sensor, the electric charge to be charged by the light signal corresponding to the foreground object is called foreground components, and also the electric charge to be charged by the light signal corresponding to the background object is called background components, with the image data obtained from the image sensor, a region wherein a pixel value includes only one of the foreground components and the background components, and a region wherein a pixel value includes both components are created.
The foreground region is a region wherein a pixel value includes the foreground components alone, and the background region is a region wherein a pixel value includes the background components alone. The mixed region is a region wherein a pixel value includes both the foreground components and the background components. The foreground region and the mixed region are regions wherein the actual world 1 light signal corresponding to the moving foreground object is projected, where distortion is caused due to the above integration effects of the image sensor. In this case, this distortion is manifested as movement blurring.
Next, FIG. 120 illustrates a configuration example of a device equivalent to the signal processing device 4 in FIG. 113 in the event of removing movement blurring as distortion caused on the image data due to the integration effects of the image sensor as described above.
That is to say, FIG. 120 illustrates a functional configuration example of the signal processing device 4 in FIG. 113 in the event of performing signal processing wherein the foreground components and the background components are separated from the input image serving as image data on which movement blurring is caused due to the integration effects of the image sensor, and an image of the foreground object having no movement blurring is generated by subjecting the foreground components to processing, and consequently, an image wherein movement blurring is removed from the input image is obtained.
In FIG. 120, the signal processing device 4 comprises a region identifying unit 17031, a movement blurring adjusted amount output unit 17032, a foreground background separating unit 17033, a processing unit determining unit 17034, a movement blurring adjusting unit 17035, and an image display unit 17036. The region identifying unit 17031 corresponds to the processing region setting unit 17001 in FIG. 113, the movement blurring adjusted amount output unit 17032 corresponds to the continuity setting unit 17002 in FIG. 113, the foreground background separating unit 17033, processing unit determining unit 17034, and movement blurring adjusting unit 17035 correspond to the actual world estimating unit 17003 and image generating unit 17004 in FIG. 113, and the image display unit 17036 corresponds to the image display unit 17005 in FIG. 113, respectively.
With the signal processing device 4 in FIG. 120, the input image including movement blurring is supplied to the region identifying unit 17031 and the foreground background separating unit 17033.
The region identifying unit 17031 identifies the foreground region, background region, and mixed region, which have described in FIG. 119, regarding the input image supplied thereto, and supplies information for identifying the foreground region, background region, and mixed region to the foreground background separating unit 17033 and the processing unit determining unit 17034 as processing region information.
The movement blurring adjusted amount output unit 17032 supplies movement vector representing movement of the foreground object in the input image to the movement blurring adjusting unit 17035 as continuity information. Here, let us say that the foreground object is moving in the horizontal direction (e.g., from left to right direction) at a constant speed as described above, and also let us say that the movement blurring adjusted amount output unit 17032 supplies the movement amount per the exposure time of the image sensor to the movement blurring adjusting unit 17035 as continuity information.
The foreground background separating unit 17033 separates the foreground components and the background components from the input image supplied thereto, based on the processing region information supplied form the region identifying unit 17031, and supplies the foreground components to the movement blurring adjusting unit 17035.
The processing unit determining unit 17034 determines a processing unit serving as a unit for subjecting the foreground region and mixed region identified by the processing region information supplied from the region identifying unit 17031 to processing for removing movement blurring at the movement blurring adjusting unit 17035, and supplies processing unit information representing the processing unit thereof to the movement blurring adjusting unit 17035.
The movement blurring adjusting unit 17035 generates an image of the foreground object including no movement blurring by performing later-described processing for each processing unit represented with the processing unit information supplied from the processing unit determining unit 17034 using the movement amount supplied from the movement blurring adjusted amount output unit 17032, and the foreground components supplied from the foreground background separating unit 17033, and supplies the generated image to the image display unit 17036. The image display unit 17036 displays the image supplied from the movement blurring adjusting unit 17035.
Next, the processing (movement blurring removal processing) by the signal processing device 4 shown in FIG. 120 will be described with reference to the flowchart in FIG. 121.
Upon the input image including movement blurring being supplied to the region identifying unit 17031 and the foreground background separating unit 17033, in step S17021, the region identifying unit 17031 identifies the foreground region, background region, and mixed region of the input image supplied thereto, and supplies information for identifying the foreground region, background region, and mixed region to the foreground background separating unit 17033 and the processing unit determining unit 17034 as processing region information. Further, in step S17021, the movement blurring adjusted amount output unit 17032 sets (detects) the movement amount representing the magnitude of movement in the horizontal direction of the foreground object in the input image, and supplies this to the movement blurring adjusting unit 17035 as continuity information.
Subsequently, the flow proceeds to step S17022 from step S17021, where the foreground background separating unit 17033 separates the foreground components and the background-components from the input image supplied thereto based on the processing region information supplied from the region identifying unit 17031. That is to say, the foreground background separating unit 17033 recognizes the foreground region, background region, and mixed region of the input image based on the processing region information, as shown in FIG. 122.
FIG. 122 illustrates a foreground region, a background region, and a mixed region in an input image, as with FIG. 119. In FIG. 122, the right side view illustrates image data serving as an input image obtained at the image sensor, as with the upper side view in FIG. 119 assuming that the horizontal direction is the horizontal direction (x direction) of the image sensor, and the vertical direction is the vertical direction (y direction) of the image sensor, and the left side view illustrates, as with the lower side view in FIG. 119, an electric charge charged (accumulated) to the image sensor assuming that the horizontal direction is the horizontal direction (x direction), and the vertical direction is the time direction (t direction). This is similarly applied to later-described FIG. 123.
In step S17022, upon the foreground background separating unit 17033 recognizing the foreground region, background region, and mixed region of the input image, the foreground background separating unit 17033 separates the foreground region, background region, and mixed region from the input image, and further, as shown in FIG. 123, separates the foreground components alone from the foreground region and mixed region, and supplies these to the movement blurring adjusting unit 17035.
That is to say, the foreground background separating unit 17033 separates the foreground components from the mixed region, and supplies the foreground components thereof, and the foreground components in the foreground region to the movement blurring adjusting unit 17035.
Here, let us say that identification of the foreground region, background region, and mixed region of the input image in step S17021, and separation of the foreground components alone from the input image in step S17022 can be performed with an arbitrary method.
Subsequently, the flow proceeds to step S17023 from step S17022, where the processing unit determining unit 17034 determines a processing unit from the foreground region and mixed region identified by the processing region information supplied from the region identifying unit 17031, and supplies processing unit information representing the processing unit thereof to the movement blurring adjusting unit 17035.
That is to say, with the entire region of the foreground region and mixed region in the input image, the processing unit determining unit 17034 determines, for example, of the pixels arrayed in a line (row) in the movement direction (here, horizontal direction) of the foreground object, arbitrary pixels in a line, which have not been taken as a processing unit, as a processing unit. Accordingly, an arbitrary one line in the horizontal direction in the entire region of the foreground region and mixed region in the input image is set as a processing unit, here.
Subsequently, the processing unit determining unit 17034 supplies the processing unit information representing the processing unit thereof to the movement blurring adjusting unit 17035, and the flow proceeds to step S17024 from step S17023.
In step S17024, by subjecting the processing unit represented with the processing unit information supplied from the processing unit determining unit 17034 to processing using the movement amount supplied from the movement blurring adjusted amount output unit 17032, and the foreground components supplied from the foreground background separating unit 17033, the movement blurring adjusting unit 17035 generates an image of the foreground object including no movement blurring regarding the processing unit thereof, and the flow proceeds to step S17025.
In step S17025, the processing unit determining unit 17034 determines regarding whether or not all lines in the horizontal direction in the entire region of the foreground region and mixed region in the input image have been set as a processing unit. In step S17025, in the event that determination is made that all lines in the horizontal direction in the entire region of the foreground region and mixed region in the input image have not been set as a processing unit, the flow returns to step S17023, where the processing unit determining unit 17034 determines an arbitrary one line which has not been taken as a processing unit, of the lines in the horizontal direction in the entire region of the foreground region and mixed region in the input image, as a processing unit, and hereafter, the same processing is repeated.
On the other hand, in the event that determination is made that all lines in the horizontal direction in the entire region of the foreground region and mixed region in the input image have been set as a processing unit, i.e., in the event that with the movement blurring adjusting unit 17035, processing has been performed regarding all lines in the horizontal direction in the entire region of the foreground region and mixed region in the input image, and thus, an image of the foreground object having no movement blurring is obtained, the movement blurring adjusting unit 17035 supplies the image of the foreground object having no movement blurring to the image display unit 17036 to display this, and ends the processing.
Next, description will be made regarding the processing of the movement blurring adjusting unit 17035 in FIG. 120.
The movement blurring adjusting unit 17035 generates an image having no movement blurring by estimating the light signal function F, and integrating (the estimated results of) the light signal function F in at least the one-dimensional direction at a predetermined unit, assuming that the pixel value of each pixel corresponding to a position in at least a one-dimensional direction of the time-space directions of input data wherein the actual world 1 light signals are projected on the image sensor made up of a plurality of pixels each having time-space integration effects, and part of the actual world 1 light signal continuity is lost, is a pixel value acquired by integrating a light signal function (actual world function) F corresponding to the actual world 1 light signal approximated with the spline function in at least the one-dimensional direction.
That is to say, assuming that the pixel value of each pixel corresponding to a position in the x direction for example, serving as a predetermined one-dimensional direction of the spatial direction of the input image wherein movement blurring is caused due to the moving foreground object, is the pixel value obtained by the light signal function F corresponding to the actual world 1 light signal approximated with a spline function integrating a physical model moving while performing phase shift in the time direction corresponding to the movement vector representing movement of the foreground object in the x direction and in the time direction, the movement blurring adjusting unit 17035 generates an image made up of pixel values wherein movement blurring of the foreground object within the input image is removed by estimating the light signal function F, and integrating a spline function serving as an approximation model approximating the light signal function F, which is a estimated result of the light signal function F thereof, in the x direction and in the time direction at a predetermined unit.
First, description will be made regarding the estimating method of the light signal function F at the movement blurring adjusting unit 17035.
The movement blurring adjusting unit 17035, here, for example, as described above, performs processing taking pixels arrayed in the horizontal direction (x direction) as a processing unit.
Now, let us say that N+1 pixels arrayed in the x direction are taken as a processing unit, and a waveform (X cross-sectional waveform) F(x) positioned in a certain vertical direction at a certain point-in-time of the light signal function F corresponding to the actual world 1 light signal projected on the processing unit is approximated with a continuous waveform such as shown in FIG. 124, e.g., a three-dimensional spline function.
FIG. 124 represents (the value of) a three-dimensional spline function serving as an approximation function approximating the light signal function F(x) corresponding to the actual world 1 light signal projected on a processing unit assuming that the horizontal direction is taken as the width direction of a processing unit (x direction of the input image), and the vertical direction is taken as a level.
Now, as shown in FIG. 124, let us say that the coordinate of the center position in the x direction of the pixel at the left end of the processing unit is x=0, and also the length of one pixel in the x direction is 1. Also, a three-dimensional spline function serving as an approximation function approximating the light signal function F corresponding to the actual world 1 light signal projected on from the center position in the x direction of the k'th pixel #k−1 (k=1, 2, and so on through N+1) from the left until the center position in the x direction of the right-adjacent pixel thereof #k, of the processing unit made up of N+1 pixels arrayed in the x direction, is represented with Ck(X). Further, the value of the spline function Ck(X) at the center position in the x direction of the pixel #k−1 is represented with Yk−1. Note that the suffix k in the spline function Ck(x) is k=1, 2, and so on through N.
In this case, the spline function Ck(x) is represented with Expression (137).




  
    
      
        
          
            C
            k
          
          ⁡
          
            (
            x
            )
          
        
        =
        
          
            
              
                M
                
                  k
                  -
                  1
                
              
              ⁡
              
                (
                
                  x
                  -
                  k
                
                )
              
            
            ⁢
            
              {
              
                1
                -
                
                  
                    (
                    
                      x
                      -
                      k
                    
                    )
                  
                  2
                
              
              }
            
          
          +
          
            
              
                M
                k
              
              ⁡
              
                (
                
                  x
                  -
                  k
                  +
                  1
                
                )
              
            
            ⁢
            
              {
              
                
                  
                    (
                    
                      x
                      -
                      k
                      +
                      1
                    
                    )
                  
                  2
                
                -
                1
              
              }
            
          
          -
          
            
              y
              
                k
                -
                1
              
            
            ⁡
            
              (
              
                x
                -
                k
              
              )
            
          
          +
          
            
              y
              k
            
            ⁡
            
              (
              
                x
                -
                k
                +
                1
              
              )
            
          
        
      
    
    
      
        (
        137
        )
      
    
  




However, in Expression (137), Mk and yk are represented with the following expression.




  
    
      
        
          
            
              (
              
                
                  
                    4
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    4
                  
                  
                    1
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    ...
                  
                  
                    ...
                  
                  
                    ...
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    4
                  
                
              
              )
            
            ⁢
            
              (
              
                
                  
                    
                      M
                      1
                    
                  
                
                
                  
                    
                      M
                      2
                    
                  
                
                
                  
                    ...
                  
                
                
                  
                    
                      M
                      
                        N
                        -
                        1
                      
                    
                  
                
              
              )
            
          
          =
          
            (
            
              
                
                  
                    b
                    1
                  
                
              
              
                
                  
                    b
                    2
                  
                
              
              
                
                  ...
                
              
              
                
                  
                    b
                    
                      N
                      -
                      1
                    
                  
                
              
            
            )
          
        
        ,
        
          

        
        ⁢
        
          
            M
            0
          
          =
          
            
              M
              N
            
            =
            0
          
        
        ,
        
          
            b
            k
          
          =
          
            
              y
              
                k
                +
                1
              
            
            -
            
              2
              ⁢
              
                y
                k
              
            
            +
            
              y
              
                k
                -
                1
              
            
          
        
      
    
    
      
        (
        138
        )
      
    
  




The spline function Ck(x) of Expression (137) is defined as N+1 variables y0, y1, and so on through yn. Accordingly, the spline function Ck(x) of Expression (137) can be obtained by yielding N+1 variables y0 through yn.
In order to yield N+1 variables y0 through yn, let us consider a physical model shown in FIG. 125.
That is to say, FIG. 125 represents a physical model wherein while the light signal represented with the light signal function F(x) approximated with the spline function Ck(X) is continuously moving (phase shifting) in the horizontal direction (x direction) by movement amount v during the exposure time of the image sensor, the light signal is projected on the pixels of the processing unit, and electric charge is charged on the pixels, i.e., an image is obtained by being integrated in the x direction and in the time direction.
The left side view in FIG. 125 illustrates the spline function Ck(x), which approximates the light signal function F(x), as with the case in FIG. 124. Also, the right side view in FIG. 125 illustrates the level of the spline function Ck(x), which approximates the light signal function F(x), assuming that the horizontal direction is the horizontal direction of the image sensor (x direction where the pixels of the processing unit are arrayed), the near-side direction is exposure time, and the vertical direction is level.
According to the physical model shown in FIG. 125, the curved surface (model) as the locus obtained by the spline function Ck(x), which approximates the light signal function F(x), continuously moving (phase shifting) in the horizontal direction (x direction) by the movement amount v during the exposure time of the image sensor, is integrated in the time direction during the exposure time alone, and also is integrated by only the length in the x direction of the pixel #k of the processing unit in the x direction, thereby obtaining the pixel value Yk of the pixel #k.
With the physical model in FIG. 125, the spline function Ck(x), which approximates the light signal function F(x), continuously moves during the exposure time, so mixture (time mixture) in the time direction of the signal of the object due to the time integration effects of the image sensor is caused at the pixel #k wherein the pixel value Yk is obtained by this physical model. Further, mixture (space mixture) in the spatial direction of the signal of the object due to the spatial integration effects of the image sensor is caused at the pixel #k as well. Accordingly, with the physical model in FIG. 125, both time mixture and space mixture are considered.
The movement blurring adjusting unit 17035 obtains (a variable Yk stipulating) the spline function Ck(x), which approximates the light signal function F(x), as the estimated value of the light signal function F(x) based on the physical model in FIG. 125 using the pixel value Yk of the pixel #k of the processing unit.
Here, let us say that the value of the light signal function F(x) to be projected on other than the processing unit is a steady value when the image sensor starts exposure.
That is to say, as described above, the value of the spline function Ck (X), which approximates the light signal function F(x), at the center position in the x direction of the pixel #k is represented with yk. Also, in this case, the coordinate of the center position in the x direction of the pixel at the left end of the processing unit is x=0, and also the length of one pixel in the x direction is 1. Accordingly, the value of the spline function Ck(x) at the position of x=k is represented with yk. Now, let us say that in a range of x<0, the value of the spline function approximating the light signal function F(x) is constantly y0 (=C1(0)), and also, in a range of x>N, the value of the spline function approximating the light signal function F(x) is constantly yN(=CN(N)).
Here, as described above, assumption that the value of the light signal function F(x) to be projected on a region (strictly, region of x<0 and x>N) other than the processing unit is a steady value when the image sensor starts exposure, is called flat assumption. Note that the flat assumption is not indispensable. That is to say, the value of the light signal function F(x) to be projected on other than the processing unit is a steady value, or for example, can be approximated with the spline function or the like, when the image sensor starts exposure.
Also, hereafter, let us say that exposure time is 1 to simplify description.
Next, description will be made regarding how to estimate the light signal function F(x), i.e., how to obtain the spline function Ck(x), which approximates the light signal function F(x), based on the physical model in FIG. 125 using the pixel value Yk of the pixel #k of the processing unit.
First, let us say that a range in the x direction where the processing unit exists is represented with a range (α, β) wherein the start point is α, and the end point is β.
In the event that the light signal function F(x) is not moving but stationary, by the light signal corresponding to the light signal function F(x) to be approximated with the spline function Ck(x) being projected on the range (α, β), a pixel value z obtained by electric charge to be charged during exposure time in the range (α, β) is represented with the following expression as an integral value wherein the spline function Ck(x) is integrated with the range (α, β). However, let us say that exposure is 1, here.




  
    
      
        
          
            
              z
              =
              
              ⁢
              
                
                  ∫
                  α
                  β
                
                ⁢
                
                  
                    
                      C
                      k
                    
                    ⁡
                    
                      (
                      x
                      )
                    
                  
                  ⁢
                  
                    d
                    x
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  M
                  
                    k
                    -
                    1
                  
                
                ⁢
                
                  {
                  
                    
                      
                        [
                        
                          
                            (
                            
                              x
                              -
                              k
                            
                            )
                          
                          ⁢
                          
                            {
                            
                              x
                              -
                              
                                
                                  1
                                  3
                                
                                ⁢
                                
                                  
                                    (
                                    
                                      x
                                      -
                                      k
                                    
                                    )
                                  
                                  3
                                
                              
                            
                            }
                          
                        
                        ]
                      
                      α
                      β
                    
                    -
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    ∫
                    α
                    β
                  
                  ⁢
                  
                    
                      {
                      
                        x
                        -
                        
                          
                            1
                            3
                          
                          ⁢
                          
                            
                              (
                              
                                x
                                -
                                k
                              
                              )
                            
                            3
                          
                        
                      
                      }
                    
                    ⁢
                    
                      d
                      x
                    
                  
                
                }
              
              +
            
          
        
        
          
            
              
              ⁢
              
                
                  M
                  k
                
                ⁢
                
                  {
                  
                    
                      
                        [
                        
                          
                            (
                            
                              x
                              -
                              k
                              +
                              1
                            
                            )
                          
                          ⁢
                          
                            {
                            
                              
                                
                                  1
                                  3
                                
                                ⁢
                                
                                  
                                    (
                                    
                                      x
                                      -
                                      k
                                      +
                                      1
                                    
                                    )
                                  
                                  3
                                
                              
                              -
                              x
                            
                            }
                          
                        
                        ]
                      
                      α
                      β
                    
                    -
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    ∫
                    α
                    β
                  
                  ⁢
                  
                    
                      {
                      
                        
                          
                            1
                            3
                          
                          ⁢
                          
                            
                              (
                              
                                x
                                -
                                k
                                +
                                1
                              
                              )
                            
                            3
                          
                        
                        -
                        x
                      
                      }
                    
                    ⁢
                    
                      d
                      x
                    
                  
                
                }
              
              -
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    
                      y
                      
                        k
                        -
                        1
                      
                    
                    ⁡
                    
                      [
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            (
                            
                              x
                              -
                              k
                            
                            )
                          
                          2
                        
                      
                      ]
                    
                  
                  α
                  β
                
                +
                
                  
                    
                      y
                      k
                    
                    ⁡
                    
                      [
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            (
                            
                              x
                              -
                              k
                              +
                              1
                            
                            )
                          
                          2
                        
                      
                      ]
                    
                  
                  α
                  β
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    1
                    4
                  
                  ⁢
                  
                    
                      
                        M
                        
                          k
                          -
                          1
                        
                      
                      ⁡
                      
                        [
                        
                          
                            2
                            ⁢
                            
                              x
                              ⁡
                              
                                (
                                
                                  x
                                  -
                                  
                                    2
                                    ⁢
                                    k
                                  
                                
                                )
                              
                            
                          
                          -
                          
                            
                              (
                              
                                x
                                -
                                k
                              
                              )
                            
                            4
                          
                        
                        ]
                      
                    
                    α
                    β
                  
                
                -
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    1
                    4
                  
                  ⁢
                  
                    
                      
                        M
                        k
                      
                      ⁡
                      
                        [
                        
                          
                            2
                            ⁢
                            
                              x
                              ⁡
                              
                                (
                                
                                  x
                                  -
                                  
                                    2
                                    ⁢
                                    k
                                  
                                  +
                                  2
                                
                                )
                              
                            
                          
                          -
                          
                            
                              (
                              
                                x
                                -
                                k
                                +
                                1
                              
                              )
                            
                            4
                          
                        
                        ]
                      
                    
                    α
                    β
                  
                
                -
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      
                        
                          y
                          
                            k
                            -
                            1
                          
                        
                        ⁡
                        
                          [
                          
                            
                              (
                              
                                x
                                -
                                k
                              
                              )
                            
                            2
                          
                          ]
                        
                      
                      α
                      β
                    
                  
                  +
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      
                        
                          y
                          k
                        
                        ⁡
                        
                          (
                          
                            x
                            -
                            k
                            +
                            1
                          
                          )
                        
                      
                      2
                    
                  
                
                ]
              
              α
              β
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    1
                    4
                  
                  ⁢
                  
                    M
                    
                      k
                      -
                      1
                    
                  
                  ⁢
                  
                    {
                    
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        
                          β
                          ⁡
                          
                            (
                            
                              β
                              -
                              
                                2
                                ⁢
                                k
                              
                            
                            )
                          
                        
                      
                      -
                      
                        
                          (
                          
                            β
                            -
                            k
                          
                          )
                        
                        4
                      
                      -
                      
                        2
                        ⁢
                        
                          
                        
                        ⁢
                        
                          α
                          ⁡
                          
                            (
                            
                              α
                              -
                              
                                2
                                ⁢
                                k
                              
                            
                            )
                          
                        
                      
                      +
                      
                        
                          (
                          
                            α
                            -
                            k
                          
                          )
                        
                        4
                      
                    
                    }
                  
                
                -
              
            
          
        
        
          
            
              
              ⁢
              
                
                  1
                  4
                
                ⁢
                
                  M
                  k
                
                ⁢
                
                  {
                  
                    
                      2
                      ⁢
                      
                        β
                        ⁡
                        
                          (
                          
                            β
                            -
                            
                              2
                              ⁢
                              k
                            
                            +
                            2
                          
                          )
                        
                      
                    
                    -
                    
                      
                        (
                        
                          β
                          -
                          k
                          +
                          1
                        
                        )
                      
                      4
                    
                    -
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    2
                    ⁢
                    
                      α
                      ⁡
                      
                        (
                        
                          α
                          -
                          
                            2
                            ⁢
                            k
                          
                          +
                          2
                        
                        )
                      
                    
                  
                  +
                  
                    
                      (
                      
                        α
                        -
                        k
                        +
                        1
                      
                      )
                    
                    4
                  
                
                }
              
              -
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    1
                    2
                  
                  ⁢
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  ⁢
                  
                    {
                    
                      
                        
                          (
                          
                            β
                            -
                            k
                          
                          )
                        
                        2
                      
                      -
                      
                        
                          (
                          
                            α
                            -
                            k
                          
                          )
                        
                        2
                      
                    
                    }
                  
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                
                  1
                  2
                
                ⁢
                
                  y
                  k
                
                ⁢
                
                  {
                  
                    
                      
                        (
                        
                          β
                          -
                          k
                          +
                          1
                        
                        )
                      
                      2
                    
                    -
                    
                      
                        (
                        
                          α
                          -
                          k
                          +
                          1
                        
                        )
                      
                      2
                    
                  
                  }
                
              
            
          
        
      
    
    
      
        (
        139
        )
      
    
  




However, if a matrix A is defined such as shown in Expression (140), Mk in Expression (139) is represented with Expression (141).




  
    
      
        
          
            (
            
              
                
                  4
                
                
                  1
                
                
                  0
                
                
                  0
                
              
              
                
                  1
                
                
                  4
                
                
                  1
                
                
                  0
                
              
              
                
                  0
                
                
                  ...
                
                
                  ...
                
                
                  ...
                
              
              
                
                  0
                
                
                  0
                
                
                  1
                
                
                  4
                
              
            
            )
          
          
            -
            1
          
        
        =
        
          A
          =
          
            (
            
              
                
                  
                    a
                    
                      0
                      ,
                      0
                    
                  
                
                
                  
                    a
                    
                      0
                      ,
                      1
                    
                  
                
                
                  ...
                
                
                  
                    a
                    
                      0
                      ,
                      
                        N
                        -
                        2
                      
                    
                  
                
              
              
                
                  
                    a
                    
                      1
                      ,
                      0
                    
                  
                
                
                  
                    a
                    
                      1
                      ,
                      1
                    
                  
                
                
                  ...
                
                
                  
                    a
                    
                      1
                      ,
                      
                        N
                        -
                        2
                      
                    
                  
                
              
              
                
                  ...
                
                
                  ...
                
                
                  ...
                
                
                  ...
                
              
              
                
                  
                    a
                    
                      
                        N
                        -
                        2
                      
                      ,
                      0
                    
                  
                
                
                  
                    a
                    
                      
                        N
                        -
                        2
                      
                      ,
                      1
                    
                  
                
                
                  ...
                
                
                  
                    a
                    
                      
                        N
                        -
                        2
                      
                      ,
                      
                        N
                        -
                        2
                      
                    
                  
                
              
            
            )
          
        
      
    
    
      
        (
        140
        )
      
    
  
  
    
      
        
          
            
              
                
              
              ⁢
              
                
                  M
                  
                    
                      
                    
                    ⁢
                    k
                  
                
                ⁢
                
                  
                
                =
                  
                ⁢
                
                  
                    ∑
                    
                      i
                      ⁢
                      
                        
                      
                      =
                      
                        
                      
                      ⁢
                      1
                    
                    
                      
                        
                      
                      ⁢
                      
                        N
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      a
                      
                        
                          
                        
                        ⁢
                        
                          
                            k
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
                            1
                          
                          ,
                          
                            
                          
                          ⁢
                          
                            i
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
                            1
                          
                        
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      b
                      
                        
                          
                        
                        ⁢
                        i
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
              
              ⁢
              
                =
                  
                ⁢
                
                  
                    ∑
                    
                      i
                      ⁢
                      
                        
                      
                      =
                      
                        
                      
                      ⁢
                      1
                    
                    
                      
                        
                      
                      ⁢
                      
                        N
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      a
                      
                        
                          
                        
                        ⁢
                        
                          
                            k
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
                            1
                          
                          ,
                          
                            
                          
                          ⁢
                          
                            i
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
                            1
                          
                        
                      
                    
                    ⁢
                    
                      (
                      
                        
                      
                      ⁢
                      
                        
                          y
                          
                            
                              
                            
                            ⁢
                            
                              i
                              ⁢
                              
                                
                              
                              +
                              
                                
                              
                              ⁢
                              1
                            
                          
                        
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        
                          2
                          ⁢
                          
                            
                          
                          ⁢
                          
                            y
                            
                              
                                
                              
                              ⁢
                              i
                            
                          
                        
                        ⁢
                        
                          
                        
                        +
                        
                          
                        
                        ⁢
                        
                          y
                          
                            
                              
                            
                            ⁢
                            
                              i
                              ⁢
                              
                                
                              
                              -
                              
                                
                              
                              ⁢
                              1
                            
                          
                        
                      
                      )
                    
                  
                
              
            
          
        
        
          
            
              
                
              
              ⁢
              
                =
                  
                ⁢
                
                  
                    
                      ∑
                      
                        i
                        ⁢
                        
                          
                        
                        =
                        
                          
                        
                        ⁢
                        2
                      
                      
                        
                          
                        
                        ⁢
                        N
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        a
                        
                          
                            
                          
                          ⁢
                          
                            
                              k
                              ⁢
                              
                                
                              
                              -
                              
                                
                              
                              ⁢
                              1
                            
                            ,
                            
                              
                            
                            ⁢
                            
                              i
                              ⁢
                              
                                
                              
                              -
                              
                                
                              
                              ⁢
                              2
                            
                          
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        y
                        
                          
                            
                          
                          ⁢
                          i
                        
                      
                    
                  
                  ⁢
                  
                    
                  
                  -
                  
                    
                  
                  ⁢
                  
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        ∑
                        
                          i
                          ⁢
                          
                            
                          
                          =
                          
                            
                          
                          ⁢
                          1
                        
                        
                          
                            
                          
                          ⁢
                          
                            N
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
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                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    y
                    
                      
                        
                      
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                +
                
                  
                
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                                ⁢
                                1
                              
                              ,
                              
                                
                              
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                                N
                                ⁢
                                
                                  
                                
                                -
                                
                                  
                                
                                ⁢
                                2
                              
                            
                          
                        
                      
                    
                    )
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    y
                    
                      
                        
                      
                      ⁢
                      
                        N
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        1
                      
                    
                  
                
                ⁢
                
                  
                
                +
              
              ⁢
              
                
              
            
          
        
        
          
            
               
              ⁢
              
                
                  a
                  
                    
                      
                    
                    ⁢
                    
                      
                        k
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        1
                      
                      ,
                      
                        
                      
                      ⁢
                      
                        N
                        ⁢
                        
                          
                        
                        -
                        
                          
                        
                        ⁢
                        2
                      
                    
                  
                
                ⁢
                
                  
                
                ⁢
                
                  y
                  
                    
                      
                    
                    ⁢
                    N
                  
                
              
            
          
        
      
    
    
      
        (
        141
        )
      
    
  




Next, as shown in FIG. 125, in the event that the light signal function F(x) moves at a constant speed in the x direction (here, e.g., from left to right direction) by the amount of pixels v during exposure time, the range of the light signal function F(x) serving as electric charge to be charged during exposure time at the pixel #k of the processing unit can be represented such as shown with a slant line in FIG. 126.
That is to say, FIG. 126 illustrates the level of the light signal function F(x), assuming that the crosswise direction is the x direction where the pixels of the processing unit are arrayed, the near-side direction is exposure time, and the lengthwise direction is level.
Now, in order to facilitate description, in FIG. 126, let us focus on the value yk alone of the spline function Ck(x), which approximates the light signal function F(x), at the center position (x=k) in the x direction of each pixel #k of the processing unit.
The light signal function F(x) moves by the amount of pixels v (hereafter, referred to as movement amount v as appropriate) from left to right at a constant speed during exposure time=1. Accordingly, as shown in FIG. 126, when starting exposure, the light signal of the value yk is projected on the pixel #k, and subsequently, by the light signal function F(x) moving from left to right, the light signal of the value yk−1 projected on the left-adjacent pixel #k−1 is projected on the pixel #k. Further along with passage of time, according to the light signal function F(x) moving from left to right, the light signal of the value yk−2 which was projected on the further left-adjacent pixel #k−2 is projected on the pixel #k, and hereafter, similarly, according to the light signal function F(x) moving along with passage of time, the light signal projected on the further left-adjacent pixel is projected on the pixel #k.
In FIG. 126, a dotted line represents a locus in the event that the light signal of the value yk moves by the movement amount v at a constant speed during exposure time. Also, in FIG. 126, a hatched parallelogram represents the range of the light signal projected on the pixel #k during exposure time, i.e., the integration range in the x direction and in the time direction of the light signal performed at the pixel #k during exposure time.
The pixel value Yk of the pixel #k becomes the value corresponding to electric charge to be charged by the light signal projected during exposure time in a range between the left end of the pixel #k (x=k−0.5) and the right end thereof (x=k+0.5). In FIG. 126, the range in the crosswise direction of the hatched integration range represents a range between the left end of the pixel #k (x=k−0.5) and the right end thereof (x=k+0.5), and the oblique direction (near-side direction) of the integration range represents exposure time.
In the event of the light signal moving, not only space mixture but also time mixture occur at the pixel #k. That is to say, the light signal moves along with passage of time, so the range in the x direction of the light signal to be integrated changes over time at the pixel #k. In FIG. 126, when the dotted line representing the movement locus thereof is positioned in the integration range regarding the hatched pixel #k, the light signal of a value yk′ becomes an object to be integrated at the pixel #k thereof.
FIG. 127 illustrates the integration range regarding the pixel #k assuming that the horizontal direction is the x direction, and the vertical direction is exposure time. That is to say, FIG. 127 is a view of the hatched integration range in FIG. 126 as viewed from the vertical direction as to the flat surface stipulated with the x direction and the direction of exposure time.
Here, even in later-described FIG. 128 through FIG. 130, and FIG. 132 through FIG. 134, the integration range regarding the pixel #k is illustrated assuming that the horizontal direction is the x direction, and the vertical direction is exposure time, as with FIG. 127.
The pixel value Yk of the pixel #k is obtained by integrating the spline function Ck′ (x), which approximates the light signals, in the integration range shown in FIG. 127, but the components of the pixel value Yk (hereafter, referred to as pixel value components as appropriate) can be classified into the four types of S1, S2, S3,p, and S4,p (P=1, 2, . . . ) shown in FIG. 127.
Now, description will be made regarding the corresponding calculating methods of the four types of pixel value components S1, S2, S3,p, and S4,p of the pixel value Yk.
FIG. 128 illustrates an integration range for calculating the pixel value component S1 of the pixel value Yk. Note that FIG. 128 is a diagram obtained by extracting a part of the integration range shown in FIG. 127.
The pixel value component S1 can be obtained by integrating the spline function Ck+1(x), which approximates the light signal to be projected on between the center position in the x direction of the pixel #k and the center position in the x direction of the right-adjacent pixel #k+1, at the time of start of exposure.
With the spline function Ck+1(x), as shown in FIG. 128, the left-side end point thereof is positioned in the center position in the x direction of the pixel #k (x=k) at the time of start of exposure, and moves from left to right by the movement amount v during exposure time=1. Also, with the spline function Ck+1(x), upon the left-side end point thereof moving from left to right by 0.5, this point is not included in the integration range regarding the pixel #k. The spline function Ck+1(x) moves by the movement amount v during exposure time=1, so the period necessary for moving by 0.5 is 1/(2 v) (=0.5/v).
Accordingly, the range of time t wherein the spline function Ck+1(x) is included in the integration range regarding the pixel #k is, as shown in the following expression, a range between 0 and 1/(2 v). However, let us say that exposure start point-in-time is 0.




  
    
      
        0
        ≤
        t
        ≤
        
          1
          
            2
            ⁢
            v
          
        
      
    
    
      
        (
        142
        )
      
    
  




Also, with the spline function Ck+1(x), a range between x=k and x=k+0.5 is included in the integration range regarding the pixel #k at the exposure start point-in-time.
The spline function Ck+1(x) moves from left to right by the movement amount v during exposure time=1, so if we say that the exposure start point-in-time is 0, the spline function Ck+1(X) moves from left to right by vt at a certain point-in-time t following start of exposure such as shown in FIG. 128. Accordingly, the range of the spline function Ck+1(X) included in the integration range regarding the pixel #k at the point-in-time t is from x=k to x=k+0.5−vt. That is, if we say that with the range in the x direction where the spline function Ck+1(x) is included in the integration range regarding the pixel #k, the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=k

β=−vt+k+0.5  (143)

The pixel value component Si of the pixel value Yk can be obtained in accordance with the following expression by integrating the spline function Ck+1(X) with the time range represented in Expression (142) and with the range in the x direction represented in Expression (143).




  
    
      
        
          
            
              
                S
                1
              
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    
                      2
                      ⁢
                      v
                    
                  
                
                ⁢
                
                  
                    ∫
                    k
                    
                      
                        -
                        vt
                      
                      +
                      k
                      +
                      0.5
                    
                  
                  ⁢
                  
                    
                      
                        C
                        
                          k
                          +
                          1
                        
                      
                      ⁡
                      
                        (
                        x
                        )
                      
                    
                    ⁢
                    
                      d
                      x
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    
                      2
                      ⁢
                      v
                    
                  
                
                ⁢
                
                  {
                  
                    
                      1
                      4
                    
                    ⁢
                    
                      M
                      k
                    
                    ⁢
                    
                      {
                      
                        
                          2
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              +
                              k
                              +
                              0.5
                            
                            )
                          
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              -
                              k
                              -
                              1.5
                            
                            )
                          
                        
                        -
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        
                          -
                          vt
                        
                        -
                        0.5
                      
                      )
                    
                    4
                  
                  -
                  
                    2
                    ⁢
                    
                      k
                      ⁡
                      
                        (
                        
                          
                            -
                            k
                          
                          -
                          2
                        
                        )
                      
                    
                  
                  +
                  1
                
                }
              
              -
              
                
                  1
                  4
                
                ⁢
                
                  M
                  
                    k
                    +
                    1
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  {
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          k
                          +
                          0.5
                        
                        )
                      
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          -
                          k
                          +
                          0.5
                        
                        )
                      
                    
                    -
                    
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          0.5
                        
                        )
                      
                      4
                    
                    +
                    
                      2
                      ⁢
                      
                        k
                        2
                      
                    
                  
                  }
                
                -
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      y
                      k
                    
                    ⁢
                    
                      {
                      
                        
                          
                            (
                            
                              vt
                              -
                              0.5
                            
                            )
                          
                          2
                        
                        -
                        1
                      
                      }
                    
                  
                  +
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      
                        
                          y
                          
                            k
                            +
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            
                              -
                              vt
                            
                            +
                            0.5
                          
                          )
                        
                      
                      2
                    
                  
                
                }
              
              ⁢
              
                d
                t
              
            
          
        
        
          
            
              =
              
              ⁢
              
                {
                
                  
                    
                      
                        
                          
                            1
                            48
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          (
                          
                            
                              
                                
                                  
                                    5
                                    ⁢
                                    
                                      y
                                      k
                                    
                                  
                                  +
                                  
                                    y
                                    
                                      k
                                      +
                                      1
                                    
                                  
                                  -
                                
                              
                            
                            
                              
                                
                                  
                                    
                                      53
                                      40
                                    
                                    ⁢
                                    
                                      M
                                      k
                                    
                                  
                                  -
                                  
                                    
                                      37
                                      40
                                    
                                    ⁢
                                    
                                      M
                                      
                                        k
                                        +
                                        1
                                      
                                    
                                  
                                
                              
                            
                          
                          )
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            
                              k
                              =
                              0
                            
                            ,
                            ...
                            ⁢
                            
                              
                            
                            ,
                            
                              N
                              -
                              1
                            
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            1
                            8
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          y
                          N
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            k
                            =
                            N
                          
                          )
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        144
        )
      
    
  




Next, FIG. 129 illustrates an integration range for calculating the pixel value component S2 of the pixel value Yk. Note that FIG. 129 is a diagram obtained by extracting a part of the integration range shown in FIG. 127.
The pixel value component S2 can be obtained by integrating the spline function Ck(x), which approximates the light signal to be projected on between the center position in the x direction of the pixel #k and the center position in the x direction of the left-adjacent pixel #k−1 thereof, within a period wherein the right end thereof exists within the integration range regarding the pixel #k at the time of start of exposure.
With the spline function Ck(x), as shown in FIG. 129, the right-side end point thereof is positioned in the center position in the x direction of the pixel #k (x=k) at the time of start of exposure, and moves from left to right by the movement amount v during exposure time=1. Also, with the spline function Ck(x), upon the right-side end point thereof moving from left to right by 0.5, this point is not included in the integration range regarding the pixel #k. The spline function Ck+1(x) moves by the movement amount v during exposure time=1, so the period necessary for moving by 0.5 is 1/(2 v) (=0.5/v).
Accordingly, the range of time t wherein the right-end end point of the spline function Ck(x) is included in the integration range regarding the pixel #k is, as shown in the following expression, a range between 0 and 1/(2 v).




  
    
      
        0
        ≤
        t
        ≤
        
          1
          
            2
            ⁢
            
              
            
            ⁢
            v
          
        
      
    
    
      
        (
        145
        )
      
    
  




Also, with the spline function Ck(x), a range between x=k−0.5 and x=k is included in the integration range regarding the pixel #k at the exposure start point-in-time.
The spline function Ck(x) moves from left to right by the movement amount v during exposure time=1, so if we say that the exposure start point-in-time is 0, the spline function Ck(x) moves from left to right by vt at a certain point-in-time t following start of exposure such as shown in FIG. 129. Accordingly, the range of the spline function Ck (x) included in the integration range regarding the pixel #k at the point-in-time t is from x=k−0.5−vt to x=k. That is, if we say that with the range in the x direction where the spline function Ck(x) is included in the integration range regarding the pixel #k at a certain point-in-time t within the period shown in Expression (145), the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=−vt+k−0.5

β=k  (146)

The pixel value component S2 of the pixel value Yk can be obtained in accordance with the following expression by integrating the spline function Ck(x) with the time range represented in Expression (145) and with the range in the x direction represented in Expression (146).




  
    
      
        
          
            
              
                S
                2
              
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    
                      2
                      ⁢
                      
                        
                      
                      ⁢
                      v
                    
                  
                
                ⁢
                
                  
                    ∫
                    
                      
                        -
                        vt
                      
                      +
                      k
                      -
                      0.5
                    
                    k
                  
                  ⁢
                  
                    
                      
                        C
                        k
                      
                      ⁡
                      
                        (
                        x
                        )
                      
                    
                    ⁢
                    
                      d
                      x
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    
                      2
                      ⁢
                      v
                    
                  
                
                ⁢
                
                  {
                  
                    
                      1
                      4
                    
                    ⁢
                    
                      M
                      
                        k
                        -
                        1
                      
                    
                    ⁢
                    
                      {
                      
                        
                          
                            -
                            2
                          
                          ⁢
                          
                            k
                            
                              
                                
                              
                              ⁢
                              2
                            
                          
                        
                        -
                        
                          2
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              +
                              k
                              -
                              0.5
                            
                            )
                          
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              -
                              k
                              -
                              0.5
                            
                            )
                          
                        
                        +
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    (
                    
                      
                        -
                        vt
                      
                      -
                      0.5
                    
                    )
                  
                  4
                
                }
              
              -
              
                
                  1
                  
                    
                      
                    
                    ⁢
                    4
                  
                
                ⁢
                
                  M
                  
                    
                      
                    
                    ⁢
                    k
                  
                
                ⁢
                
                  {
                  
                    
                      2
                      ⁢
                      k
                      ⁢
                      
                        (
                        
                          
                            -
                            k
                          
                          +
                          2
                        
                        )
                      
                    
                    -
                    1
                    -
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          k
                          -
                          0.5
                        
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    (
                    
                      
                        -
                        vt
                      
                      -
                      k
                      +
                      1.5
                    
                    )
                  
                  +
                  
                    
                      (
                      
                        
                          -
                          vt
                        
                        +
                        0.5
                      
                      )
                    
                    4
                  
                
                }
              
              +
              
                
                  1
                  2
                
                ⁢
                
                  
                    
                      y
                      
                        k
                        -
                        1
                      
                    
                    ⁡
                    
                      (
                      
                        
                          -
                          vt
                        
                        +
                        0.5
                      
                      )
                    
                  
                  2
                
              
              +
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    1
                    2
                  
                  ⁢
                  
                    y
                    k
                  
                  ⁢
                  
                    {
                    
                      1
                      -
                      
                        
                          (
                          
                            
                              -
                              vt
                            
                            +
                            0.5
                          
                          )
                        
                        2
                      
                    
                    }
                  
                
                }
              
              ⁢
              
                d
                t
              
            
          
        
        
          
            
              =
              
              ⁢
              
                {
                
                  
                    
                      
                        
                          
                            1
                            48
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          (
                          
                            
                              
                                
                                  
                                    11
                                    ⁢
                                    
                                      y
                                      
                                        
                                          
                                        
                                        ⁢
                                        k
                                      
                                    
                                  
                                  +
                                  
                                    7
                                    ⁢
                                    
                                      y
                                      
                                        
                                          
                                        
                                        ⁢
                                        
                                          k
                                          ⁢
                                          
                                            
                                          
                                          -
                                          
                                            
                                          
                                          ⁢
                                          1
                                        
                                      
                                    
                                  
                                  -
                                
                              
                            
                            
                              
                                
                                  
                                    
                                      203
                                      
                                        
                                          
                                        
                                        ⁢
                                        40
                                      
                                    
                                    ⁢
                                    
                                      M
                                      
                                        
                                          
                                        
                                        ⁢
                                        k
                                      
                                    
                                  
                                  -
                                  
                                    
                                      187
                                      
                                        
                                          
                                        
                                        ⁢
                                        40
                                      
                                    
                                    ⁢
                                    
                                      M
                                      
                                        
                                          
                                        
                                        ⁢
                                        
                                          k
                                          ⁢
                                          
                                            
                                          
                                          -
                                          
                                            
                                          
                                          ⁢
                                          1
                                        
                                      
                                    
                                  
                                
                              
                            
                          
                          )
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            
                              k
                              =
                              1
                            
                            ,
                            ...
                            ⁢
                            
                              
                            
                            ,
                            N
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            3
                            8
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          y
                          0
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            k
                            =
                            0
                          
                          )
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        147
        )
      
    
  




FIG. 130 illustrates an integration range for calculating the pixel value component S3,p of the pixel value Yk. Note that FIG. 130 is a diagram obtained by extracting a part of the integration range shown in FIG. 127.
Now, description will be made regarding the spline function Ck′(x) to be integrated for calculating the pixel value component S3,p of the pixel value Yk other than the spline function Ck+1(x) with reference to FIG. 131.
Note that FIG. 131, as with FIG. 126, illustrates the level of the spline function, which approximates the light signal function F(x), assuming that the crosswise direction is the x direction where the pixels of the processing unit are arrayed, the near-side direction is exposure time, and the lengthwise direction is level.
The spline functions move from left to right following start of exposure. According to movement during exposure time, the spline functions to be included within the integration range regarding the pixel #k shown with a slant line in FIG. 131 become the spline function Ck′ (x) to be integrated for calculating the pixel value component S3,p of the pixel value Yk other than the spline function Ck+1 (x).
As described above, the spline functions move from left to right following start of exposure, so according to the movement thereof, the left end thereof is sometimes included within the integration range regarding the pixel #k. The spline function Ck′(x) other than the spline function Ck+1 (x) is restricted to the spline function Ck−p+1(x) on the left side of the spline function Ck+1 (x) at the time of start of exposure. Note that a variable p is an integer equal to or greater than 1.
Here, the spline function Ck−p+1(x) exists in a range between x=k−p and x=k−p+1 at the time of start of exposure, as shown in FIG. 131.
The spline function Ck−p+1(x) moves in the x direction (from left to right) by the movement amount v during exposure time, so the left end of the spline function Ck−p+1(x) positioned at x=k−p at the time of start of exposure moves to the position of x=k−p+v immediately after passage of exposure time.
Accordingly, with the spline function Ck−p+1(x) of which the left end enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time, the variable p satisfies the following expression.

k−p+v≧k+0.5  (148)

Upon Expression (148) being reordered regarding p, the following expression is obtained.

p≦v−0.5  (149)

According to Expression (149), the spline function Ck−p+1(x) of which the left end enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time, becomes the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5]. Note that [v−0.5] represents the maximum integer equal to or less than v−0.5.
Now, description will be made regarding integration of the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5], of the spline functions to be integrated for calculating the pixel value component S3,p of the pixel value Yk.
As described above, with the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5], the left end thereof enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time. Accordingly, the spline function Ck−p+1(X) of p=1, 2, and so on through [v−0.5] moves by the width in the x direction of the pixel #k, i.e., by 1 here in the integration range regarding the pixel #k. The period necessary for moving by 1 with the movement amount v is 1/v, so the range of the time t wherein the left-end end point of the spline function Ck−p+1 (X) of p=1, 2, and so on through [v−0.5] is included in the integration range regarding the pixel #k is, as shown in FIG. 130, a range from 0 to 1/v, and can be represented with the following expression.




  
    
      
        0
        ≤
        t
        ≤
        
          1
          v
        
      
    
    
      
        (
        150
        )
      
    
  




Note that now, let us say that the point-in-time t when the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] moves by the movement amount v, the left-end end point thereof reaches the left end of the integration range regarding the pixel #k (x=k−0.5) is 0.
When the point-in-time t is 0, with the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5], the range from x=k−p to x=k−p+1 thereof exists in the integration range regarding the pixel #k. The spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5], at the certain time-in-point t until the left-end end point thereof reaches the right end of the integration range regarding the pixel #k (x=k+0.5), moves from left to right by vt from the position when the time-in-point t is 0. Accordingly, with a period since the point-in-time of 0 until the certain point-in-time t when the left-end end point of the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] reaches the right end of the integration range regarding the pixel #k (x=k+0.5), the range wherein the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] exists in the integration range regarding the pixel #k is from x=k−p to x=−vt+k−p+1.
That is, if we say that with the range in the x direction where the left-end end point of the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] exists in the integration range regarding the pixel #k at the certain point-in-time t, the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=k−p 

β=−vt+k−p+1  (151)

Of the pixel value component S3,p of the pixel value Yk, the pixel value components of p=1, 2, and so on through [v−0.5] can be obtained in accordance with the following expression by integrating the spline function Ck−p+1(x) with the time range represented in Expression (150) and with the range in the x direction represented in Expression (151).




  
    
      
        
          
            
              
                S
                
                  3
                  ,
                  p
                
              
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    
                      
                        
                      
                      ⁢
                      v
                    
                  
                
                ⁢
                
                  
                    ∫
                    
                      k
                      -
                      p
                    
                    
                      
                        -
                        vt
                      
                      +
                      k
                      -
                      p
                      +
                      1
                    
                  
                  ⁢
                  
                    
                      
                        C
                        
                          k
                          -
                          p
                          +
                          1
                        
                      
                      ⁡
                      
                        (
                        x
                        )
                      
                    
                    ⁢
                    
                      d
                      x
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    v
                  
                
                ⁢
                
                  {
                  
                    
                      1
                      4
                    
                    ⁢
                    
                      M
                      
                        k
                        -
                        p
                      
                    
                    ⁢
                    
                      {
                      
                        
                          2
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              +
                              k
                              -
                              p
                              +
                              1
                            
                            )
                          
                          ⁢
                          
                            (
                            
                              
                                -
                                vt
                              
                              -
                              k
                              +
                              p
                              -
                              1
                            
                            )
                          
                        
                        -
                      
                      ⁢
                      
                        
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        -
                        vt
                      
                      )
                    
                    4
                  
                  -
                  
                    2
                    ⁢
                    
                      (
                      
                        k
                        -
                        p
                      
                      )
                    
                    ⁢
                    
                      (
                      
                        
                          -
                          k
                        
                        +
                        p
                        -
                        2
                      
                      )
                    
                  
                  +
                  
                    
                      (
                      
                        -
                        1
                      
                      )
                    
                    4
                  
                
                }
              
              -
            
          
        
        
          
            
              
              ⁢
              
                
                  1
                  4
                
                ⁢
                
                  M
                  
                    k
                    -
                    p
                    +
                    1
                  
                
                ⁢
                
                  {
                  
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          k
                          -
                          p
                          +
                          1
                        
                        )
                      
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          -
                          k
                          +
                          p
                          +
                          1
                        
                        )
                      
                    
                    -
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        
                          -
                          vt
                        
                        +
                        1
                      
                      )
                    
                    4
                  
                  -
                  
                    2
                    ⁢
                    
                      (
                      
                        k
                        -
                        p
                      
                      )
                    
                    ⁢
                    
                      (
                      
                        
                          -
                          k
                        
                        +
                        p
                      
                      )
                    
                  
                
                }
              
              -
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      y
                      
                        k
                        -
                        p
                      
                    
                    ⁢
                    
                      {
                      
                        
                          
                            (
                            
                              -
                              vt
                            
                            )
                          
                          2
                        
                        -
                        
                          
                            (
                            
                              -
                              1
                            
                            )
                          
                          2
                        
                      
                      }
                    
                  
                  +
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      
                        
                          y
                          
                            k
                            -
                            p
                            +
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            
                              -
                              vt
                            
                            +
                            1
                          
                          )
                        
                      
                      2
                    
                  
                
                }
              
              ⁢
              
                d
                t
              
            
          
        
        
          
            
              =
              
              ⁢
              
                {
                
                  
                    
                      
                        
                          
                            1
                            60
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          (
                          
                            
                              
                                
                                  
                                    20
                                    ⁢
                                    
                                      y
                                      
                                        k
                                        -
                                        p
                                      
                                    
                                  
                                  +
                                  
                                    10
                                    ⁢
                                    
                                      y
                                      
                                        k
                                        -
                                        p
                                        +
                                        1
                                      
                                    
                                  
                                  -
                                
                              
                            
                            
                              
                                
                                  
                                    8
                                    ⁢
                                    
                                      M
                                      
                                        k
                                        -
                                        p
                                      
                                    
                                  
                                  -
                                  
                                    7
                                    ⁢
                                    
                                      M
                                      
                                        k
                                        -
                                        p
                                        +
                                        1
                                      
                                    
                                  
                                
                              
                            
                          
                          )
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            p
                            ≤
                            k
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            1
                            2
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          y
                          0
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            p
                            >
                            k
                          
                          )
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        152
        )
      
    
  




Next, FIG. 132 illustrates an integration range for calculating the pixel value component S3,p of the pixel value Yk. Note that FIG. 132 is a diagram obtained by extracting a part of the integration range shown in FIG. 127.
As described above, in this case, the spline function moves from left to right following start of exposure, so according to the movement thereof, sometimes enters within the integration range regarding the pixel #k. The spline function Ck′(x) other than the spline function Ck+1 (x) is restricted to the spline function Ck−p+1(x) on the left side of the spline function Ck+1 (x) at the time of start of exposure. Note that a variable p is an integer equal to or greater than 1.
Here, the spline function Ck−p+1(x) exists in a range between x=k−p and x=k−p+1 at the time of start of exposure, such as shown in FIG. 131.
The spline function Ck−p+1(x) moves in the x direction (from left to right) by the movement amount v during exposure time, so the left end of the spline function Ck−p+1(x) positioned at x=k−p at the time of start of exposure moves to the position of x=k−p+v immediately after passage of exposure time.
Accordingly, with the spline function Ck−p+1(x) of which the left end enters the left end of the integration range regarding the pixel #k (x=k−0.5) during exposure time, but does not escape from the integration range, i.e., does not move to the right end position of the integration range regarding the pixel #k (x=k+0.5), the variable p satisfies the following expression.

k−0.5<k−p+v<k+0.5  (153)

Upon Expression (153) being put in order regarding the p, the following expression is obtained.

v−0.5<p<v+0.5  (154)

The variable p is an integer value, so the variable p satisfying Expression (154) can be represented with the following expression.

p=[k+0.5]  (155)

Note that in Expression (155), [v+0.5] represents the maximum integer equal to or less than v+0.5.
According to Expression (155), the spline function Ck−p+1(x) of which the left end enters the integration range regarding the pixel #k, and does not escape from the integration range during exposure time, becomes the spline function Ck−p+1(x) of p=[v+0.5].
Now, description will be made regarding integration of the spline function Ck−p+1(x) of p=[v+0.5], of the spline functions to be integrated for calculating the pixel value component S3,p of the pixel value Yk.
As described above, with the spline function Ck−p+1(x) of p=[v+0.5], the left end thereof enters the left end of the integration range regarding the pixel #k (x=k−0.5) during exposure time. At the point of the left end of the spline function Ck−p+1(x) of p=[v+0.5] moving to a certain position within the integration range regarding the pixel #k, the exposure ends.
Now, let us say that the point-in-time t when the spline function Ck−p+1(x) of p=[v+0.5] moves by the movement amount v, the left-end end point thereof reaches the left end of the integration range regarding the pixel #k (x=k−0.5) is 0. In this case, the range of a period t wherein the left-end end point of the spline function Ck−p+1(x) of p=[v+0.5] is included in the integration range regarding the pixel #k until end of exposure is such as shown in FIG. 132.
That is to say, the range of the period t wherein the left-end end point of the spline function Ck−p+1(x) of p=[v+0.5] is included in the integration range regarding the pixel #k until end of exposure is a period obtained by subtracting the sum of a period 1/(2 v) for integrating the spline function Ck+1 (x) to calculate the pixel value component S1, and a period 1/v for integrating the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] to calculate the pixel value component S3,p from 1 serving as exposure time.
The number of the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] is represented with p−1 when p=[v+0.5], so the sum of the period 1/v for integrating the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] is (p−1)/V.
Accordingly, a period obtained by subtracting the sum (p−1)/v of the period 1/(2 v) for integrating the spline function Ck+1(x) and the period 1/v for integrating the spline function Ck−p+1(x) of p=1, 2, and so on through [v−0.5] for calculating the pixel value component S3,p from 1 serving as exposure time becomes 1−(p−1⁄2)/v(=1−1/(2 v)−(p−1)/v).
As described above, the range of time t wherein the left-end end point of the spline function Ck−p+1(x) of p=[v+0.5] is included in the integration range regarding the pixel #k is, as shown in the following expression, a range between 0 and 1−(p−1⁄2)/v.




  
    
      
        0
        ≤
        t
        ≤
        
          1
          -
          
            
              1
              v
            
            ⁢
            
              (
              
                p
                -
                
                  1
                  2
                
              
              )
            
          
        
      
    
    
      
        (
        156
        )
      
    
  




Also, when the point-in-time t is 0, with the spline function Ck−p+1(x) of p=[v+0.5], the range from x=k−p to x=k−p+1 thereof exists in the integration range regarding the pixel #k. With a certain point-in-time t until end of exposure, the spline function Ck−p+1(x) of p=[v+0.5] moves from left to right by vt from the position when the point-in-time t is 0. Accordingly, with a period since the point-in-time of 0 until the certain point-in-time t when the exposure ends, the range wherein the left-end end point of the spline function Ck−p+1(x) of p=[v+0.5] exists in the integration range regarding the pixel #k, is from x=k−p to x=−vt+k−p+1.
That is, if we say that with the range in the x direction where the left-end end point of the spline function Ck−p+1(x) of p=[v+0.5] exists in the integration range regarding the pixel #k at the certain point-in-time t, the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=k−p 

β=−vt+k−p+1  (157)

Of the pixel value component S3,p of the pixel value Yk, the pixel value components of p=[v+0.5] can be obtained in accordance with the following expression by integrating the spline function Ck−p+1(x) with the time range represented in Expression (156) and with the range in the x direction represented in Expression (157).




  
    
      
        
          S
          
            3
            ,
            p
          
        
        =
        
          
            
              ∫
              0
              
                {
                
                  1
                  -
                  
                    
                      1
                      v
                    
                    ⁢
                    
                      (
                      
                        p
                        -
                        
                          1
                          2
                        
                      
                      )
                    
                  
                
                }
              
            
            ⁢
            
              
                ∫
                
                  k
                  -
                  p
                
                
                  
                    -
                    vt
                  
                  +
                  k
                  -
                  p
                  +
                  1
                
              
              ⁢
              
                
                  
                    C
                    
                      k
                      -
                      p
                      +
                      1
                    
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  t
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            {
            
              
                
                  
                    
                      
                        
                          
                            
                              
                                
                                  
                                    1
                                    48
                                  
                                  ·
                                  
                                    1
                                    v
                                  
                                
                                ⁢
                                
                                  {
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        p
                                      
                                      -
                                      
                                        2
                                        ⁢
                                        v
                                      
                                      -
                                      1
                                    
                                    )
                                  
                                
                              
                            
                          
                          
                            
                              
                                {
                                
                                  
                                    
                                      (
                                      
                                        
                                          2
                                          ⁢
                                          p
                                        
                                        -
                                        
                                          2
                                          ⁢
                                          v
                                        
                                        -
                                        1
                                      
                                      )
                                    
                                    2
                                  
                                  -
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    12
                                    }
                                  
                                  ⁢
                                  
                                    y
                                    
                                      k
                                      -
                                      p
                                    
                                  
                                
                                -
                                
                                  {
                                  
                                    
                                      
                                        (
                                        
                                          
                                            2
                                            ⁢
                                            p
                                          
                                          -
                                          
                                            2
                                            ⁢
                                            v
                                          
                                          +
                                          1
                                        
                                        )
                                      
                                      3
                                    
                                    -
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    8
                                    }
                                  
                                  ⁢
                                  
                                    y
                                    
                                      k
                                      -
                                      p
                                      +
                                      1
                                    
                                  
                                
                                +
                              
                            
                          
                          
                            
                              
                                (
                                
                                  
                                    2
                                    ⁢
                                    p
                                  
                                  -
                                  
                                    2
                                    ⁢
                                    v
                                  
                                  -
                                  1
                                
                                )
                              
                            
                          
                          
                            
                              
                                {
                                
                                  
                                    
                                      3
                                      40
                                    
                                    ⁢
                                    
                                      
                                        (
                                        
                                          
                                            2
                                            ⁢
                                            p
                                          
                                          -
                                          
                                            2
                                            ⁢
                                            v
                                          
                                          -
                                          1
                                        
                                        )
                                      
                                      4
                                    
                                  
                                  -
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        p
                                      
                                      -
                                      
                                        2
                                        ⁢
                                        v
                                      
                                      -
                                      1
                                    
                                    )
                                  
                                  2
                                
                                +
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            6
                            }
                          
                          ⁢
                          
                            M
                            
                              k
                              -
                              p
                            
                          
                          ⁢
                          
                            {
                            
                              
                                
                                  3
                                  40
                                
                                ⁢
                                
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        p
                                      
                                      -
                                      
                                        2
                                        ⁢
                                        v
                                      
                                      +
                                      1
                                    
                                    )
                                  
                                  5
                                
                              
                              -
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              (
                              
                                
                                  2
                                  ⁢
                                  p
                                
                                -
                                
                                  2
                                  ⁢
                                  v
                                
                                +
                                1
                              
                              )
                            
                            3
                          
                          +
                        
                      
                    
                    
                      
                        
                          
                            
                              
                                28
                                5
                              
                              }
                            
                            ⁢
                            
                              M
                              
                                k
                                -
                                p
                                +
                                1
                              
                            
                          
                          }
                        
                      
                    
                  
                
                
                  
                    when
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        p
                        ≤
                        k
                      
                      )
                    
                  
                
              
              
                
                  
                    
                      
                        1
                        8
                      
                      ·
                      
                        1
                        v
                      
                    
                    ⁢
                    
                      (
                      
                        
                          2
                          ⁢
                          p
                        
                        -
                        
                          2
                          ⁢
                          v
                        
                        +
                        3
                      
                      )
                    
                  
                
                
                  
                    when
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        p
                        >
                        k
                      
                      )
                    
                  
                
              
              
                
                  
                    
                      (
                      
                        
                          2
                          ⁢
                          v
                        
                        -
                        
                          2
                          ⁢
                          p
                        
                        +
                        1
                      
                      )
                    
                    ⁢
                    
                      y
                      0
                    
                  
                
                
                  
                    
                  
                
              
            
          
        
      
    
    
      
        (
        158
        )
      
    
  




Next, FIG. 133 illustrates an integration range for calculating the pixel value component S4,p of the pixel value Yk. Note that FIG. 133 is a diagram obtained by extracting a part of the integration range shown in FIG. 127.
Now, the spline function Ck′ (x) to be integrated for calculating the pixel value component S4,p of the pixel value Yk other than the spline function Ck+1(x) is restricted to the spline function Ck−p(x) of which the right end exists more left than the left end of the integration range regarding the pixel #k at the time of start of exposure.
Here, the spline function Ck−p(x) exists in a range between x=k−p−1 and x=k−p at the time of start of exposure.
The spline function Ck−p(x) moves in the x direction (from left to right) by the movement amount v during exposure time, so the right end of the spline function Ck−p(x) positioned at x=k−p at the time of start of exposure moves to the position of x=k−p+v immediately after passage of exposure time.
Accordingly, with the spline function Ck−p(x) of which the right end enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time, the variable p satisfies the same expression as the above Expression (148) k−p+v≧k+0.5, i.e., expression (v−0.5)≧p.
As described above, the right end of the spline function Ck−p(x) enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time, and the spline function Ck−p+1(x) becomes the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5]. Note that [v−0.5] represents the maximum integer equal to or less than v−0.5.
Now, first, description will be made regarding integration of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5], of the spline functions to be integrated for calculating the pixel value component S4,p of the pixel value Yk.
As described above, with the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5], the right end thereof enters the left end of the integration range regarding the pixel #k (x=k−0.5), and moves to from the right end position (x=k+0.5) onward during exposure time. Accordingly, the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] moves by the width in the x direction of the pixel #k, i.e., by 1 here in the integration range regarding the pixel #k. The period necessary for moving by 1 with the movement amount v is 1/v, so the range of the time t wherein the right-end end point of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] is included in the integration range regarding the pixel #k is, as shown in FIG. 133, a range from 0 to 1/v, and can be represented with the following expression.




  
    
      
        0
        ≤
        t
        ≤
        
          1
          v
        
      
    
    
      
        (
        159
        )
      
    
  




Here, let us say that the point-in-time t when the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] moves by the movement amount v, the right-end end point thereof reaches the left end of the integration range regarding the pixel #k (x=k−0.5) is 0.
The right-end end point of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] reaches the left end of the integration range regarding the pixel #k (x=k−0.5) at the time-in-point t=0, and subsequently after passage of time t, moves from left to right by vt. In the event that the right-end end point of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] reaches the right end of the integration range regarding the pixel #k (x=k+0.5), and a range from x=k−p−1 to x=k−p exists in the integration range regarding the pixel #k.
Accordingly, with a certain point-in-time t until the right-end end point of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] reaches the right end of the integration range regarding the pixel #k (x=k+0.5), the range wherein the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] exists in the integration range regarding the pixel #k is from x=k−p−vt to x=k−p.
That is, if we say that with the range in the x direction where the right-end end point of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] exists in the integration range regarding the pixel #k at the certain point-in-time t, the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=−vt+k−p 

β=k−p  (160)

Of the pixel value component S4,p of the pixel value Yk, the pixel value components of p=1, 2, and so on through [v−0.5] can be obtained in accordance with the following expression by integrating the spline function Ck−p(x) with the time range represented in Expression (159) and with the range in the x direction represented in Expression (160).




  
    
      
        
          
            
              
                S
                
                  4
                  ,
                  p
                
              
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    v
                  
                
                ⁢
                
                  
                    ∫
                    
                      
                        -
                        vt
                      
                      +
                      k
                      -
                      p
                    
                    
                      k
                      -
                      p
                    
                  
                  ⁢
                  
                    
                      
                        C
                        
                          k
                          -
                          p
                        
                      
                      ⁡
                      
                        (
                        x
                        )
                      
                    
                    ⁢
                    
                      d
                      x
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  ∫
                  0
                  
                    1
                    v
                  
                
                ⁢
                
                  {
                  
                    
                      1
                      4
                    
                    ⁢
                    
                      M
                      
                        k
                        -
                        p
                        -
                        1
                      
                    
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  {
                  
                    
                      
                        -
                        2
                      
                      ⁢
                      
                        
                          (
                          
                            k
                            ⁢
                            
                              
                            
                            -
                            
                              
                            
                            ⁢
                            p
                          
                          )
                        
                        2
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          k
                          -
                          p
                        
                        )
                      
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          -
                          k
                          +
                          p
                        
                        )
                      
                    
                    +
                    
                      
                        (
                        
                          -
                          vt
                        
                        )
                      
                      4
                    
                  
                  }
                
                -
              
            
          
        
        
          
            
              
              ⁢
              
                
                  1
                  4
                
                ⁢
                
                  M
                  
                    k
                    -
                    p
                  
                
                ⁢
                
                  {
                  
                    
                      
                        -
                        2
                      
                      ⁢
                      
                        (
                        
                          k
                          -
                          p
                        
                        )
                      
                      ⁢
                      
                        (
                        
                          k
                          -
                          p
                          -
                          2
                        
                        )
                      
                    
                    -
                    1
                    -
                    
                      2
                      ⁢
                      
                        (
                        
                          
                            -
                            vt
                          
                          +
                          k
                          -
                          p
                        
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    (
                    
                      
                        -
                        vt
                      
                      -
                      k
                      -
                      p
                      +
                      2
                    
                    )
                  
                  +
                  
                    
                      (
                      
                        
                          -
                          vt
                        
                        +
                        1
                      
                      )
                    
                    4
                  
                
                }
              
              +
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      
                        
                          y
                          
                            k
                            -
                            p
                            -
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            -
                            vt
                          
                          )
                        
                      
                      2
                    
                  
                  +
                  
                    
                      1
                      2
                    
                    ⁢
                    
                      y
                      
                        k
                        -
                        p
                      
                    
                    ⁢
                    
                      {
                      
                        1
                        -
                        
                          
                            (
                            
                              
                                -
                                vt
                              
                              +
                              1
                            
                            )
                          
                          2
                        
                      
                      }
                    
                  
                
                }
              
              ⁢
              
                d
                t
              
            
          
        
        
          
            
              =
              
              ⁢
              
                {
                
                  
                    
                      
                        
                          
                            1
                            60
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          (
                          
                            
                              
                                
                                  
                                    20
                                    ⁢
                                    
                                      y
                                      
                                        k
                                        -
                                        p
                                      
                                    
                                  
                                  +
                                  
                                    10
                                    ⁢
                                    
                                      y
                                      
                                        k
                                        -
                                        p
                                        -
                                        1
                                      
                                    
                                  
                                  -
                                
                              
                            
                            
                              
                                
                                  
                                    8
                                    ⁢
                                    
                                      M
                                      
                                        k
                                        -
                                        p
                                      
                                    
                                  
                                  -
                                  
                                    7
                                    ⁢
                                    
                                      M
                                      
                                        k
                                        -
                                        p
                                        -
                                        1
                                      
                                    
                                  
                                
                              
                            
                          
                          )
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            p
                            ≤
                            
                              k
                              -
                              1
                            
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            1
                            2
                          
                          ·
                          
                            1
                            v
                          
                        
                        ⁢
                        
                          y
                          0
                        
                      
                    
                    
                      
                        when
                        ⁢
                        
                          
                        
                        ⁢
                        
                          (
                          
                            p
                            >
                            
                              k
                              -
                              1
                            
                          
                          )
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        161
        )
      
    
  




Next, FIG. 134 illustrates an integration range for calculating the pixel value component S4,p of the pixel value Yk. Note that FIG. 134 is the same diagram as the integration range shown in FIG. 127.
As described above, in this case, the spline function moves from left to right following start of exposure, so according to the movement thereof, the right end thereof sometimes enters within the integration range regarding the pixel #k. The spline function Ck′(x) other than the spline function Ck+1(x) is restricted to the spline function Ck−p(x) on the left side of the spline function Ck(x) at the time of start of exposure. Note that a variable p is an integer equal to or greater than 1.
Here, the spline function Ck−p(x) exists in a range between x=k−p−1 and x=k−p at the time of start of exposure.
The spline function Ck−p(x) moves in the x direction (from left to right) by the movement amount v during exposure time, so the right end of the spline function Ck−p(x) positioned at x=k−p at the time of start of exposure moves to the position of x=k−p+v immediately after passage of exposure time.
Accordingly, with the spline function Ck−p(x) of which the right end enters the left end of the integration range regarding the pixel #k (x=k−0.5) during exposure time, but does not escape from the integration range, i.e., does not move to the right end position of the integration range regarding the pixel #k (x=k+0.5), the variable p satisfies the same expression as the above Expression (153) k−0.5<k−p+v<k+0.5, i.e., p=[v+0.5]. Note that [v+0.5] represents the maximum integer equal to or less than v+0.5.
That is to say, the spline function Ck−p(x) of which the right end enters the integration range regarding the pixel #k, and does not escape from the integration range during exposure time, becomes the spline function Ck−p(x) of p=[v+0.5].
Now, description will be made regarding integration of the spline function Ck−p(x) of p=[v+0.5], of the spline functions to be integrated for calculating the pixel value component S4,p of the pixel value Yk.
As described above, with the spline function Ck−p(x) of p=[v+0.5], the right end thereof enters the left end of the integration range regarding the pixel #k (x=k−0.5) during exposure time. At the point of the right end of the spline function Ck−p(x) of p=[v+0.5] moving to a certain position within the integration range regarding the pixel #k, the exposure ends.
Now, let us say that the point-in-time t when the spline function Ck−p(x) of p=[v+0.5] moves by the movement amount v, the left-end end point thereof reaches the left end of the integration range regarding the pixel #k (x=k−0.5) is 0. In this case, the range of a period t wherein the left-end end point of the spline function Ck−p(x) of p=[v+0.5] is included in the integration range regarding the pixel #k until end of exposure is such as shown in FIG. 134.
That is to say, as with the case described in FIG. 132, the range of the period t wherein the right-end end point of the spline function Ck−p(x) of p=[v+0.5] is included in the integration range regarding the pixel #k until end of exposure is a period obtained by subtracting the sum of a period 1/(2 v) for integrating the spline function Ck+1(x) to calculate the pixel value component S1, and a period 1/v for integrating the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] to calculate the pixel value component S4,p from 1 serving as exposure time.
The number of the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] is represented with p−1 when p=[v+0.5], so the sum of the period 1/v for integrating the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] is (p−1)/v.
Accordingly, a period obtained by subtracting the sum (p−1)/v of the period 1/(2 v) for integrating the spline function Ck+1(x) and the period 1/v for integrating the spline function Ck−p(x) of p=1, 2, and so on through [v−0.5] from 1 serving as exposure time becomes 1−(p−1⁄2)/v (=1−1/(2 v)−(p−1)/v).
As described above, the range of time t wherein the right-end end point of the spline function Ck−p(x) of p=[v+0.5] is included in the integration range regarding the pixel #k is, as shown in the following expression, a range between 0 and 1−(p−1⁄2)/v.




  
    
      
        0
        ≤
        t
        ≤
        
          1
          -
          
            
              1
              v
            
            ⁢
            
              (
              
                p
                -
                
                  1
                  2
                
              
              )
            
          
        
      
    
    
      
        (
        162
        )
      
    
  




Also, according to the spline function Ck−p(x) of p=[v+0.5] moving from left to right during exposure time, the right end thereof reaches the left end of the integration range regarding the pixel #k at the time-in-point t=0, and subsequently after passage of time t, moves from left to right by vt from the position at the point-in-time t=0.
Accordingly, of the range between x=k−p−1 and x=k−p of the spline function Ck−p(x) of p=[v+0.5], the range existing in the integration range regarding the pixel #k at the point-in-time t is from x=k−p−vt to x=k−p.
That is, if we say that with the range in the x direction where the right-end end point of the spline function Ck−p(x) of p=[v+0.5] exists in the integration range regarding the pixel #k at the certain point-in-time t, the start point (point on the left side) thereof is represented with α, and the end point (point on the right side) thereof is represented with β, the start point α and the end point β are represented with the following expression.

α=−vt+k−p 

β=k−p  (163)

Of the pixel value component S4,p of the pixel value Yk, the pixel value components of p=[v+0.5] can be obtained in accordance with the following expression by integrating the spline function Ck−p(x) with the time range represented in Expression (162) and with the range in the x direction represented in Expression (163).




  
    
      
        
          S
          
            4
            ,
            p
          
        
        =
        
          
            
              ∫
              0
              
                {
                
                  1
                  -
                  
                    
                      1
                      v
                    
                    ⁢
                    
                      (
                      
                        p
                        -
                        
                          1
                          2
                        
                      
                      )
                    
                  
                
                }
              
            
            ⁢
            
              
                ∫
                
                  
                    -
                    vt
                  
                  +
                  k
                  -
                  p
                
                
                  k
                  -
                  p
                
              
              ⁢
              
                
                  
                    C
                    
                      k
                      -
                      p
                    
                  
                  ⁡
                  
                    (
                    x
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  t
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            {
            
              
                
                  
                    
                      
                        
                          
                            
                              
                                
                                  
                                    
                                      
                                        
                                          
                                            
                                              
                                                1
                                                
                                                  
                                                    
                                                  
                                                  ⁢
                                                  48
                                                
                                              
                                              ·
                                              
                                                1
                                                
                                                  
                                                    
                                                  
                                                  ⁢
                                                  v
                                                
                                              
                                            
                                            ⁢
                                            
                                              {
                                              
                                                
                                                  (
                                                  
                                                    
                                                      2
                                                      ⁢
                                                      
                                                        
                                                      
                                                      ⁢
                                                      p
                                                    
                                                    ⁢
                                                    
                                                      
                                                    
                                                    -
                                                    
                                                      
                                                    
                                                    ⁢
                                                    
                                                      2
                                                      ⁢
                                                      
                                                        
                                                      
                                                      ⁢
                                                      v
                                                    
                                                    ⁢
                                                    
                                                      
                                                    
                                                    -
                                                    
                                                      
                                                    
                                                    ⁢
                                                    1
                                                  
                                                  )
                                                
                                                2
                                              
                                            
                                          
                                        
                                      
                                      
                                        
                                          
                                            
                                              
                                                (
                                                
                                                  
                                                    2
                                                    ⁢
                                                    p
                                                  
                                                  -
                                                  
                                                    2
                                                    ⁢
                                                    v
                                                  
                                                  +
                                                  5
                                                
                                                )
                                              
                                              ⁢
                                              
                                                y
                                                
                                                  
                                                    
                                                  
                                                  ⁢
                                                  
                                                    k
                                                    ⁢
                                                    
                                                      
                                                    
                                                    -
                                                    
                                                      
                                                    
                                                    ⁢
                                                    p
                                                  
                                                
                                              
                                            
                                            -
                                          
                                        
                                      
                                      
                                        
                                          
                                            
                                              
                                                
                                                  (
                                                  
                                                    
                                                      2
                                                      ⁢
                                                      p
                                                    
                                                    -
                                                    
                                                      2
                                                      ⁢
                                                      v
                                                    
                                                    -
                                                    1
                                                  
                                                  )
                                                
                                                3
                                              
                                              ⁢
                                              
                                                y
                                                
                                                  k
                                                  -
                                                  p
                                                  -
                                                  1
                                                
                                              
                                            
                                            +
                                          
                                        
                                      
                                      
                                        
                                          
                                            
                                              (
                                              
                                                
                                                  2
                                                  ⁢
                                                  p
                                                
                                                -
                                                
                                                  2
                                                  ⁢
                                                  v
                                                
                                                -
                                                1
                                              
                                              )
                                            
                                            3
                                          
                                        
                                      
                                    
                                  
                                
                                
                                  
                                    
                                      {
                                      
                                        
                                          
                                            3
                                            40
                                          
                                          ⁢
                                          
                                            
                                              (
                                              
                                                
                                                  2
                                                  ⁢
                                                  p
                                                
                                                -
                                                
                                                  2
                                                  ⁢
                                                  v
                                                
                                                -
                                                1
                                              
                                              )
                                            
                                            2
                                          
                                        
                                        +
                                        
                                          3
                                          4
                                        
                                      
                                    
                                  
                                
                                
                                  
                                    
                                      
                                        
                                          (
                                          
                                            
                                              2
                                              ⁢
                                              p
                                            
                                            -
                                            
                                              2
                                              ⁢
                                              v
                                            
                                            -
                                            1
                                          
                                          )
                                        
                                        +
                                        2
                                      
                                      }
                                    
                                  
                                
                              
                            
                          
                          
                            
                              
                                
                                  M
                                  
                                    
                                      
                                    
                                    ⁢
                                    
                                      k
                                      ⁢
                                      
                                        
                                      
                                      -
                                      
                                        
                                      
                                      ⁢
                                      p
                                    
                                  
                                
                                -
                                
                                  
                                    (
                                    
                                      
                                        2
                                        ⁢
                                        p
                                      
                                      -
                                      
                                        2
                                        ⁢
                                        v
                                      
                                      -
                                      1
                                    
                                    )
                                  
                                  3
                                
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          {
                          
                            
                              
                                3
                                40
                              
                              ⁢
                              
                                
                                  (
                                  
                                    
                                      2
                                      ⁢
                                      p
                                    
                                    -
                                    
                                      2
                                      ⁢
                                      v
                                    
                                    -
                                    1
                                  
                                  )
                                
                                2
                              
                            
                            -
                            1
                          
                          }
                        
                      
                    
                    
                      
                        
                          
                            M
                            
                              k
                              -
                              p
                              -
                              1
                            
                          
                          }
                        
                      
                    
                  
                
                
                  
                    when
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        p
                        ≤
                        
                          k
                          -
                          1
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    
                      
                        1
                        8
                      
                      ·
                      
                        1
                        v
                      
                    
                    ⁢
                    
                      
                        (
                        
                          
                            2
                            ⁢
                            p
                          
                          -
                          
                            2
                            ⁢
                            v
                          
                          -
                          1
                        
                        )
                      
                      2
                    
                    ⁢
                    
                      y
                      0
                    
                  
                
                
                  
                    when
                    ⁢
                    
                      
                    
                    ⁢
                    
                      (
                      
                        p
                        >
                        
                          k
                          -
                          1
                        
                      
                      )
                    
                  
                
              
            
          
        
      
    
    
      
        (
        164
        )
      
    
  




The pixel value Yk of the pixel #k obtained from the image sensor is the sum of the pixel value component S1 in Expression (144), the pixel value component S2 in Expression (147), the pixel value component S3,p in Expression (152) and Expression (158), Expression (161), and Expression (164), so can be obtained from the following expression.

S1+S2+S3,p+S4,p=Yk  (165)

The suffix k of the pixel value Yk is represented with N+1 integer values in a range of 0 through N+1, so according to Expression (165), N+1 equations can be formulated. Also, the number of the unknown variables y0 through yN to be obtained are also N+1, so the N+1 unknown variables y0 through yN, and furthermore, the spline functions C0(x) through CN(x) defined with the variables y0 through yN can be obtained by solving the N+1 equations obtained from Expression (165) as a simultaneous linear equation.
That is to say, according to Expression (165), N+1 equations represented with the following Expression (166) through Expression (170) can be obtained by substituting Expression (144), Expression (147), Expression (152), Expression (158), Expression (161), and Expression (164).




  
    
      
        
          Y
          0
        
        =
        
          
            1
            v
          
          ⁢
          
            {
            
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    (
                    
                      -
                      
                        37
                        
                          48
                          ·
                          40
                        
                      
                    
                    )
                  
                  ⁢
                  
                    (
                    
                      
                        
                          a
                          
                            0
                            ,
                            
                              i
                              -
                              2
                            
                          
                        
                        ⁢
                        2
                        ⁢
                        
                          a
                          
                            0
                            ,
                            
                              i
                              -
                              1
                            
                          
                        
                      
                      +
                      
                        a
                        
                          0
                          ,
                          i
                        
                      
                    
                    )
                  
                  ⁢
                  
                    y
                    i
                  
                
              
              +
              
                
                  (
                  
                    v
                    -
                    
                      1
                      48
                    
                  
                  )
                
                ⁢
                
                  y
                  0
                
              
              +
              
                
                  1
                  48
                
                ⁢
                
                  y
                  1
                
              
            
            }
          
        
      
    
    
      
        (
        166
        )
      
    
  
  
    
      
        
          Y
          k
        
        =
        
          
            1
            v
          
          ⁢
          
            {
            
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  N
                
                ⁢
                
                  y
                  j
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    -
                    1
                  
                
              
              -
              
                
                  1
                  2
                
                ⁢
                
                  y
                  k
                
              
              +
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    +
                    1
                  
                
              
              +
              
                
                  (
                  
                    v
                    -
                    k
                    +
                    
                      1
                      2
                    
                  
                  )
                
                ⁢
                
                  y
                  0
                
              
              +
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          37
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            +
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        
                          1
                          4
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            ∑
                            
                              j
                              =
                              1
                            
                            k
                          
                          ⁢
                          
                            (
                            
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      j
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
            }
          
        
      
    
    
      
        (
        167
        )
      
    
  




Where, in Expression (167), k is an integer in a range of 1 through P−1. Also, P is the maximum integer equal to or less than v+0.5 ([v+0.5]).




  
    
      
        
          Y
          k
        
        =
        
          
            1
            v
          
          ⁢
          
            {
            
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  k
                
                ⁢
                
                  y
                  j
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    -
                    1
                  
                
              
              -
              
                
                  1
                  2
                
                ⁢
                
                  y
                  k
                
              
              +
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    +
                    1
                  
                
              
              +
              
                
                  1
                  6
                
                ⁢
                
                  {
                  
                    1
                    +
                    
                      
                        1
                        8
                      
                      ⁢
                      
                        (
                        
                          
                            2
                            ⁢
                            k
                          
                          -
                          
                            2
                            ⁢
                            v
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      
                        {
                        
                          
                            4
                            ⁢
                            
                              (
                              
                                k
                                -
                                v
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                k
                                -
                                v
                                +
                                2
                              
                              )
                            
                          
                          -
                          17
                        
                        }
                      
                    
                  
                  }
                
                ⁢
                
                  y
                  0
                
              
              -
              
                
                  1
                  6
                
                ⁢
                
                  {
                  
                    1
                    +
                    
                      
                        1
                        8
                      
                      ⁢
                      
                        (
                        
                          
                            2
                            ⁢
                            k
                          
                          -
                          
                            2
                            ⁢
                            v
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      
                        {
                        
                          
                            4
                            ⁢
                            
                              (
                              
                                k
                                -
                                v
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                k
                                -
                                v
                                +
                                2
                              
                              )
                            
                          
                          +
                          7
                        
                        }
                      
                    
                  
                  }
                
                ⁢
                
                  y
                  1
                
              
              +
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          37
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            +
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        
                          1
                          4
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            ∑
                            
                              j
                              =
                              1
                            
                            k
                          
                          ⁢
                          
                            (
                            
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      j
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                      -
                      
                        
                          1
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                k
                              
                              -
                              
                                2
                                ⁢
                                v
                              
                              +
                              1
                            
                            )
                          
                          3
                        
                        ⁢
                        
                          {
                          
                            
                              12
                              ⁢
                              
                                (
                                
                                  k
                                  -
                                  v
                                
                                )
                              
                              ⁢
                              
                                (
                                
                                  k
                                  -
                                  v
                                  +
                                  1
                                
                                )
                              
                            
                            -
                            37
                          
                          }
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                0
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  0
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                0
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
            }
          
        
      
    
    
      
        (
        168
        )
      
    
  




Note that in Expression (168), k is P.




  
    
      
        
          Y
          k
        
        =
        
          
            1
            v
          
          ⁢
          
            {
            
              
                
                  ∑
                  
                    j
                    =
                    
                      k
                      -
                      P
                    
                  
                  k
                
                ⁢
                
                  y
                  j
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    -
                    1
                  
                
              
              -
              
                
                  1
                  2
                
                ⁢
                
                  y
                  k
                
              
              +
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    +
                    1
                  
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  
                    (
                    
                      
                        2
                        ⁢
                        P
                      
                      -
                      
                        2
                        ⁢
                        v
                      
                      -
                      1
                    
                    )
                  
                  3
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                    -
                    1
                  
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  
                    (
                    
                      
                        2
                        ⁢
                        P
                      
                      -
                      
                        2
                        ⁢
                        v
                      
                      +
                      1
                    
                    )
                  
                  3
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                    +
                    1
                  
                
              
              -
              
                
                  1
                  6
                
                ⁢
                
                  {
                  
                    5
                    -
                    
                      
                        1
                        2
                      
                      ⁢
                      
                        (
                        
                          
                            2
                            ⁢
                            P
                          
                          -
                          
                            2
                            ⁢
                            v
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      
                        {
                        
                          
                            
                              (
                              
                                
                                  2
                                  ⁢
                                  P
                                
                                -
                                
                                  2
                                  ⁢
                                  v
                                
                                -
                                1
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                P
                                -
                                v
                                +
                                1
                              
                              )
                            
                          
                          -
                          3
                        
                        }
                      
                    
                  
                  }
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                  
                
              
              +
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          37
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            +
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            -
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        
                          1
                          4
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            ∑
                            
                              j
                              =
                              
                                k
                                -
                                P
                              
                            
                            k
                          
                          ⁢
                          
                            (
                            
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      k
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                      -
                      
                        
                          1
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                P
                              
                              -
                              
                                2
                                ⁢
                                v
                              
                              +
                              1
                            
                            )
                          
                          3
                        
                        ⁢
                        
                          {
                          
                            
                              3
                              ⁢
                              
                                
                                  (
                                  
                                    
                                      2
                                      ⁢
                                      P
                                    
                                    -
                                    
                                      2
                                      ⁢
                                      v
                                    
                                    -
                                    1
                                  
                                  )
                                
                                2
                              
                            
                            -
                            40
                          
                          }
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                P
                              
                              -
                              
                                2
                                ⁢
                                v
                              
                              +
                              1
                            
                            )
                          
                          3
                        
                        ⁢
                        
                          {
                          
                            
                              12
                              ⁢
                              
                                (
                                
                                  P
                                  -
                                  v
                                
                                )
                              
                              ⁢
                              
                                (
                                
                                  P
                                  -
                                  v
                                  +
                                  1
                                
                                )
                              
                            
                            -
                            37
                          
                          }
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        
                          1
                          60
                        
                        ⁢
                        
                          
                            {
                            
                              23
                              +
                              
                                
                                  1
                                  16
                                
                                ⁢
                                
                                  (
                                  
                                    
                                      2
                                      ⁢
                                      P
                                    
                                    -
                                    
                                      2
                                      ⁢
                                      v
                                    
                                    -
                                    1
                                  
                                  )
                                
                                ⁢
                                
                                  {
                                  
                                    
                                      
                                        
                                          (
                                          
                                            
                                              2
                                              ⁢
                                              P
                                            
                                            -
                                            
                                              2
                                              ⁢
                                              v
                                            
                                            -
                                            1
                                          
                                          )
                                        
                                        2
                                      
                                      ·
                                      
                                        {
                                        
                                          
                                            3
                                            ⁢
                                            
                                              
                                                (
                                                
                                                  
                                                    2
                                                    ⁢
                                                    P
                                                  
                                                  -
                                                  
                                                    2
                                                    ⁢
                                                    v
                                                  
                                                  -
                                                  1
                                                
                                                )
                                              
                                              2
                                            
                                          
                                          +
                                          
                                            15
                                            ⁢
                                            
                                              (
                                              
                                                
                                                  2
                                                  ⁢
                                                  P
                                                
                                                -
                                                
                                                  2
                                                  ⁢
                                                  v
                                                
                                                -
                                                1
                                              
                                              )
                                            
                                          
                                          +
                                          20
                                        
                                        }
                                      
                                    
                                    +
                                    120
                                  
                                  }
                                
                              
                            
                            }
                          
                          ·
                          
                            (
                            
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      k
                                      -
                                      P
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
            }
          
        
      
    
    
      
        (
        169
        )
      
    
  




Note that in Expression (169), k is an integer in a range of P+1 through N−1.




  
    
      
        
          Y
          k
        
        =
        
          
            1
            v
          
          ⁢
          
            {
            
              
                
                  ∑
                  
                    j
                    =
                    
                      k
                      -
                      P
                    
                  
                  k
                
                ⁢
                
                  y
                  j
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  y
                  
                    k
                    -
                    1
                  
                
              
              -
              
                
                  23
                  48
                
                ⁢
                
                  y
                  k
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  
                    (
                    
                      
                        2
                        ⁢
                        P
                      
                      -
                      
                        2
                        ⁢
                        v
                      
                      -
                      1
                    
                    )
                  
                  3
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                    -
                    1
                  
                
              
              -
              
                
                  1
                  48
                
                ⁢
                
                  
                    (
                    
                      
                        2
                        ⁢
                        P
                      
                      -
                      
                        2
                        ⁢
                        v
                      
                      +
                      1
                    
                    )
                  
                  3
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                    +
                    1
                  
                
              
              -
              
                
                  5
                  6
                
                ⁢
                
                  {
                  
                    5
                    -
                    
                      
                        1
                        2
                      
                      ⁢
                      
                        (
                        
                          
                            2
                            ⁢
                            P
                          
                          -
                          
                            2
                            ⁢
                            v
                          
                          -
                          1
                        
                        )
                      
                      ⁢
                      
                        {
                        
                          
                            
                              (
                              
                                
                                  2
                                  ⁢
                                  P
                                
                                -
                                
                                  2
                                  ⁢
                                  v
                                
                                -
                                1
                              
                              )
                            
                            ⁢
                            
                              (
                              
                                P
                                -
                                v
                                +
                                1
                              
                              )
                            
                          
                          -
                          3
                        
                        }
                      
                    
                  
                  }
                
                ⁢
                
                  y
                  
                    k
                    -
                    P
                  
                
              
              +
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          37
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          2
                        
                        ⁢
                        
                          
                            ∑
                            
                              j
                              =
                              
                                k
                                -
                                P
                              
                            
                            
                              k
                              -
                              1
                            
                          
                          ⁢
                          
                            (
                            
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      j
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    j
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                      -
                      
                        
                          1
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                P
                              
                              -
                              
                                2
                                ⁢
                                v
                              
                              +
                              1
                            
                            )
                          
                          3
                        
                        ⁢
                        
                          {
                          
                            
                              3
                              ⁢
                              
                                
                                  (
                                  
                                    
                                      2
                                      ⁢
                                      P
                                    
                                    -
                                    
                                      2
                                      ⁢
                                      v
                                    
                                    -
                                    1
                                  
                                  )
                                
                                2
                              
                            
                            -
                            40
                          
                          }
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        
                          1
                          
                            48
                            ·
                            40
                          
                        
                        ⁢
                        
                          
                            (
                            
                              
                                2
                                ⁢
                                P
                              
                              -
                              
                                2
                                ⁢
                                v
                              
                              +
                              1
                            
                            )
                          
                          3
                        
                        ⁢
                        
                          {
                          
                            
                              12
                              ⁢
                              
                                (
                                
                                  P
                                  -
                                  v
                                
                                )
                              
                              ⁢
                              
                                (
                                
                                  P
                                  -
                                  v
                                  +
                                  1
                                
                                )
                              
                            
                            -
                            37
                          
                          }
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  P
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        
                          1
                          60
                        
                        ⁢
                        
                          
                            {
                            
                              23
                              +
                              
                                
                                  1
                                  16
                                
                                ⁢
                                
                                  (
                                  
                                    
                                      2
                                      ⁢
                                      P
                                    
                                    -
                                    
                                      2
                                      ⁢
                                      v
                                    
                                    -
                                    1
                                  
                                  )
                                
                                ⁢
                                
                                  {
                                  
                                    
                                      
                                        
                                          (
                                          
                                            
                                              2
                                              ⁢
                                              P
                                            
                                            -
                                            
                                              2
                                              ⁢
                                              v
                                            
                                            -
                                            1
                                          
                                          )
                                        
                                        2
                                      
                                      ·
                                      
                                        {
                                        
                                          
                                            3
                                            ⁢
                                            
                                              
                                                (
                                                
                                                  
                                                    2
                                                    ⁢
                                                    P
                                                  
                                                  -
                                                  
                                                    2
                                                    ⁢
                                                    v
                                                  
                                                  -
                                                  1
                                                
                                                )
                                              
                                              2
                                            
                                          
                                          +
                                          
                                            15
                                            ⁢
                                            
                                              (
                                              
                                                
                                                  2
                                                  ⁢
                                                  P
                                                
                                                -
                                                
                                                  2
                                                  ⁢
                                                  v
                                                
                                                -
                                                1
                                              
                                              )
                                            
                                          
                                          +
                                          20
                                        
                                        }
                                      
                                    
                                    +
                                    120
                                  
                                  }
                                
                              
                            
                            }
                          
                          ·
                          
                            (
                            
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    2
                                  
                                
                              
                              -
                              
                                2
                                ⁢
                                
                                  a
                                  
                                    
                                      k
                                      -
                                      P
                                      -
                                      1
                                    
                                    ,
                                    
                                      i
                                      -
                                      1
                                    
                                  
                                
                              
                              +
                              
                                a
                                
                                  
                                    k
                                    -
                                    P
                                    -
                                    1
                                  
                                  ,
                                  i
                                
                              
                            
                            )
                          
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
            }
          
        
      
    
    
      
        (
        170
        )
      
    
  




Note that in Expression (170), k is N.
The N+1 unknown variables y0 through yN, and furthermore, the spline functions C0(x) through CN(x) defined with the variables y0 through yN can be obtained by solving the N+1 equations of Expression (166) through Expression (170) as a simultaneous linear equation, i.e., the spline functions C0(x) through CN(x) which approximate the light signal function F(x) corresponding to the actual world 1 light signal to be projected on the processing unit.
Incidentally, according to the physical model shown in FIG. 125, the curved surface serving as a locus obtained by the spline function Ck(x), which approximates the light signal function F(x), continuously moving in the horizontal direction (x direction) by the movement amount v during the exposure time of the image sensor, is integrated in the time direction during the exposure time alone, and also is integrated by only the length in the x direction of the pixel #k of the processing unit in the x direction, thereby obtaining the pixel value Yk of the pixel #k.
The spline function Ck(x) which approximates the light signal function F(x) continuously moves by the movement amount v in the horizontal direction (x direction), so that the range in the x direction of the spline function Ck(x) to be integrated during exposure time changes at the pixel #k, and thus, the range in the x direction of the spline function Ck(x) to be integrated for each point-in-time during exposure time changes at the pixel #k, so that the pixel value Yk obtained as a result of integration at the pixel #k results in the pixel value including movement blurring.
Accordingly, in order to remove movement blurring from the pixel value Yk of the pixel #k, an arrangement may be made wherein the range in the x direction of the spline function Ck(x) to be integrated during exposure time does not change at the pixel #k.
That is, if we say that the pixel value having no movement blurring regarding the pixel #k is represented with Xk, this pixel value Xk having no movement blurring can be obtained by integrating a curved surface (model) to be obtained by assuming that the spline function Ck(x) which approximates the light signal function F(x) does not move in the x direction from the position at the time of start of exposure during exposure time, in the time direction during exposure time, and also integrating (reintegrating) this in the x direction by the length of the x direction of the pixel #k of the processing unit.
Now, if we say that exposure time is 1, the above integration is equal to integrating the spline function Ck(x) by the length in the x direction of the pixel #k. Accordingly, the pixel value Xk having no movement blurring regarding the pixel #k can be obtained by setting a range between the start edge and the end edge (from the left end to the right end) in the x direction of the pixel #k to the integration range (α, β) in the above Expression (139). That is to say, the pixel value Xk having no movement blurring can be obtained with the following expression.




  
    
      
        
          X
          0
        
        =
        
          
            
              1
              8
            
            ⁢
            
              (
              
                
                  7
                  ⁢
                  
                    y
                    0
                  
                
                +
                
                  y
                  1
                
              
              )
            
          
          -
          
            
              7
              64
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        0
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          0
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        0
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        171
        )
      
    
  
  
    
      
        
          
            X
            k
          
          =
          
            
              
                1
                8
              
              ⁢
              
                (
                
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  +
                  
                    6
                    ⁢
                    
                      y
                      k
                    
                  
                  +
                  
                    y
                    
                      k
                      +
                      1
                    
                  
                
                )
              
            
            -
            
              
                1
                64
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        18
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              2
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        172
        )
      
    
  
  
    
      
        
          X
          N
        
        =
        
          
            
              1
              8
            
            ⁢
            
              (
              
                
                  y
                  
                    N
                    -
                    1
                  
                
                +
                
                  7
                  ⁢
                  
                    y
                    N
                  
                
              
              )
            
          
          -
          
            
              7
              64
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          
                            N
                            -
                            2
                          
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        173
        )
      
    
  




Note that in Expression (172), k is an integer value in a range of 1 through N−1. Also, the reason why a case is classified into three cases, i.e., k=0, k=1 through N−1, and k=N to obtain the pixel value Xk having no movement blurring is caused by the above flat assumption. That is to say, flat assumption affects the left end pixel #0 and the right end pixel #N of the processing unit, so that the pixel values X0 and XN are obtained with a different expression from the case at the other pixels #1 through #N−1 of the processing unit.
As described above, the pixel value Xk closer to the actual world 1, i.e., here, the pixel value Xk having no movement blurring can be obtained by estimating the light signal function F(x), and integrating the spline function Ck(x) which approximates the light signal function F(x) as the estimation result assuming that change over time does not exist.
Incidentally, Expression (171) through Expression (173) has attempted to obtain the pixel value Xk by integrating the spline function Ck(x) which approximates the light signal function F(x) astride the width in the x direction of the pixel #k of the processing unit, but a pixel value having higher resolution can be obtained by integrating the spline function Ck(x) which approximates the light signal function F(x) astride a finer width, i.e., by setting finer a range than the width in the x direction of the pixel #k to the integration range (α, β) in the above Expression (139).
Specifically, for example, now, let us consider virtual pixels obtained by dividing the pixel #k in the x direction, and let us represent the right-side pixel and the left-side pixel obtained by dividing the pixel #k in the x direction as virtual pixels #k,left and #k,right. Further, let us represent the pixel values having no movement blurring of the virtual pixels #k,left and #k,right as Xk,left and Xk,right respectively.
The pixel values Xk,left and Xk,right having no movement blurring, for example, as shown in FIG. 136, can be obtained by integrating a curved surface (model) to be obtained by assuming that the spline function Ck(x) which approximates the light signal function F(x) does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction in increments of the width in the x direction of the virtual pixels #Xk,left and #Xk,right obtained by dividing the pixel #k of the processing unit.
Accordingly, the pixel values #Xk,left and #Xk,right can be obtained with the following expression.




  
    
      
        
          X
          
            0
            ,
            left
          
        
        =
        
          y
          0
        
      
    
    
      
        (
        174
        )
      
    
  
  
    
      
        
          X
          
            0
            ,
            right
          
        
        =
        
          
            
              1
              4
            
            ⁢
            
              (
              
                
                  3
                  ⁢
                  
                    y
                    0
                  
                
                +
                
                  y
                  1
                
              
              )
            
          
          -
          
            
              7
              32
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        0
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          0
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        0
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        175
        )
      
    
  
  
    
      
        
          
            X
            
              k
              ,
              left
            
          
          =
          
            
              
                1
                4
              
              ⁢
              
                (
                
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  +
                  
                    3
                    ⁢
                    
                      y
                      k
                    
                  
                
                )
              
            
            -
            
              
                1
                32
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        9
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    ]
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              2
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        176
        )
      
    
  
  
    
      
        
          
            X
            
              k
              ,
              right
            
          
          =
          
            
              
                1
                4
              
              ⁢
              
                (
                
                  
                    3
                    ⁢
                    
                      y
                      k
                    
                  
                  +
                  
                    3
                    ⁢
                    
                      y
                      
                        k
                        +
                        1
                      
                    
                  
                
                )
              
            
            -
            
              
                1
                32
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        9
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
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                              ⁢
                              
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                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
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                              ⁢
                              
                                a
                                
                                  k
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                            +
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    ]
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              2
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        177
        )
      
    
  
  
    
      
        
          X
          
            N
            ,
            left
          
        
        =
        
          
            
              1
              4
            
            ⁢
            
              (
              
                
                  y
                  
                    N
                    -
                    1
                  
                
                +
                
                  3
                  ⁢
                  
                    y
                    N
                  
                
              
              )
            
          
          -
          
            
              7
              32
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          
                            N
                            -
                            2
                          
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        178
        )
      
    
  
  
    
      
        
          X
          
            N
            ,
            right
          
        
        =
        
          y
          N
        
      
    
    
      
        (
        179
        )
      
    
  




According to the pixel values #Xk,left and #Xk,right obtained with Expression (174) through Expression (179), an image of which the number of pixels in the crosswise direction is double the original number of pixels (double-density image in the crosswise direction) can be obtained, so that movement blurring is removed, and further a high-resolution image can be obtained.
In the above case, the pixel #k has been divided into two, but the divided number of the pixel #k is not restricted to two. Also, here, a high-resolution image higher than the original image (input image) has been attempted to be obtained by dividing the pixel #k, but an image having a desired resolution can be obtained by adjusting the integration range for integrating a curved surface obtained by assuming that the spline function Ck(x) which approximates the light signal function F(x) does not move from the position at the time of start of exposure during exposure time. That is, if we say that exposure time is 1, an image having a desired resolution can be obtained by setting desired values to the integration range (α, β) in Expression (139).
In the event of yielding an image having a high resolution by obtaining the pixel values of the virtual pixels obtained by dividing the pixel #k, the boundaries of the virtual pixels making up the image are constrained with the boundary of the original pixel #k, but in the event of yielding an image having a desired resolution by directly adjusting the integration range (α, β) in Expression (139), the image does not need to receive such a constraint.
Note that here, the actual world 1 light signals approximated with the spline function are estimated considering mixture (space mixture and time mixture) due to the integration effects in the x direction and in the time t direction, so this estimating method belongs to the above two-dimensional approximating method (and two-dimensional reintegrating method). Accordingly, the method for estimating the actual world 1 light signals by the spline function approximating the actual world 1 light signals can be performed considering mixture due to the integration effects in an arbitrary two-dimensional direction in the time-space directions, such as the y direction and the t direction, or the x direction and the y direction other than the x direction and the t direction, as described with the two-dimensional approximating method. For example, in the event that a fine line having continuity wherein the line continues in a certain tilted direction is displayed on an input image, when processing is performed considering mixture due to the integration effects in the x direction and in the y direction, the number of pixels wherein the fine line proceeds to the x direction when proceeding by one pixel in the y direction is taken as continuity information representing the direction θ of the fine line, and Expression (166) through Expression (170) are calculated using the direction θ instead of the movement amount v thereof, whereby the spline function which approximates the actual world 1 can be obtained.
Further, the method for estimating the actual world 1 light signals by the spline function approximating the actual world 1 light signals can be applied to the above one-dimensional approximating method (and one-dimensional reintegrating method), and the three-dimensional approximating method (and three-dimensional reintegrating method) other than the two-dimensional approximating method. That is to say, the actual world 1 light signal is estimated by approximating the actual world 1 light signal with the spline function, considering mixture due to the integration effects in the x direction, y direction, or t direction alone, whereby an image having high image quality can be generated. Also, the actual world 1 light signal is estimated by approximating the actual world 1 light signal with the spline function, considering mixture due to the integration effects in all the directions of the x direction, y direction, and t direction, whereby an image having high image quality can be generated.
Next, FIG. 137 illustrates a configuration example of the movement blurring adjusting unit 17035 in FIG. 120 which generates an image having no movement blurring, and further, an image having a high resolution as necessary by the spline function approximating the actual world 1 light signals (light signal function F(x)) as described above.
In FIG. 137, the movement blurring adjusting unit 17035 comprises a physical model adapting unit 17051, a physical model value acquiring unit 17052, and a remixing unit 17053 in FIG. 120. Also, in FIG. 137, an arrangement is made wherein the movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032, the foreground components supplied from the foreground background separating unit 17033, and the processing unit information supplied from the processing unit determining unit 17034 are supplied to the physical model adapting unit 17051.
The physical model adapting unit 17051 comprises a modeling unit 17061, an equation creating unit 17062, and a simultaneous equation acquiring unit 17063.
The movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032 in FIG. 120, and the processing unit information supplied from the processing unit determining unit 17034 are supplied to the modeling unit 17061.
The modeling unit 17061 recognizes the number of pixels making up the processing unit (e.g., N+1 pixels in the physical model in FIG. 125) based on the processing unit information supplied from the processing unit determining unit 17034. Further, the modeling unit 17061 obtains, for example, the physical model information in FIG. 125 such as P(=[v+0.5]) in Expression (166) through Expression (170) from the number of pixels making up the processing unit and the movement amount v, and further, supplies the physical model information including the number of pixels making up the processing unit and the movement amount v to the equation creating unit 17062. Also, the modeling unit 17061 recognizes the position of the processing unit in the input image, and supplies information representing the position to the simultaneous equation acquiring unit 17063 via the equation creating unit 17062.
The equation creating unit 17062 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17061, and supplies these to the simultaneous equation acquiring unit 17063. Note that the equations of Expression (166) through Expression (170) to be created at the equation creating unit 17062 are equations wherein the variable v thereof is substituted with a specific value of the movement amount v serving as continuity information supplied to the modeling unit 17061 from the movement blurring adjusted amount output unit 17032 in FIG. 120.
The simultaneous equation acquiring unit 17063 recognizes the position of the processing unit in the input image from the information representing the position of the processing unit in the input image supplied from the modeling unit 17061 via the equation creating unit 17062, and acquires the pixel value of the pixel of the processing unit from the foreground components supplied from the foreground background separating unit 17033 in FIG. 120 based on the position thereof. Further, the simultaneous equation acquiring unit 17063 substitutes the pixel value of the pixel of the processing unit for the equations of Expression (166) through Expression (170) supplied from the equation creating unit 17062, and thus, acquires N+1 simultaneous equations, and supplies these to the physical model value acquiring unit 17052.
The physical model value acquiring unit 17052 comprises a simultaneous equation computing unit 17064, and the simultaneous equation supplied from the simultaneous equation acquiring unit 17063 is supplied to the simultaneous equation computing unit 17064. The simultaneous equation computing unit 17064 computes (solves) the simultaneous equation supplied from the simultaneous equation acquiring unit 17063, and thus, obtains N+1 variables yk which define the spline functions in Expression (137) and Expression (138) which approximate the actual world 1 signals, and supplies these to the remixing unit 17053.
The remixing unit 17053 obtains and outputs a pixel value having no movement blurring by integrating a curved surface to be obtained by assuming that the spline function, which is defined with the variables yk supplied from the simultaneous equation computing unit 17064, does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width in the x direction of the pixel #k of the processing unit.
Also, in the event that the remixing unit 17053 performs integration in the x direction, for example, in increments of the width in the x direction of the pixel #k of the processing unit, the pixel values represented with Expression (171) through Expression (173) are obtained, the image of the pixel values is configured with the same number of pixels as the input image. Also, in the event that the remixing unit 17053 performs integration in the x direction, for example, in increments of the 1⁄2 width in the x direction of the pixel #k of the processing unit, the pixel values represented with Expression (174) through Expression (179) are obtained, and with the image of the pixel values thereof, the pixels in the horizontal direction are configured with double the number of pixels in the horizontal direction of the input image.
Next, description will be made regarding the processing of the movement blurring adjusting unit 17035 in FIG. 137 with reference to the flowchart in FIG. 138.
First of all, in step S17051, the modeling unit 17061 acquires the movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032 in FIG. 120, and the processing unit information supplied from the processing unit determining unit 17034, and the flow proceeds to step S17052. In step S17052, the modeling unit 17061 subjects the actual world 1 light signal projected on the processing unit represented with the processing unit information acquired in step S17051 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17061 recognizes the number of pixels making up the processing unit based on the processing unit information supplied from the processing unit determining unit 17034. Further, the modeling unit 17061 obtains the physical model information in FIG. 125 from the number of pixels making up the processing unit, and the movement amount v acquired in step S17051, and supplies the physical model information to the equation creating unit 17062, and the flow proceeds to step S17053 from step S17052.
In step S17053, the equation creating unit 17062 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17061, supplies these to the simultaneous equation acquiring unit 17063, and the flow proceeds to step S17054.
Note that the processing in steps S17052 and S17053 is performed regarding all of the processing units to be determined at the processing unit determining unit 17034 in FIG. 120.
In step S17054, the simultaneous equation acquiring unit 17063 selects a processing unit which has not been taken as the processing unit of interest, of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 as the processing unit of interest, acquires the pixel values Yk of the pixels of the processing unit of interest from the foreground components supplied from the foreground background separating unit 17033 in FIG. 120, and the flow proceeds to step S17055. In step S17055, the simultaneous equation acquiring unit 17063 substitutes the pixel values Yk of the pixels of the processing unit of interest for the equations of Expression (166) through Expression (170) regarding the processing unit of interest supplied from the equation creating unit 17062, and thus, acquires simultaneous equations for the same amount as the number of pixels of the processing unit of interest, and supplies these to the physical model value acquiring unit 17052.
Subsequently, the flow proceeds to step S17056 from step S17055, where the simultaneous equation acquiring unit 17063 determines regarding whether or not all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 have been taken as the processing unit of interest, and in the event that determination is made that all of the processing units have not been taken as the processing unit of interest, the flow returns to step S17054. In this case, in step S17054, the simultaneous equation acquiring unit 17063 newly selects a processing unit as the processing unit of interest, which has not been taken as the processing unit of interest, of the processing units obtained at the processing unit determining unit 17034 in FIG. 120, and hereafter, the same processing is repeated.
Also, in the event that determination is made in step S17056 that all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 have been taken as the processing unit of interest, i.e., in the event that simultaneous equations have been obtained regarding all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120, the flow proceeds to step S17057, where the simultaneous equation computing unit 17064 computes (solves) the simultaneous equations supplied from the simultaneous equation acquiring unit 17063, and thus, obtains the spline functions in Expression (137) and Expression (138) which approximates the actual world 1 signals, supplies these to the remixing unit 17053, and the flow proceeds to step S17058.
In step S17058, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the simultaneous equation computing unit 17064. That is to say, the remixing unit 17053 obtains pixel values having no movement blurring for each processing unit by integrating a curved surface to be obtained by assuming that each of the spline functions obtained for each processing unit, supplied from the simultaneous equation computing unit 17064 does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width in the x direction of the pixel #k of the processing unit, and the flow proceeds to step S17059 from step S17058. In step S17059, the remixing unit 17053 outputs the image made up of the pixel values having no movement blurring obtained for each processing unit, i.e., the image of the foreground object having no movement blurring, and the processing ends.
As described above, assuming that the pixel value of each pixel corresponding to a position in the x direction of the space directions of the input image wherein the actual world 1 light signals are projected on a plurality of pixels each having time-space integration effects, and the movement amount of the foreground object within the input image wherein part of the actual world 1 light signal continuity is lost, is set, is a pixel value acquired by the light signal function (actual world function) F(x) corresponding to the actual world 1 light signal approximated with the spline function integrating a physical model representing to move while phase-shifting in the time direction according to the movement amount of the foreground object in the x direction and in the time direction, an arrangement is made to estimate the light signal function F(x), and as a result of the estimation thereof, the spline function which approximates the light signal function F(x) can be obtained.
Further, an arrangement has been made wherein an image made up of the pixel values wherein the movement blurring of the foreground object within the input image is removed is generated by integrating (reintegrating) the spline function which approximates the light signal function F(x) thereof in the x direction and in the time direction in predetermined increments, whereby the image obtained by removing the movement blurring from the input image can be obtained.
That is to say, in general, a certain degree of movement blurring is allowed in photography such as a normal television broadcast, and a movie, and also, movement blurring is sometimes utilized as visual effects by adjusting the shutter time of a camera. However, in the event that movement blurring occurs on an image obtained by imaging with a camera, it is basically difficult to remove the movement blurring from the image including the movement blurring, and in the event that excessive movement blurring occurs on the obtained image, the image including the movement blurring is discarded as a photography failure.
Also, examples of a conventional method for removing movement blurring include a method for performing processing using a Wiener filter most appropriate for the movement direction and movement amount thereof. However, the processing using a Wiener filter brings out an advantage in an ideal state (as to an ideal image), but collapse sometimes occurs as to a real image such as subjected to quantization, and further including noise.
On the other hand, as described above, in the event of estimating the light signal function F(x), and integrating the spline function which approximates the light signal function F(x) as the estimated result thereof, a distinct image of which movement blurring is removed can be obtained even from a real image such as subjected to quantization and further including noise.
Note that with the technique for removing movement blurring by estimating the light signal function F(x), and integrating the spline function which approximates the light signal function F(x) as the estimated result thereof, even in the event that the movement amount of the foreground object and so forth, which is a cause of movement blurring, is smaller than the size of a pixel, movement blurring can be removed precisely.
Also, in the event of estimating the light signal function F(x), and integrating the spline function which approximates the light signal function F(x) as the estimated result thereof, movement blurring can be removed, and also the number of pixels of the image which can be obtained can be increased according to the setting of an integration range when integrating the spline function. That is to say, the number of pixels of an image can be increased with, for example, class classification adapting processing, linear interpolation processing, or the like, but for example, upon the image of which movement blurring was removed with processing using a Wiener filter being subjected to class classification adapting processing or linear interpolation processing, collapse caused with the processing using a Wiener filer is sometimes emphasized. On the other hand, in the event of estimating the light signal function F(x), and integrating the spline function which approximates the light signal function F(x) as the estimated result thereof, removal of movement blurring and increase of the number of pixels of the image which can be obtained can be done simultaneously without performing class classification adapting processing, linear interpolation processing, or the like. Here, according to increase of the number of pixels of the image, the resolution of the image can be improved, or the image can be magnified. Also, the resolution in the time direction can be improved as well as the number of pixels of the image which can be obtained, i.e., increase of the resolution in the spatial direction, depending on the setting of an integration range when integrating the spline function which approximates the light signal function F(x).
Note that in the event of estimating the light signal function F(x), in addition to employing the physical model shown in FIG. 125 wherein the actual world 1 light signals are approximated with a function which changes smoothly (here, spline function), and the function which smoothly changes continuously moves, a physical model wherein the actual world 1 light signals are approximated with a stepwise function which takes a steady value in increments of the width of a pixel, and the stepwise function moves in a scatter manner in increments of the width of a pixel can be employed. In this case, the value of the stepwise function which approximates the actual world 1 light signals to be projected on the pixels is constant within the pixels, so space mixture is not caused, but the stepwise function moves in a scatter manner in increments of the width of a pixel, so with before and after movement thereof, the different value of the stepwise function is projected on the pixels, so that time mixture is caused. Accordingly, the physical model wherein the actual world 1 light signals are approximated with a stepwise function which takes a steady value in increments of the width of a pixel, and the stepwise function moves in a scatter manner in increments of the width of a pixel can be conceived as a model considering not space mixture but time mixture alone.
The physical model using the stepwise function considers time mixture as with the physical model using the function which changes smoothly, so even in the event of employing the physical model using the stepwise function, movement blurring can be removed. However, the physical model using the function which changes smoothly considers not only time mixture but also space mixture, so in the event of employing the physical model using the function which changes smoothly can perform higher precision processing than the case of the physical model using the stepwise function.
Next, for example, in the event of focusing on the actual world 1 light signals to be projected on small regions such as one pixel of an image sensor, change of the light signal in such a small region is generally small. Accordingly, in the event of estimating the actual world 1 light signals, the actual world 1 light signals can be estimated more precisely by introducing a constraint condition wherein change (disorderliness) of the light signal at a pixel is small.
Now, for example, as described above, let us say that the actual world 1 light signals are approximated with the three-dimensional spline function, and a constraint condition wherein change of the light signal at a pixel is small is introduced. Now, the term “change of the light signal at a pixel is small” means that change in the pixel value of the portion equivalent to finer resolution than a pixel is small. Also, the term “change of the light signal at a pixel is small” means that an in-pixel tilt is small if we say that the amount-of-change of the pixel value at a certain position within the pixel is an in-pixel tilt.
A constraint condition wherein change of the light signal at a pixel is small can be described with, for example, an expression wherein the difference between the maximum value and the minimum value of the light signal at the pixel is equal to or less than (less than) a predetermined threshold.
Now, hereafter, an expression which describes such a constraint condition is referred to as an constraint condition expression as appropriate.
In order to describe a constraint condition expression assuming that the difference between the maximum value and the minimum value of the light signal at the pixel is equal to or less than a predetermined threshold, the maximum value and the minimum value of the light signal at one pixel are necessary. However, according to the above three-dimensional spline function, the actual world 1 light signal at one pixel is approximated with a curve equivalent to a curve represented with a three-dimensional expression, it is difficult to describe the constraint condition expression using the maximum value and the minimum value at a pixel on such a curve.
Accordingly, here, for example, as shown in FIG. 139, let us say that a constraint condition expression assuming that the pixel values at three small regions obtained by equally dividing one pixel region into three regions are equal is employed as a constraint condition expression which describes a constraint condition assuming that change of the light signal within a pixel is small.
Here, employing a constraint condition expression assuming that one pixel is divided into the number of small regions other than three, and the pixel values of the respective small regions are equal may be possible. However, in the event of employing the three-dimensional spline function as the spline function which approximates the actual world 1 light signals, one pixel needs to be divided into three or more small regions.
FIG. 139 illustrates, assuming that the horizontal direction is the x direction, and the vertical direction is the level direction of the actual world 1 light signal, the three-dimensional spline function which approximates the light signal.
Now, let us say that the pixel values obtained by projecting the actual world 1 light signals to be approximated with the spline function on three small regions obtained by dividing the x direction of a certain pixel into three equal regions are, as shown in FIG. 139, represented with SL, SC, and SR in order from the pixel value of the small region on the left side. Note that the pixel values SL, SC, and SR are equal to integral values obtained by integrating the curve of the actual world 1 light signal to be approximated with the spline function with each range equally dividing the x direction of one pixel into three, i.e., are equal to an area surrounded by the curve of the actual world 1 light signal to be approximated with the spline function, the x axis, and a straight line parallel to the level direction equally dividing the x direction of one pixel into three.
The constraint condition expression assuming that the pixel values SL, SC, and SR at three small regions obtained by equally dividing the region of one pixel into three are equal can be represented with the following expression.

SL=SC=SR  (180)

Note that a condition wherein the pixel values at three small regions obtained by equally dividing the region of one pixel into three are equal is equivalent to a condition wherein change of the light signal at a pixel is small.
The constraint condition expression of Expression (180) can be divided into the following two constraint condition expressions.

SL−SC=0  (181)

SC−SR=0  (182)

As described above, the pixel values SL, SC, and SR are integral values obtained by integrating the curve of the actual world 1 light signal to be approximated with the spline function with each range equally dividing the x direction of one pixel into three, so can be obtained in accordance with the following expression by assuming that the integral range (α, β) of Expression (139) is a range equally dividing the x direction of one pixel into three.




  
    
      
        
          S
          L
        
        =
        
          
            
              -
              
                31
                
                  4
                  ·
                  81
                
              
            
            ⁢
            
              M
              
                k
                -
                1
              
            
          
          -
          
            
              38
              
                4
                ·
                81
              
            
            ⁢
            
              M
              k
            
          
          +
          
            
              1
              9
            
            ⁢
            
              y
              
                k
                -
                1
              
            
          
          +
          
            
              2
              9
            
            ⁢
            
              y
              k
            
          
        
      
    
    
      
        (
        183
        )
      
    
  
  
    
      
        
          S
          C
        
        =
        
          
            
              -
              
                71
                
                  4
                  ·
                  36
                  ·
                  36
                
              
            
            ⁢
            
              M
              
                k
                -
                1
              
            
          
          -
          
            
              121
              
                2
                ·
                36
                ·
                36
              
            
            ⁢
            
              M
              k
            
          
          -
          
            
              71
              
                4
                ·
                36
                ·
                36
              
            
            ⁢
            
              M
              
                k
                +
                1
              
            
          
          +
          
            
              1
              72
            
            ⁢
            
              y
              
                k
                -
                1
              
            
          
          +
          
            
              11
              36
            
            ⁢
            
              y
              k
            
          
          +
          
            
              1
              72
            
            ⁢
            
              y
              
                k
                +
                1
              
            
          
        
      
    
    
      
        (
        184
        )
      
    
  
  
    
      
        
          S
          R
        
        =
        
          
            
              -
              
                38
                
                  4
                  ·
                  81
                
              
            
            ⁢
            
              M
              k
            
          
          -
          
            
              31
              
                4
                ·
                81
              
            
            ⁢
            
              M
              
                k
                +
                1
              
            
          
          +
          
            
              2
              9
            
            ⁢
            
              y
              k
            
          
          +
          
            
              1
              9
            
            ⁢
            
              y
              
                k
                +
                1
              
            
          
        
      
    
    
      
        (
        185
        )
      
    
  




Note that Mk in Expression (183) through Expression (185) is represented with the above (140) and Expression (141).
According to the constraint condition expression of Expression (181), N−1 constraint condition expressions shown in the following expression can be obtained by substituting Expression (183) and Expression (184) for the pixel values SL and SC respectively.




  
    
      
        
          
            
              
                1
                72
              
              ⁢
              
                (
                
                  
                    7
                    ⁢
                    
                      y
                      
                        k
                        -
                        1
                      
                    
                  
                  -
                  
                    6
                    ⁢
                    
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                      k
                    
                  
                  -
                  
                    y
                    
                      k
                      +
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                )
              
            
            +
            
              
                1
                
                  4
                  ·
                  36
                  ·
                  36
                
              
              ⁢
              
                
                  ∑
                  
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                ⁢
                
                  
                    {
                    
                      
                        
                          -
                          425
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      -
                      
                        366
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        71
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
          =
          0
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        186
        )
      
    
  




Also, according to the constraint condition expression of Expression (182), N−1 constraint condition expressions shown in the following expression can be obtained by substituting Expression (184) and Expression (185) for the pixel values SC and SR respectively.




  
    
      
        
          
            
              
                1
                72
              
              ⁢
              
                (
                
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  -
                  
                    6
                    ⁢
                    
                      y
                      k
                    
                  
                  -
                  
                    7
                    ⁢
                    
                      y
                      
                        k
                        +
                        1
                      
                    
                  
                
                )
              
            
            +
            
              
                1
                
                  4
                  ·
                  36
                  ·
                  36
                
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          -
                          71
                        
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        366
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        425
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
          =
          0
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        187
        )
      
    
  




Accordingly, according to introduction of the constraint conditions, 2 (N−1) constraint condition expressions in total of Expression (186) and Expression (187) can be obtained.
FIG. 140 is a diagram for describing a method for estimating the actual world using a constraint conditional expression.
According to the physical model shown in FIG. 125, N+1 equations shown in Expression (166) through Expression (170) can be obtained (generated). Now, in the above cases, flat assumption has been introduced, of N+1 equations shown in Expression (166) through Expression (170), the three of Expression (166) through Expression (168) are expressions to be affected by flat assumption, and the other two expressions of Expression (169) and Expression (170) are expressions not to be affected by flat assumption.
In addition, according to introduction of the constraint conditions, 2 (N−1) constraint condition expressions represented with Expression (186) and Expression (187) can be obtained.
Accordingly, according to introduction of the constraint conditions, 3N−1 (=N+1+2 (N−1)) equations in total of Expression (166) through Expression (170), Expression (186), and Expression (187) can be obtained.
That is to say, with the physical model shown in FIG. 125, the number of the variables yk which define the spline function which approximates the actual world 1 light signals are N+1, but on the other hand, 3N−1 equations greater than the number of the variables yk can be obtained.
3N−1 equations greater than the number of the unknown variables yk cannot be solved as a simultaneous equation. Accordingly, here, let us say that the variables yk to minimize the sum-of-squares of errors occurring at each of the 3N−1 equations are obtained, i.e., the 3N−1 equations made up of Expression (166) through Expression (168) to be affected by flat assumption, Expression (169) through Expression (170) not to be affected by flat assumption, and the constraint condition expressions of Expression (186) and Expression (187) are solved with the least-square method, as shown in FIG. 140.
First, let us consider the sum-of-square-of-errors in the N+1 equations of Expression (166) through Expression (170).
Now, let us say that the N+1 equations of Expression (166) through Expression (170) are represented with a matrix and column vector, as shown in the following expression.




  
    
      
        
          
            (
            
              
                
                  
                    A
                    
                      0
                      ,
                      0
                    
                  
                
                
                  
                    A
                    
                      0
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    A
                    
                      0
                      ,
                      N
                    
                  
                
              
              
                
                  
                    A
                    
                      1
                      ,
                      0
                    
                  
                
                
                  
                    A
                    
                      1
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    A
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
              
              
                
                  
                    A
                    
                      N
                      ,
                      0
                    
                  
                
                
                  
                    A
                    
                      N
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    A
                    
                      N
                      ,
                      N
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    y
                    0
                  
                
              
              
                
                  
                    y
                    1
                  
                
              
              
                
                  ⋯
                
              
              
                
                  
                    y
                    N
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  Y
                  0
                
              
            
            
              
                
                  Y
                  1
                
              
            
            
              
                ⋯
              
            
            
              
                
                  Y
                  N
                
              
            
          
          )
        
      
    
    
      
        (
        188
        )
      
    
  




In Expression (188), errors ek of the right side and the left side are represented with Expression (189).




  
    
      
        
          
            e
            k
          
          =
          
            
              Y
              k
            
            -
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  A
                  
                    k
                    ,
                    i
                  
                
                ⁢
                
                  y
                  i
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                0
              
              ,
              ⋯
              ⁢
              
                
              
              ,
              N
            
            )
          
        
      
    
    
      
        (
        189
        )
      
    
  




Now, as described above, of N+1 equations shown in Expression (166) through Expression (170), the three of Expression (166) through Expression (168) are expressions to be affected by flat assumption, and the other two expressions of Expression (169) and Expression (170) are expressions not to be affected by flat assumption.
Accordingly, let us consider to divide the sum-of-squares of errors in the N+1 equations of Expression (166) through Expression (170) into sum-of-squares E1 of errors in Expression (166) through Expression (168) to be affected by flat assumption, and sum-of-squares E2 of errors in Expression (169) and Expression (170) not to be affected by flat assumption.
The sum-of-squares E1 and E2 of errors are represented as follows as the sum-of-squares of errors ek represented with Expression (189).




  
    
      
        
          E
          1
        
        =
        
          
            
              ∑
              
                k
                =
                0
              
              P
            
            ⁢
            
              
                (
                
                  e
                  k
                
                )
              
              2
            
          
          =
          
            
              ∑
              
                k
                =
                0
              
              P
            
            ⁢
            
              
                (
                
                  
                    Y
                    k
                  
                  -
                  
                    
                      ∑
                      
                        i
                        =
                        0
                      
                      N
                    
                    ⁢
                    
                      
                        A
                        
                          k
                          ,
                          i
                        
                      
                      ⁢
                      
                        y
                        i
                      
                    
                  
                
                )
              
              2
            
          
        
      
    
    
      
        (
        190
        )
      
    
  
  
    
      
        
          E
          2
        
        =
        
          
            
              ∑
              
                k
                =
                
                  P
                  +
                  1
                
              
              N
            
            ⁢
            
              
                (
                
                  e
                  k
                
                )
              
              2
            
          
          =
          
            
              ∑
              
                k
                =
                
                  P
                  +
                  1
                
              
              N
            
            ⁢
            
              
                (
                
                  
                    Y
                    k
                  
                  -
                  
                    
                      ∑
                      
                        i
                        =
                        0
                      
                      N
                    
                    ⁢
                    
                      
                        A
                        
                          k
                          ,
                          i
                        
                      
                      ⁢
                      
                        y
                        i
                      
                    
                  
                
                )
              
              2
            
          
        
      
    
    
      
        (
        191
        )
      
    
  




Note that in Expression (190) and Expression (191), P is a value represented with expression P=[v+0.5] using the movement amount v, i.e., the maximum integer value equal to or less than v+0.5.
Next, let us consider the sum-of-squares of errors in the N−1 constraint condition expressions of Expression (186).
Now, let us say that the N−1 constraint condition expressions of Expression (186) are represented with a matrix and column vector, as shown in the following expression.




  
    
      
        
          
            (
            
              
                
                  
                    B
                    
                      1
                      ,
                      0
                    
                  
                
                
                  
                    B
                    
                      1
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    B
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  
                    B
                    
                      2
                      ,
                      0
                    
                  
                
                
                  
                    B
                    
                      2
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    B
                    
                      2
                      ,
                      N
                    
                  
                
              
              
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
              
              
                
                  
                    B
                    
                      
                        N
                        -
                        1
                      
                      ,
                      0
                    
                  
                
                
                  
                    B
                    
                      
                        N
                        -
                        1
                      
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    B
                    
                      
                        N
                        -
                        1
                      
                      ,
                      N
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    y
                    0
                  
                
              
              
                
                  
                    y
                    1
                  
                
              
              
                
                  ⋯
                
              
              
                
                  
                    y
                    N
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                0
              
            
            
              
                0
              
            
            
              
                ⋯
              
            
            
              
                0
              
            
          
          )
        
      
    
    
      
        (
        192
        )
      
    
  




In Expression (192), errors ek of the right side and the left side are represented with Expression (193).




  
    
      
        
          
            e
            k
          
          =
          
            0
            -
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  B
                  
                    k
                    ,
                    i
                  
                
                ⁢
                
                  y
                  i
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        193
        )
      
    
  




Accordingly, if we represent the sum-of-squares of errors ek of Expression (193) as E3, the sum-of-squares E3 of the errors ek is represented as follows.




  
    
      
        
          E
          3
        
        =
        
          
            
              ∑
              
                k
                =
                1
              
              
                N
                -
                1
              
            
            ⁢
            
              
                (
                
                  e
                  k
                
                )
              
              2
            
          
          =
          
            
              ∑
              
                k
                =
                1
              
              
                N
                -
                1
              
            
            ⁢
            
              
                (
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    N
                  
                  ⁢
                  
                    
                      B
                      
                        k
                        ,
                        i
                      
                    
                    ⁢
                    
                      y
                      i
                    
                  
                
                )
              
              2
            
          
        
      
    
    
      
        (
        194
        )
      
    
  




Next, let us consider the sum-of-squares of errors in the N−1 constraint condition expressions of Expression (187).
Now, let us say that the N−1 constraint condition expressions of Expression (187) are represented with a matrix and column vector, as shown in the following expression.




  
    
      
        
          
            (
            
              
                
                  
                    C
                    
                      1
                      ,
                      0
                    
                  
                
                
                  
                    C
                    
                      1
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    C
                    
                      1
                      ,
                      N
                    
                  
                
              
              
                
                  
                    C
                    
                      2
                      ,
                      0
                    
                  
                
                
                  
                    C
                    
                      2
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    C
                    
                      2
                      ,
                      N
                    
                  
                
              
              
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
                
                  ⋯
                
              
              
                
                  
                    C
                    
                      
                        N
                        -
                        1
                      
                      ,
                      0
                    
                  
                
                
                  
                    C
                    
                      
                        N
                        -
                        1
                      
                      ,
                      1
                    
                  
                
                
                  ⋯
                
                
                  
                    C
                    
                      
                        N
                        -
                        1
                      
                      ,
                      N
                    
                  
                
              
            
            )
          
          ⁢
          
            (
            
              
                
                  
                    y
                    0
                  
                
              
              
                
                  
                    y
                    1
                  
                
              
              
                
                  ⋯
                
              
              
                
                  
                    y
                    N
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                0
              
            
            
              
                0
              
            
            
              
                ⋯
              
            
            
              
                0
              
            
          
          )
        
      
    
    
      
        (
        195
        )
      
    
  




In Expression (195), errors ek of the right side and the left side are represented with Expression (196).




  
    
      
        
          
            e
            k
          
          =
          
            0
            -
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  C
                  
                    k
                    ,
                    i
                  
                
                ⁢
                
                  y
                  i
                
              
            
          
        
        ,
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                k
                =
                1
              
              ,
              ⋯
              ⁢
              
                
              
              ,
              
                N
                -
                1
              
            
            )
          
        
      
    
    
      
        (
        196
        )
      
    
  




Accordingly, if we represent the sum-of-squares of errors ek of Expression (196) as E4, the sum-of-squares E4 of the errors ek is represented as follows.




  
    
      
        
          E
          4
        
        =
        
          
            
              ∑
              
                k
                =
                1
              
              
                N
                -
                1
              
            
            ⁢
            
              
                (
                
                  e
                  k
                
                )
              
              2
            
          
          =
          
            
              ∑
              
                k
                =
                1
              
              
                N
                -
                1
              
            
            ⁢
            
              
                (
                
                  
                    ∑
                    
                      i
                      =
                      0
                    
                    N
                  
                  ⁢
                  
                    
                      C
                      
                        k
                        ,
                        i
                      
                    
                    ⁢
                    
                      y
                      i
                    
                  
                
                )
              
              2
            
          
        
      
    
    
      
        9197
        )
      
    
  




If we represent the sum-of-squares of errors in the left side and the right side of equations of the 3N−1 Expression (166) through Expression (170), Expression (186), and Expression (187) as E, the sum-of-squares E of errors is the sum of the sum-of-squares E1 of Expression (190), the sum-of-squares E2 of Expression (191), the sum-of-squares E3 of Expression (194), and the sum-of-squares E4 of Expression (197), so can be obtained by computing the following expression.

E=E1+E2+E3+E4  (198)

Obtaining the variables yk to minimize the sum-of-squares E of errors represented with Expression (198) allows the spline function to be defined by the variables yk to approximate the actual world 1 light signals in the physical model shown in FIG. 125 more precisely, and also reduces change in the pixels.
Now, the sum-of-squares E of errors represented with Expression (198) can be roughly divided into three types of the sum-of-squares E1 of errors in expressions to be affected by flat assumption, the sum-of-squares E2 of errors in expressions not to be affected by flat assumption, and the sum-of-squares E3+E4 of errors in constraint condition expressions.
Accordingly, here, let us say that of the above three types errors, for example, with the weight as to the sum-of-squares E2 of errors in expressions not to be affected by flat assumption as a standard (as 1), as shown in FIG. 140, the weight as to the sum-of-squares E1 of errors in expressions to be affected by flat assumption is represented with W1, and also the weight as to the sum-of-squares E3+E4 of errors in constraint condition expressions is represented with W2, the sum-of-squares E of errors in the left side and the right side of expressions of the 3N−1 Expression (166) through Expression (170), Expression (186), and Expression (187) is represented with Expression (199) instead of Expression (198).

E=W1·E1+E2+W2(E3+E4)  (199)

The weight W1 and weight W2 in Expression (199) allows the balance between the errors caused in expressions to be affected by flat assumption, the errors caused in expressions not to be affected by flat assumption, and the errors caused in constraint condition expressions to be adjusted.
The weight W1 represents a degree of laying weight on flat assumption in the event of obtaining the spline function which approximates the actual world 1 light signals. For example, in the event of setting the weight W1 to 1, the spline function which approximates the actual world 1 light signals can be obtained by equally treating expressions to be affected by flat assumption and expressions not to be affected by flat assumption. Also, for example, in the event of setting the weight W1 to 0, the spline function which approximates the actual world 0 light signals can be obtained without considering errors due to flat assumption.
The weight W2 represents a degree of laying weight on constraint conditions in the event of obtaining the spline function which approximates the actual world 1 light signals. The greater a value to be employed as the weight W2 is, the smaller change to be requested as the spline function which approximates the actual world 1 light signals is. As for the weight W1, a value equal to or greater than 0 can be employed, for example. In the event that flat assumption approximates the actual world 1 light signals precisely, the spline function which approximates the actual world 1 light signals precisely can be obtained by setting a value equal to or greater than 1 to the weight W1. As for the weight W2, a value of 10−5 through 0.1 or so can be employed, for example.
Now, according to Expression (199), the weight as to the errors caused in expressions not to be affected by flat assumption can be relatively adjusted by adjusting the weight W1 as to the errors caused in expressions to be affected by flat assumption, and the weight W2 as to the errors caused in constraint condition expressions. However, in Expression (199), in addition to the weight W1 and weight W2, an arrangement may be made wherein weight as to errors caused in expressions not to be affected by flat assumption is provided, thereby directly adjusting the weight.
The variables yk to minimize the sum-of-squares E of errors represented with Expression (199) are the variables yk for setting 0 to a value for subjecting the sum-of-squares E of errors to partial differentiation with the variables Yk as shown in the following Expression.




  
    
      
        
          
            
              ∂
              E
            
            
              ∂
              
                y
                n
              
            
          
          =
          
            
              
                
                  W
                  1
                
                ·
                
                  
                    ∂
                    
                      E
                      1
                    
                  
                  
                    ∂
                    
                      y
                      n
                    
                  
                
              
              +
              
                
                  ∂
                  
                    E
                    2
                  
                
                
                  ∂
                  
                    y
                    n
                  
                
              
              +
              
                
                  W
                  2
                
                ⁡
                
                  (
                  
                    
                      
                        ∂
                        
                          E
                          3
                        
                      
                      
                        ∂
                        
                          y
                          n
                        
                      
                    
                    +
                    
                      
                        ∂
                        
                          E
                          4
                        
                      
                      
                        ∂
                        
                          y
                          n
                        
                      
                    
                  
                  )
                
              
            
            =
            0
          
        
        ,
        
          

        
        ⁢
        
          where
          ⁢
          
            
          
          ⁢
          
            (
            
              
                n
                =
                0
              
              ,
              ...
              ⁢
              
                
              
              ,
              N
            
            )
          
        
      
    
    
      
        (
        200
        )
      
    
  




Upon the sum-of-squares E1 of Expression (190), the sum-of-squares E2 of Expression (191), the sum-of-squares E3 of Expression (194), and the sum-of-squares E4 of Expression (197) being substituted for Expression (200) and calculated, the normal equations of Expression (200) is obtained.




  
    
      
        
          
            
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The normal equations of Expression (201) are N+1 dimensional simultaneous linear equations, and the spline function Ck(x) of Expression (137) which is defined with the variables yk can be obtained by solving this Expression (201).
Upon the normal equations of Expression (201) being represented with a matrix and column vector, these become such as shown in Expression (202).




  
    
      
        
          
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        (
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        )
      
    
  




Following the spline function Ck(x) which approximates the actual world 1 light signals being obtained, an image having an arbitrary resolution and no movement blurring can be obtained by performing reintegration as with the case wherein constraint condition expressions are not introduced.
That is, if we say that exposure time is 1, an image having a desired resolution and no movement blurring can be obtained by setting desired values to the integration range (α, β) in Expression (139).
Specifically, for example, an image having the same resolution as the original image can be obtained by computing the above Expression (171) through Expression (173). Also, for example, an image having double the resolution in the horizontal direction of the original image can be obtained by computing the above Expression (174) through Expression (179).
Now, it can be conceived that flat assumption provides a constraint condition wherein the actual world 1 light signals in regions other than the region of the processing unit are steady values. In this case, the weight W2 can be regarded as the weight as to a constraint condition expression which describes such a constraint condition.
Next, FIG. 141 illustrates another configuration example of the movement blurring adjusting unit 17035 in FIG. 120 which generates an image having no movement blurring, and further, an image having a high resolution as necessary by the spline function approximating the actual world 1 light signals (light signal function F(x)), as described above. Note that in the drawings, the portions which correspond to those in the case of FIG. 12025 are denoted with the same reference numerals, and hereafter the description thereof will be omitted as appropriate.
With the movement blurring adjusting unit 17035 in FIG. 141, the spline function which approximates the actual world 1 light signal regarding an input image can be obtained using the 2 (N−1) constraint condition expressions shown in Expression (186) and Expression (187), which describe a constraint condition, as well as the N+1 equations shown in Expression (166) through Expression (170) to be obtained based on the physical model shown in FIG. 125, thereby generating an image having a desired resolution and no movement blurring.
That is to say, in FIG. 141, the movement blurring adjusting unit 17035 comprises a physical model adapting unit 17081, an in-pixel constraining-equation creating unit 17082, a physical model value acquiring unit 17083, and a remixing unit 17053. In FIG. 141, an arrangement is made wherein the movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032, and the processing unit information supplied from the processing unit determining unit 17034 are supplied to the physical model adapting unit 17081. Also, the foreground components supplied from the foreground background separating unit 17033 in FIG. 120 are arranged to be supplied to the physical model value acquiring unit 17083.
The physical model adapting unit 17081 comprises a modeling unit 17091, and an equation creating unit 17092.
The movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032 in FIG. 120, and the processing unit information supplied from the processing unit determining unit 17034 are supplied to the modeling unit 17091.
The modeling unit 17091 recognizes the number of pixels making up the processing unit (e.g., N+1 pixels in the physical model in FIG. 125) based on the processing unit information supplied from the processing unit determining unit 17034, as with the modeling unit 17061 in FIG. 137. Further, the modeling unit 17091 obtains the physical model information in FIG. 125 from the number of pixels making up the processing unit, and the movement amount v, and supplies the physical model information to the in-pixel constraining-equation creating unit 17082, and the equation creating unit 17092, as with the modeling unit 17061 in FIG. 137.
The equation creating unit 17092 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17091, and supplies these to the physical model value acquiring unit 17083. Note that the equations of Expression (166) through Expression (170) to be created at the equation creating unit 17092 are equations wherein the variable v thereof is substituted with a specific value of the movement amount v serving as continuity information supplied to the modeling unit 17091 from the movement blurring adjusted amount output unit 17032 in FIG. 120.
The in-pixel constraining-equation creating unit 17082 recognizes the number of pixels N+1 making up the processing unit from the information supplied from the modeling unit 17091, creates the constraint condition expressions shown in Expression (186) through Expression (187), and supplies these to the physical model value acquiring unit 17083.
The physical model value acquiring unit 17083, which comprises a least-square method adapting unit 17093, obtains (the variables yk which define) the spline function of Expression (137) by adapting the least-square method to the equations of Expression (166) through Expression (170) supplied from the equation creating unit 17092, and the constraint condition expressions shown in Expression (186) and Expression (187) supplied from the in-pixel constraining-equation creating unit 17082, and solving these.
That is to say, the least-square method adapting unit 17093 acquires the pixel values of the pixels of the processing unit from the foreground components supplied from the foreground background separating unit 17033 in FIG. 120, obtains (the variables yk which define) the spline function of Expression (137) by substituting the pixel values thereof for the normal equation of Expression (201) (or Expression (202)) to be obtained from the equations of Expression (166) through Expression (170) supplied from the equation creating unit 17092, and the constraint condition expressions shown in Expression (186) and Expression (187) supplied from the in-pixel constraining-equation creating unit 17082 and solving these, and supplies the obtained spline function to the remixing unit 17053.
Note that in the event that the least-square method adapting unit 17093 solves the normal equations of Expression (201), the weight W1 and weight W2 are necessary, but let us say that fixed values are set to the weight W1 and weight W2 at the least-square method adapting unit 17093 beforehand, for example.
Next, description will be made regarding the processing of the movement blurring adjusting unit 17035 in FIG. 141 with reference to the flowchart in FIG. 142.
First of all, in step S17081, the modeling unit 17091 acquires the movement amount v serving as continuity information supplied from the movement blurring adjusted amount output unit 17032 in FIG. 120, and the processing unit information supplied from the processing unit determining unit 17034, and the flow proceeds to step S17082. In step S17082, the modeling unit 17091 subjects the actual world 1 light signal projected on the processing unit represented with the processing unit information acquired in step S17081 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17091 recognizes the number of pixels making up the processing unit based on the processing unit information supplied from the processing unit determining unit 17034. Further, the modeling unit 17091 obtains the physical model information in FIG. 125 from the number of pixels making up the processing unit, and the movement amount v acquired in step S17081, and supplies the physical model information to the in-pixel constraining-equation creating unit 17082 and the equation creating unit 17092, and the flow proceeds to step S17083 from step S17082.
In step S17083, the equation creating unit 17092 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17091, supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17084.
In step S17084, the in-pixel constraining-equation creating unit 17082 creates the constraint condition expressions shown in Expression (186) and Expression (187), supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17085.
Note that the processing in steps S17082 through S17084 is performed regarding all of the processing units to be determined at the processing unit determining unit 17034 in FIG. 120.
In step S17085, the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 selects a processing unit which has not been taken as the processing unit of interest, of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 as the processing unit of interest, acquires the pixel values Yk of the pixels of the processing unit of interest from the foreground components supplied from the foreground background separating unit 17033 in FIG. 120, and the flow proceeds to step S17086.
In step S17086, the least-square method adapting unit 17093 obtains the normal equation of Expression (201) by substituting the pixel values Yk of the pixels of the processing unit of interest for the equations of Expression (166) through Expression (170) regarding the processing unit of interest supplied from the equation creating unit 17092, and the constraint condition expressions shown in Expression (186) and Expression (187) supplied from the in-pixel constraining-equation creating unit 17082, and further formulating the normal equation of Expression (201) using the weight W1 and weight W2, and the flow proceeds to step S17087.
In step S17087, the least-square method adapting unit 17093 determines regarding whether or not all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 have been taken as the processing unit of interest, and in the event that determination is made that all of the processing units have not been taken as the processing unit of interest, the flow returns to step S17085. In this case, in step S17085, the least-square method adapting unit 17093 newly selects a processing unit as the processing unit of interest, which has not been taken as the processing unit of interest, of the processing units obtained at the processing unit determining unit 17034 in FIG. 120, and hereafter, the same processing is repeated.
Also, in the event that determination is made in step S17087 that all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120 have been taken as the processing unit of interest, i.e., in the event that normal equations have been obtained regarding all of the processing units obtained at the processing unit determining unit 17034 in FIG. 120, the flow proceeds to step S17088, where the least-square method adapting unit 17093 obtains (the variables yk which define) the spline function of Expression (137) regarding each processing unit by solving the normal equations obtained regarding all of the processing units, i.e., obtains the spline functions of Expression (137) and Expression (138) which approximate the actual world 1 signals, supplies these to the remixing unit 17053, and the flow proceeds to step S17089.
In step S17089, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the least-square method adapting unit 17093. That is to say, the remixing unit 17053 obtains pixel values having no movement blurring for each processing unit by integrating a curved surface to be obtained by assuming that each of the spline functions obtained for each processing unit supplied from the least-square adapting unit 17093 does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width in the x direction of the pixel #k of the processing unit, and the flow proceeds to step S17090 from step S17089. In step S17090, the remixing unit 17053 outputs the image made up of the pixel values having no movement blurring obtained for each processing unit, i.e., the image of the foreground object having no movement blurring, and the processing ends.
As described above, assuming that the pixel value of each pixel corresponding to a position in the x direction of the space directions of the input image wherein the actual world 1 light signals are projected on a plurality of pixels each having time-space integration effects, and the movement amount of the foreground object within the input image wherein part of the actual world 1 light signal continuity is lost, is set, is a pixel value acquired by the light signal function (actual world function) F(x) corresponding to the actual world 1 light signal approximated with the spline function integrating a physical model representing to move while phase-shifting in the time direction according to the movement amount of the foreground object in the x direction and in the time direction, an arrangement is further made to estimate the light signal function F(x) by employing a constraint condition expression which provides a constraint condition wherein change in the pixel value within a pixel represented with the spline function which approximates the light signal function F(x) is small, and as a result of the estimation thereof, the spline function which approximates the light signal function F(x) precisely can be obtained.
Further, an arrangement has been made wherein an image made up of the pixel values wherein the movement blurring of the foreground object within the input image is removed is generated by integrating (reintegrating) the spline function which approximates the light signal function F(x) thereof in the x direction and in the time direction in predetermined increments, whereby the image having a desired resolution obtained by removing the movement blurring from the input image can be obtained.
Note that a constraint condition wherein change in the pixel value is small may be applied to the time direction as well as the spatial direction (x direction in the above case).
Next, with the signal processing device 4 in FIG. 113, the processing for estimating the actual world at the actual world estimating unit 17003, and the processing for generating an image using the estimated result of the actual world at the image generating unit 17004 are integrally referred to as actual processing, hereafter.
FIG. 143 illustrates a configuration example of an actual processing unit 17100 for performing the actual processing.
The actual processing unit 17100 is supplied with an input image to be subjected to the actual processing, and parameters necessary for the actual processing (the processing for estimating the actual world and the processing for generating an image using the estimated result of the actual world). The actual processing unit 17100 comprises the actual world estimating unit 17003, and the image generating unit 17004. With the actual world estimating unit 17003, the processing for estimating the actual world is performed using an input image and parameters necessary for the actual processing. With the image generating unit 17004, for example, an image obtained by removing movement blurring from the input image, an image having higher resolution than the input image, an image obtained by removing movement blurring from the input image, and also having higher resolution than the input image, or the like is generated using the estimated result of the actual world.
Now, examples of the parameters necessary for the actual processing, which are supplied to the actual processing unit 17100, include the processing region information output from the processing region setting unit 17001 in FIG. 113, the continuity information output from the continuity setting unit 17002, and further the weight W1 and weight W2 introduced in Expression (199).
FIG. 144 illustrates a configuration example of the actual processing unit 17100 in FIG. 143 in the case of performing processing for obtaining an image by removing movement blurring from an input image including movement blurring, or processing for obtaining an image from which movement blurring is removed and also having higher resolution than the input image. Note that in the drawings, the portions which correspond to those in the case of the movement blurring adjusting unit 17035 in FIG. 137 are denoted with the same reference numerals, and hereafter the description thereof will be omitted as appropriate.
The actual processing unit 17100 in FIG. 144 is supplied with an input image, and also is supplied with the processing region information from the processing region setting unit 17001 in FIG. 113 as the necessary parameter for the actual processing, and also is supplied with the continuity information from the continuity setting unit 17002 as the necessary parameter for the actual processing. Now, let us say that in FIG. 144, an object displayed in the processing region represented with the processing region information in an input image is, for example, moving in the horizontal direction at a constant speed, and thus, movement blurring occurs in the processing region. Further, let us say that in FIG. 144, the movement amount v of the object displayed in the processing region is employed as continuity information. Note that an image wherein a fine line as described above is displayed in the oblique direction may be employed as an input image. In this case, the processing region information needs to be information representing a region including the fine line in the input image (processing region), and the continuity information needs to be information representing the direction (angle) of the fine line.
In FIG. 144, the input image is supplied to a pre-processing unit 17101. Also, the processing region information of the parameters necessary for the actual processing is supplied to the modeling unit 17061 of the physical model adapting unit 17051, and the pre-processing unit 17101. Further, the continuity information of the parameters necessary for the actual processing is supplied to the modeling unit 17061 of the physical model adapting unit 17051.
The pre-processing unit 17101 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the simultaneous equation acquiring unit 17063 of the physical model adapting unit 17051.
Next, description will be made regarding the processing of the actual processing unit 17100 in FIG. 144 with reference to the flowchart in FIG. 145.
First of all, in step S17101, the modeling unit 17061 acquires the processing region information supplied from the processing region setting unit 17001 in FIG. 113, and the movement amount v serving as continuity information supplied from the continuity setting unit 17002 as the parameters necessary for the actual processing, also the pre-processing unit 17101 acquires the processing region information supplied from the processing region setting unit 17001 in FIG. 113 as the parameters necessary for the actual processing, and the flow proceeds to step S17102. In step S17102, the pre-processing unit 17101 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the simultaneous equation acquiring unit 17063 of the physical model adapting unit 17051.
Subsequently, the flow proceeds to step S17103 from step S17102, where the modeling unit 17061 subjects the actual world 1 light signal projected on the processing region represented with the processing region information acquired in step S17101 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17061 recognizes the number of pixels making up each horizontal line of the processing region based on the processing region information supplied from the processing region setting unit 17001. Here, each horizontal line of the processing region is equivalent to the processing unit described with the movement blurring adjusting unit 17035 in FIG. 137. Further, the modeling unit 17061 obtains the physical model information in FIG. 125 from the number of pixels making up each horizontal line of the processing region, and the movement amount v acquired in step S17101, and supplies the physical model information to the equation creating unit 17062, and the flow proceeds to step S17104 from step S17103.
In step S17104, the equation creating unit 17062 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17061, supplies these to the simultaneous equation acquiring unit 17063, and the flow proceeds to step S17105.
Note that the processing in steps S17103 and S17104 is performed regarding all of the horizontal lines of the processing region represented with the processing region information.
In step S17105, the simultaneous equation acquiring unit 17063 selects a horizontal line which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region represented with the processing region information, acquires the pixel values Yk of the pixels of the horizontal line of interest from the pixel values of the processing region supplied from the pre-processing unit 17101, and the flow proceeds to step S17106. In step S17106, the simultaneous equation acquiring unit 17063 substitutes the pixel values Yk of the pixels of the horizontal line of interest for the equations of Expression (166) through Expression (170) regarding the horizontal line of interest supplied from the equation creating unit 17062, and thus, acquires simultaneous equations for the same amount as the number of pixels of the horizontal line of interest, and supplies these to the physical model value acquiring unit 17052.
Subsequently, the flow proceeds to step S17107 from step S17106, the simultaneous equation computing unit 17064 of the physical model value acquiring unit 17052 computes (solves) the simultaneous equation regarding the horizontal line of interest supplied from the simultaneous equation acquiring unit 17063, and thus, obtains the spline functions in Expression (137) and Expression (138) which approximate the actual world 1 signals projected on the horizontal line of interest, supplies these to the remixing unit 17053, and the flow proceeds to step S17108.
In step S17108, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the simultaneous equation computing unit 17064. That is to say, as for the spline function regarding the horizontal line supplied from the simultaneous equation computing unit 17064, the remixing unit 17053 obtains pixel values having no movement blurring regarding the horizontal line of interest by integrating a curved surface to be obtained by assuming that the spline function thereof does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width in the x direction of the pixel #k of the processing region, and the flow proceeds to step S17109 from step S17108.
In step S17109, the simultaneous equation acquiring unit 17063 determines regarding whether or not all of the horizontal lines of the processing region represented with the processing region information have been taken as the horizontal line of interest, and in the event that determination is made that all of the horizontal lines have not been taken as the horizontal line of interest, the flow returns to step S17105. In this case, in step S17105, the simultaneous equation acquiring unit 17063 newly selects a processing region as the horizontal line of interest, which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region, and hereafter, the same processing is repeated.
Also, in step S17109, in the event that determination is made that all of the horizontal lines of the processing region have been taken as the horizontal line of interest, i.e., in the event that pixels having no movement blurring are obtained regarding all of the horizontal lines of the processing region, the flow proceeds to step S17110, where the remixing unit 17053 outputs the pixel values having no movement blurring obtained regarding all of the horizontal lines of the processing region, i.e., the image of the processing region having no movement blurring, and the processing ends.
As described above, the actual processing unit 17100 in FIG. 144 can obtain an image from which movement blurring is removed, having a high resolution as necessary, as with the case of the movement blurring adjusting unit 17035 in FIG. 137.
Next, FIG. 146 illustrates another configuration example of the actual processing unit 17100 in FIG. 143 in the case of performing processing for obtaining an image by removing movement blurring from an input image including movement blurring, or processing for obtaining an image from which movement blurring is removed and also having higher resolution than the input image. Note that in the drawings, the portions which correspond to those in the case of the movement blurring adjusting unit 17035 in FIG. 141 or the actual processing unit 17100 in FIG. 144 are denoted with the same reference numerals, and hereafter the description thereof will be omitted as appropriate.
The actual processing unit 17100 in FIG. 146 is supplied with an input image, and also is supplied with the processing region information from the processing region setting unit 17001 in FIG. 113, and also is supplied with the continuity information from the continuity setting unit 17002. Now, let us say that in FIG. 146, as with the case in the above FIG. 144, an object displayed in the processing region represented with the processing region information in an input image is, for example, moving in the horizontal direction at a constant speed, and thus, movement blurring occurs in the processing region. Further, let us say that in FIG. 146, the movement amount v of the object displayed in the processing region is employed, for example, as continuity information.
In FIG. 146, the input image is supplied to a pre-processing unit 17101. Also, the processing region information of the parameters necessary for the actual processing is supplied to the modeling unit 17091 of the physical model adapting unit 17081, and the pre-processing unit 17101. Further, the continuity information of the parameters necessary for the actual processing is supplied to the modeling unit 17091 of the physical model adapting unit 17081.
Also, in FIG. 146, an arrangement is made wherein the weight W1 and weight W2 in Expression (201) are supplied to the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 as the parameters necessary for the actual processing as well as the processing region information and the continuity information. Note that in FIG. 146, as for the weight W1 and weight W2 as the parameters necessary for the actual processing, for example, fixed values may be set thereto beforehand. Also, the weight W1 and weight W2 may be input as the assisting information by the user operating the user I/F 17006, for example. Further, As for the weight W1 and weight W2, a variable value according to the features of the image of the processing region may be employed, for example.
Next, description will be made regarding the processing of the actual processing unit 17100 in FIG. 146 with reference to the flowchart in FIG. 147.
First of all, in step S17131, the modeling unit 17091 acquires the processing region information supplied from the processing region setting unit 17001 in FIG. 113, and the movement amount v serving as continuity information supplied from the continuity setting unit 17002 as the parameters necessary for the actual processing. Further, in step S17131, the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 acquires the weight W1 and weight W2 serving as the assisting information supplied from the user I/F 17006 or the like as the parameters necessary for the actual processing, and the flow proceeds to step S17132. In step S17132, the pre-processing unit 17101 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the least-square method adapting unit 17093 of the physical model value acquiring unit 17083.
Subsequently, the flow proceeds to step S17133 from step S17132, where the modeling unit 17091 subjects the actual world 1 light signal projected on the horizontal line of the processing region represented with the processing region information acquired in step S17131 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17091 recognizes the number of pixels making up each horizontal line of the processing region based on the processing region information supplied from the processing region setting unit 17001. Further, the modeling unit 17091 obtains the physical model information in FIG. 125 from the number of pixels making up each horizontal line of the processing region, and the movement amount v acquired in step S17131, and supplies the physical model information to the in-pixel constraining-equation creating unit 17082 and the equation creating unit 17092, and the flow proceeds to step S17134 from step S17133.
In step S17134, the equation creating unit 17092 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17091, supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17135.
In step S17135, the in-pixel constraining-equation creating unit 17082 creates the constraint condition expressions shown in Expression (186) and Expression (187), supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17136.
Note that the processing in steps S17133 through S17135 is performed regarding all of the horizontal lines of the processing region.
In step S17136, the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 selects a horizontal line which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region, acquires the pixel values Yk of the pixels of the horizontal line of interest from the pixel values of the processing region supplied from the pre-processing unit 17101, and the flow proceeds to step S17137.
In step S17137, the least-square method adapting unit 17093 acquires the normal equation of Expression (201) by substituting the pixel values Yk of the pixels of the horizontal line of interest for the equations of Expression (166) through Expression (170) regarding the horizontal line of interest supplied from the equation creating unit 17092, and the constraint condition expressions shown in Expression (186) and Expression (187) supplied from the in-pixel constraining-equation creating unit 17082, and further formulating the normal equation of Expression (201) using the weight W1 and weight W2, and the flow proceeds to step S17138.
In step S17138, the least-square method adapting unit 17093 obtains (the variables yk which define) the spline function of Expression (137) regarding the horizontal line of interest by solving the normal equations obtained regarding the horizontal line of interest, i.e., obtains the spline functions of Expression (137) and Expression (138) which approximate the actual world 1 signals, and supplies these to the remixing unit 17053, and the flow proceeds to step S17139.
In step S17139, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the least-square method adapting unit 17093. That is to say, as for each of the spline functions obtained regarding the horizontal line of interest supplied from the least-square method adapting unit 17093, the remixing unit 17053 obtains pixel values having no movement blurring regarding the horizontal line of interest by integrating a curved surface to be obtained by assuming that the spline function thereof does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width in the x direction of the pixel #k of the processing region, and the flow proceeds to step S17140 from step S17139.
In step S17140, the least-square method adapting unit 17093 determines regarding whether or not all of the horizontal lines of the processing region have been taken as the horizontal line of interest, and in the event that determination is made that all of the horizontal lines have not been taken as the horizontal line of interest, the flow returns to step S17136. In this case, in step S17136, the least-square method adapting unit 17093 newly selects a horizontal line as the horizontal line of interest, which has not been taken as the horizontal line of interest, of the processing region, and hereafter, the same processing is repeated.
Also, in step S17140, in the event that determination is made that all of the horizontal lines of the processing region have been taken as the horizontal line of interest, i.e., in the event that pixel values having no movement blurring are obtained regarding all of the horizontal lines of the processing region, the flow proceeds to step S17141, where the remixing unit 17053 outputs the pixel values having no movement blurring obtained regarding all of the horizontal lines of the processing region, i.e., the image of the processing region having no movement blurring, and the processing ends.
As described above, the actual processing unit 17100 in FIG. 146 can obtain an image from which movement blurring is removed, having a high resolution as necessary, as with the case of the movement blurring adjusting unit 17035 in FIG. 141.
Next, the actual processing unit 17100 in FIG. 144 and FIG. 146 has generated an image obtained by removing movement blurring from an input image, or an image obtained by removing movement blurring from an input image, and also improving resolution which exceeds that in the input image, assuming that movement blurring occurs on the input image, but the actual processing unit 17100 may generate an image having high resolution from an input image having no movement blurring. Note that generating an image having high resolution can be regarded as generating a magnified image as viewed from a different point of view.
In the event of generating an image having high resolution from an input image having no movement blurring, with the physical model shown in FIG. 125, the physical model having the movement amount v of 0 should be considered.
FIG. 148 is a diagram illustrating a physical model in the case of the physical model in FIG. 125 of which the movement amount v is 0.
Accordingly, FIG. 148 represents a physical model wherein the light signal represented with the light signal function F(x) approximated with the spline function Ck(x) is projected on the pixels of the processing unit in a stationary state during the exposure time of the image sensor, and electric charge is charged on the pixels, thereby obtaining an image.
Here, the left side view in FIG. 148 illustrates the spline function Ck(x), which approximates the light signal function F(x), as with the case in FIG. 124. Also, the right side view in FIG. 148 illustrates the level of the spline function Ck(x), which approximates the light signal function F(x), assuming that the horizontal direction is the horizontal direction of the image sensor (x direction where the pixels of the processing unit are arrayed), the near-side direction is exposure time, and the vertical direction is level.
According to the physical model shown in FIG. 148, the curved surface serving as a locus obtained by the spline function Ck(x), which approximates the light signal function F(x), moving in the direction of the exposure time of the image sensor, is integrated in the time direction during the exposure time alone, and also is integrated by only the length in the x direction of the pixel #k of the processing unit in the x direction, thereby obtaining the pixel value Yk of the pixel #k.
With the physical model in FIG. 148, the spline function Ck(x), which approximates the light signal function F(x), does not move in the spatial direction during the exposure time, so mixture (space mixture) in the spatial direction of the signal of the object due to the spatial integration effects of the image sensor is caused at the pixel #k wherein the pixel value Yk is obtained by this physical model, but mixture (time mixture) in the time direction of the signal of the object due to the time integration effects of the image sensor is not caused.
According to the physical model in FIG. 148, the pixel value Yk of the pixel #k can be obtained by setting a range between the start edge and the end edge (from the left end to the right end) in the x direction of the pixel #k to the integration range (α, β) in the above Expression (139), if exposure time is assumed to be 1, as with the case described with FIG. 135. That is to say, with the physical model in FIG. 148, the pixel value Yk can be obtained with the following expression.




  
    
      
        
          Y
          0
        
        =
        
          
            
              1
              8
            
            ⁢
            
              (
              
                
                  7
                  ⁢
                  
                    y
                    0
                  
                
                +
                
                  y
                  1
                
              
              )
            
          
          -
          
            
              7
              64
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        0
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          0
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        0
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        203
        )
      
    
  
  
    
      
        
          
            Y
            k
          
          =
          
            
              
                1
                8
              
              ⁢
              
                (
                
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  +
                  
                    6
                    ⁢
                    
                      y
                      k
                    
                  
                  +
                  
                    y
                    
                      k
                      +
                      1
                    
                  
                
                )
              
            
            -
            
              
                1
                64
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        
                          
                            
                              7
                              ⁢
                              
                                (
                                
                                  
                                    a
                                    
                                      
                                        k
                                        -
                                        2
                                      
                                      ,
                                      
                                        i
                                        -
                                        2
                                      
                                    
                                  
                                  -
                                  
                                    2
                                    ⁢
                                    
                                      a
                                      
                                        
                                          k
                                          -
                                          2
                                        
                                        ,
                                        
                                          i
                                          -
                                          1
                                        
                                      
                                    
                                  
                                  +
                                  
                                    a
                                    
                                      
                                        k
                                        -
                                        2
                                      
                                      ,
                                      i
                                    
                                  
                                
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              18
                              ⁢
                              
                                (
                                
                                  
                                    a
                                    
                                      
                                        k
                                        -
                                        1
                                      
                                      ,
                                      
                                        i
                                        -
                                        2
                                      
                                    
                                  
                                  -
                                  
                                    2
                                    ⁢
                                    
                                      a
                                      
                                        
                                          k
                                          -
                                          1
                                        
                                        ,
                                        
                                          i
                                          -
                                          1
                                        
                                      
                                    
                                  
                                  +
                                  
                                    a
                                    
                                      
                                        k
                                        -
                                        1
                                      
                                      ,
                                      i
                                    
                                  
                                
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            7
                            ⁢
                            
                              (
                              
                                
                                  a
                                  
                                    k
                                    ,
                                    
                                      i
                                      -
                                      2
                                    
                                  
                                
                                -
                                
                                  2
                                  ⁢
                                  
                                    a
                                    
                                      k
                                      ,
                                      
                                        i
                                        -
                                        1
                                      
                                    
                                  
                                
                                +
                                
                                  a
                                  
                                    k
                                    ,
                                    i
                                  
                                
                              
                              )
                            
                          
                        
                      
                    
                    }
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
        
        ,
        
          

        
        ⁢
        
          where
          ⁢
          
            

          
          (
          
            
              k
              =
              1
            
            ,
            2
            ,
            ⋯
            ⁢
            
              
            
            ,
            
              N
              -
              1
            
          
          )
        
      
    
    
      
        (
        204
        )
      
    
  
  
    
      
        
          Y
          N
        
        =
        
          
            
              1
              8
            
            ⁢
            
              (
              
                
                  y
                  
                    N
                    -
                    1
                  
                
                +
                
                  7
                  ⁢
                  
                    y
                    N
                  
                
              
              )
            
          
          -
          
            
              7
              64
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          
                            N
                            -
                            2
                          
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        
                          N
                          -
                          2
                        
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        205
        )
      
    
  




Now, let us say that with the physical model in FIG. 148 as well, flat assumption is employed. The reason why a case is classified into three cases, i.e., k=0, k=1 through N−1, and k=N to obtain the pixel value Yk is caused due to flat assumption, as with the case described with FIG. 135. Note that the flat assumption is not indispensable.
As for Expression (203) through Expression (205), N+1 equations can be formulated in total, and the unknown variables yk which define the spline function Ck(x) exist for the amount of N+1 as well. Accordingly, the light signal function F(x) can be estimated, i.e., here, the spline function Ck(x) which approximates the light signal function F(x) can be obtained by substituting the pixel values Yk obtained from the image sensor for Expression (203) through Expression (205), formulating N+1 simultaneous equations, i.e., N+1 dimensional simultaneous linear equations, and solving the N+1 dimensional simultaneous linear equations.
Following the spline function Ck(x) which approximates the light signal function F(x) being obtained, the pixel value of a pixel having an arbitrary resolution can be obtained by integrating the spline function Ck(x) in a predetermined range in the x direction. That is, if we say that exposure time is 1, the pixel value of a pixel having an arbitrary resolution can be obtained by setting a desired range to the integration range (α, β) in the above Expression (139).
Specifically, for example, now, let us consider virtual pixels obtained by dividing the pixel #k into two in the x direction, and let us represent the right-side pixel and the left-side pixel obtained by dividing the pixel #k into two in the x direction as virtual pixels #k,left and #k,right. Further, let us represent the pixel values of the virtual pixels #k,left and #k,right as Xk,left and Xk,right respectively.
The pixel values Xk,left and Xk,right, as shown in FIG. 149 as with FIG. 136, can be obtained by integrating a curved surface to be obtained by assuming that the spline function Ck(x) which approximates the light signal function F(x) does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction in increments of the width in the x direction of the virtual pixels #k,left and #k,right obtained by dividing the pixel #k of the processing unit.
In this case, the pixel values Xk,left and Xk,right can be obtained with the following expression.




  
    
      
        
          X
          
            0
            ,
            left
          
        
        =
        
          y
          0
        
      
    
    
      
        (
        206
        )
      
    
  
  
    
      
        
          X
          
            0
            ,
            right
          
        
        =
        
          
            
              1
              4
            
            ⁢
            
              (
              
                
                  3
                  ⁢
                  
                    y
                    0
                  
                
                +
                
                  y
                  1
                
              
              )
            
          
          -
          
            
              7
              32
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  0
                
                N
              
              ⁢
              
                
                  (
                  
                    
                      a
                      
                        0
                        ,
                        
                          i
                          -
                          2
                        
                      
                    
                    -
                    
                      2
                      ⁢
                      
                        a
                        
                          0
                          ,
                          
                            i
                            -
                            1
                          
                        
                      
                    
                    +
                    
                      a
                      
                        0
                        ,
                        i
                      
                    
                  
                  )
                
                ⁢
                
                  y
                  i
                
              
            
          
        
      
    
    
      
        (
        207
        )
      
    
  
  
    
      
        
          
            X
            
              k
              ,
              left
            
          
          =
          
            
              
                1
                4
              
              ⁢
              
                (
                
                  
                    y
                    
                      k
                      -
                      1
                    
                  
                  +
                  
                    3
                    ⁢
                    
                      y
                      k
                    
                  
                
                )
              
            
            -
            
              
                1
                32
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  2
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    2
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        9
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                    
                    ]
                  
                  ⁢
                  
                    y
                    i
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          where
          ⁢
          
            

          
          (
          
            
              k
              =
              1
            
            ,
            2
            ,
            ⋯
            ⁢
            
              
            
            ,
            
              N
              -
              1
            
          
          )
        
      
    
    
      
        (
        208
        )
      
    
  
  
    
      
        
          
            X
            
              k
              ,
              right
            
          
          =
          
            
              
                1
                4
              
              ⁢
              
                (
                
                  
                    3
                    ⁢
                    
                      y
                      k
                    
                  
                  +
                  
                    y
                    
                      k
                      +
                      1
                    
                  
                
                )
              
            
            -
            
              
            
            ⁢
            
              
                1
                32
              
              ⁢
              
                
              
              ⁢
              
                
                  ∑
                  
                    i
                    =
                    0
                  
                  N
                
                ⁢
                
                  
                    {
                    
                      
                        9
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  
                                    k
                                    -
                                    1
                                  
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                
                                  k
                                  -
                                  1
                                
                                ,
                                i
                              
                            
                          
                          )
                        
                      
                      +
                      
                        7
                        ⁢
                        
                          (
                          
                            
                              a
                              
                                k
                                ,
                                
                                  i
                                  -
                                  2
                                
                              
                            
                            -
                            
                              2
                              ⁢
                              
                                a
                                
                                  k
                                  ,
                                  
                                    i
                                    -
                                    1
                                  
                                
                              
                            
                            +
                            
                              a
                              
                                k
                                ,
                                i
                              
                            
                          
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According to the pixel values Xk,left and Xk,right obtained with Expression (206) through Expression (211), a high-resolution image of which the number of pixels in the crosswise direction is double the original number of pixels (double-density image in the crosswise direction) can be obtained.
In the above case, the pixel #k has been divided into two, but the divided number of the pixel #k is not restricted to two. Also, here, a high-resolution image higher than the original image (input image) has been attempted to be obtained by dividing the pixel #k, but an image having a desired resolution can be obtained by adjusting the integration range in the x direction for integrating a curved surface obtained by assuming that the spline function Ck(x) which approximates the light signal function F(x) does not move from the position at the time of start of exposure during exposure time. That is, if we say that exposure time is 1, an image having a desired resolution can be obtained by setting desired values to the integration range (α, β) in Expression (139).
Note that in the above case, the actual world 1 light signals do not change over time, so integration effects in the time direction does not need to be considered. That is to say, here, the actual world 1 light signals approximated with the spline function are estimated considering mixture (space mixture) alone due to the integration effects in the x direction, so this estimating method belongs to the above one-dimensional approximating method (and one-dimensional reintegrating method).
Also, in the above case, an image of which the resolution in the crosswise direction is increased has been generated considering mixture (space mixture) due to the integration effects in the x direction, but an image of which both resolutions in the crosswise direction and in the lengthwise direction are increased can be generated by employing the physical model in FIG. 148 considering mixture (space mixture) due to the integration effects in the y direction as to the image of which the resolution in the crosswise direction is increased. In addition, for example, an image of which both resolutions in the crosswise direction and in the lengthwise direction are increased can be generated by employing the physical model in FIG. 148 considering mixture (space mixture) due to the integration effects in the two-dimensional direction of the x direction and the y direction as to the input image.
The actual processing unit 17100 in FIG. 143, as described above, allows to generate a high-resolution image from an input image having no movement blurring, i.e., to create so-called image resolution (resolution in the spatial direction).
FIG. 150 illustrates a configuration example of the actual processing unit 17100 for generating a high-resolution image from an input image having no movement blurring as described above.
The actual processing unit 17100 in FIG. 150 is supplied with an input image, and also is supplied with the processing region information from the processing region setting unit 17001 in FIG. 113 as the necessary parameter for the actual processing, and also is supplied with the continuity information from the continuity setting unit 17002 as the necessary parameter for the actual processing. Now, let us say that in FIG. 150, an object displayed on the processing region represented with the processing region information in the input image is at a standstill. Further, let us say that in FIG. 150, information representing that the object displayed in the processing region is at a standstill for example, i.e., the movement amount v of the object is 0 for example, is employed as continuity information.
With the actual processing unit 17100, the input image is supplied to the pre-processing unit 17200. Also, the processing region information of the parameters necessary for the actual processing is supplied to the modeling unit 17211 of the physical model adapting unit 17201, and the pre-processing unit 17200. Further, the continuity information of the parameters necessary for the actual processing is supplied to the modeling unit 17211 of the physical model adapting unit 17201.
The pre-processing unit 17200 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the simultaneous equation acquiring unit 17213 of the physical model adapting unit 17201.
The physical model adapting unit 17201 comprises a modeling unit 17211, an equation creating unit 17212, and a simultaneous equation acquiring unit 17213.
The modeling unit 17211 recognizes the number of pixels making up each horizontal line of the processing region (e.g., N+1 pixels in the physical model in FIG. 148) based on the processing region information supplied from the processing region setting unit 17001. Further, the modeling unit 17211 determines to apply the physical model in FIG. 148 from information representing that the movement amount v serving as the continuity information is 0, and supplies the number of pixels making up each horizontal line of the processing region to the equation creating unit 17212 as the physical model information in FIG. 148. Also, the modeling unit 17211 recognizes the position of the processing region in the input image, and supplies information representing the position thereof to the simultaneous equation acquiring unit 17213 via the equation creating unit 17212.
The equation creating unit 17212 creates the equations shown in Expression (203) through Expression (205) from the physical model information supplied from the modeling unit 17211, and supplies these to the simultaneous equation acquiring unit 17213.
The simultaneous equation acquiring unit 17213 recognizes the position of the processing region in the input image from the information representing the position of the processing region in the input image supplied from the modeling unit 17211 via the equation creating unit 17212, and acquires the pixel value of the pixel for each horizontal line of the processing region from the pixel values of the processing region supplied from the pre-processing unit 17200 based on the position thereof. Further, the simultaneous equation acquiring unit 17213 substitutes the pixel value of the pixel of each horizontal line of the processing region for the equations of Expression (203) through Expression (205) supplied from the equation creating unit 17212, and thus, acquires N+1 simultaneous equations for each horizontal line, and supplies these to the physical model value acquiring unit 17202.
The physical model value acquiring unit 17202 comprises a simultaneous equation computing unit 17214, and the simultaneous equation supplied from the simultaneous equation acquiring unit 17213 is supplied to the simultaneous equation computing unit 17214. The simultaneous equation computing unit 17214 computes (solves) the simultaneous equation supplied from the simultaneous equation acquiring unit 17213, and thus, obtains N+1 variables yk which define the spline functions in Expression (137) and Expression (138) which approximate the actual world 1 signals, and supplies these to the remixing unit 17203.
The remixing unit 17203 obtains and outputs the pixel value of a high-resolution pixel by integrating a curved surface to be obtained by assuming that the spline function, which is defined with the variables yk supplied from the simultaneous equation computing unit 17214, does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the 1⁄2 width in the x direction of the pixel #k of the processing region.
Note that in the event that the remixing unit 17203 performs integration in the x direction, for example, in increments of the 1⁄2 width in the x direction of the pixel #k of the processing region, the pixel values represented with Expression (206) through Expression (211) are obtained, and with the image of the pixel values thereof, the pixels in the horizontal direction are configured with double the number of pixels in the horizontal direction of the input image.
Next, description will be made regarding the processing of the actual processing unit 17100 in FIG. 150 with reference to the flowchart in FIG. 151.
First of all, in step S17201, the modeling unit 17211 acquires the processing region information supplied from the processing region setting unit 17001 in FIG. 113, and information representing that the movement amount v serving as continuity information supplied from the continuity setting unit 17002 is 0 as the parameters necessary for the actual processing, also the pre-processing unit 17200 acquires the processing region information supplied from the processing region setting unit 17001 in FIG. 113 as the parameters necessary for the actual processing, and the flow proceeds to step S17202. In step S17202, the pre-processing unit 17200 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the simultaneous equation acquiring unit 17213 of the physical model adapting unit 17201.
Subsequently, the flow proceeds to step S17203 from step S17202, where the modeling unit 17211 subjects the actual world 1 light signal projected on the processing region represented with the processing region information acquired in step S17201 to modeling after the physical model shown in FIG. 148.
That is to say, the modeling unit 17211 recognizes the number of pixels making up each horizontal line of the processing region based on the processing region information supplied from the processing region setting unit 17001. Further, the modeling unit 17211 determines to apply the physical model in FIG. 148 from information representing that the movement amount v serving as the continuity information is 0, and supplies the number of pixels making up each horizontal line of the processing region to the equation creating unit 17212 as the physical model information in FIG. 148, and the flow proceeds to step S17204 from step S17203.
In step S17204, the equation creating unit 17212 creates the equations shown in Expression (203) through Expression (205) from the physical model information supplied from the modeling unit 17211, supplies these to the simultaneous equation acquiring unit 17213, and the flow proceeds to step S17205.
Note that the processing in steps S17203 and S17204 is performed regarding all of the horizontal lines of the processing region represented with the processing region information.
In step S17205, the simultaneous equation acquiring unit 17213 selects a horizontal line which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region represented with the processing region information as the horizontal line of interest, acquires the pixel values Yk of the pixels of the horizontal line of interest from the pixel values of the processing region supplied from the pre-processing unit 17200, and the flow proceeds to step S17206. In step S17206, the simultaneous equation acquiring unit 17213 substitutes the pixel values Yk of the pixels of the horizontal line of interest for the equations of Expression (203) through Expression (205) regarding the horizontal line of interest supplied from the equation creating unit 17212, and thus, acquires simultaneous equations for the same amount as the number of pixels of the horizontal line of interest, and supplies these to the physical model value acquiring unit 17202.
Subsequently, the flow proceeds to step S17207 from step S17206, the simultaneous equation computing unit 17214 of the physical model value acquiring unit 17202 computes (solves) the simultaneous equation regarding the horizontal line of interest supplied from the simultaneous equation acquiring unit 17213, and thus, obtains the spline functions in Expression (137) and Expression (138) which approximate the actual world 1 signals projected on the horizontal line of interest, supplies these to the remixing unit 17203, and the flow proceeds to step S17208.
In step S17208, the remixing unit 17203 performs remixing (reintegration) using the spline functions supplied from the simultaneous equation computing unit 17214. That is to say, as for the spline function regarding the horizontal line of interest supplied from the simultaneous equation computing unit 17214, the remixing unit 17203 obtains high-resolution pixel values regarding the horizontal line of interest by integrating a curved surface to be obtained by assuming that the spline function thereof does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the 1⁄2 width in the x direction of the pixel #k of the processing region, and the flow proceeds to step S17209 from step S17208.
In step S17209, the simultaneous equation acquiring unit 17213 determines regarding whether or not all of the horizontal lines of the processing region represented with the processing region information have been taken as the horizontal line of interest, and in the event that determination is made that all of the horizontal lines have not been taken as the horizontal line of interest, the flow returns to step S17205. In this case, in step S17205, the simultaneous equation acquiring unit 17213 newly selects a processing region as the horizontal line of interest, which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region, and thereafter, the same processing is repeated.
Also, in step S17209, in the event that determination is made that all of the horizontal lines of the processing region have been taken as the horizontal line of interest, i.e., in the event that pixels having no movement blurring are obtained regarding all of the horizontal lines of the processing region, the flow proceeds to step S17210, where the remixing unit 17203 outputs the high-resolution pixel values obtained regarding all of the horizontal lines of the processing region, i.e., the high-resolution image of the processing region, and the processing ends.
As described above, the actual processing unit 17100 in FIG. 150 can obtain a high-resolution image from an image having no movement blurring.
Note that estimation of the actual world 1, i.e., in the event of obtaining the spline functions of Expression (137) and Expression (138) which approximate the actual world 1 signals, the least-square method may be employed using the equations of Expression (203) through Expression (205), and the constraint condition expressions described with FIG. 139 and FIG. 140 as well as solving the expressions of Expression (203) through Expression (205) as a simultaneous equation.
As described above, the light signal function F(x) is estimated assuming that the pixel value of each pixel corresponding to a position in the x direction of the time-space directions of image data wherein the actual world light signals are projected on a plurality of pixels each having time-space integration effects, and part of the actual world light signal continuity is lost, is a pixel value acquired by integrating a light signal function (actual world function) F(x) corresponding to the actual world 1 light signal approximated with the spline function. An image is generated by integrating the spline function serving as the estimated result in the x direction in predetermined increments, whereby a high-resolution image can be obtained regarding a still image.
Next, description will be made regarding the processing of the signal processing device 4 in FIG. 113, in the event that the processing region setting unit 17001 in FIG. 113, the continuity setting unit 17002, or the actual world estimating unit 17003 performs processing using the assisting information.
FIG. 152 is a flowchart describing the processing of the signal processing device 4 in FIG. 113, in the event that the processing region setting unit 17001, the continuity setting unit 17002, or the actual world estimating unit 17003 performs processing using the assisting information.
With the signal processing device 4 in FIG. 113, the actual world is estimated based on continuity, and accordingly, processing for removing movement blurring which occurs due to temporal-direction mixing (temporal mixing) of the signals of objects, due to temporal integration effects of the sensor 2, or the like is performed.
That is to say, in an input image obtained by a taking an image in the actual world 1 wherein an object such as an automobile or the like is moving, with the sensor 2 which is an image sensor, the object moves over time, so light signals of that object and light signals of portions other than that object are mixed (temporal mixing) due to temporal integration effects of the sensor 2, thereby causing so-called movement blurring at the boundary portions of the object and the like. With the signal processing device 4 in FIG. 113, a high-image-quality output image of which the movement blurring caused due to such time mixture is removed from the input image is generated, and consequently, an output image wherein the movement blurring is removed from the input image is obtained.
With the signal processing device 4 shown in FIG. 113, first, in step S17301, pre-processing is performed, and the flow proceeds to step S17302. That is to say, the signal processing device 4 supplies one frame or one field of input image for example, supplied from the sensor 2 (FIG. 1) as data 3, to the processing region setting unit 17001, continuity setting unit 17002, actual world estimating unit 17003, image generating unit 17004, and image display unit 17005. That is to say, the signal processing device 4 supplies one frame or one field of input image for example, supplied from the sensor 2 serving as an image sensor (FIG. 1) as data 3, to the processing region setting unit 17001, continuity setting unit 17002, actual world estimating unit 17003, image generating unit 17004, and image display unit 17005. Further, the signal processing unit 4 displays an input image on the image display unit 17005.
Note here, for example, that an image with movement blurring due to temporal mixing, obtained by the taking a scene wherein an object such as the automobile moves in the horizontal direction at a constant speed with the sensor 2, is input to the signal processing device 4 as an input image.
In step S17302, the user I/F 17006 determines whether or not there has been some sort of user input, by the user operating the user I/F 17006. In step S17302, in the event that determination is made that user input has not been done, i.e., in the event that the user has not performed any operations, the flow returns to step S17302.
Also, in step S17302, in the event that determination is made that there has been user input, i.e., in the event that the user has viewed the input image displayed on the image display unit 17005 and operated the user I/F 17006, thereby making user input indicating some sort of instruction or information, the flow proceeds to step S17303, where the user I/F 17006 determines whether or not the user input is user instructions instructing ending of the processing of the signal processing device 4.
In the event that determination is made in step S17303 that the user input is ending instructions, the signal processing device 4 ends the processing.
Also, in the event that determination is made in step S17303 that the user input is not ending instructions, the flow proceeds to step S17304, where the user I/F 17006 determines whether or not the user input is assisting information. In step S17304, in the event that determination is made that the user input is not the assisting information, the flow returns to step S17302.
Also, in the event that determination is made in step S17304 that the user input is assisting information, the flow proceeds to step S17305, where the user I/F 17006 supplies the assisting information to the processing region setting unit 17001, continuity setting unit 17002, or actual world estimating unit 17006, and the flow proceeds to step S17306.
In step S17306, the processing region setting unit 17001 sets the processing region based on the input image, and supplies the processing region information identifying the processing region to the continuity setting unit 17002, actual world estimating unit 17003, and image generating unit 17004, and the flow proceeds to step S17307. Now, in the event that assisting information has been supplied from the user I/F 17006 in that immediately-preceding step S17305, the processing region setting unit 17001 performs setting of the processing region using that assisting information.
In step S17307, the continuity setting unit 17002 recognizes the processing region in the input image, from the processing region information supplied from the processing region setting unit 17001. Further, the continuity setting unit 17002 sets continuity of the actual world 1 signals that has been lost in the image data of the processing region, and supplies continuity information indicating the continuity thereof to the actual world estimating unit 17003, and the flow proceeds to step S17308. Now, in the event that assisting information has been supplied from the user I/F 17006 in that immediately-preceding step S17305, the continuity setting unit 17002 performs setting of continuity using that assisting information.
In step S17308, the actual world estimating unit 17003 estimates actual world 1 signals regarding to the image data with in the processing region of the input image, according to the continuity of the corresponding actual world 1 signals.
That is to say, at the actual world estimating unit 17003, the model generating unit 17011 recognizes the processing region in the input image, from the processing region information supplied from the processing region setting unit 17001, and also recognizes continuity of the actual world 1 signals corresponding to the image data in the processing region (here, for example, the movement amount of the object displayed on the processing region), from the continuity information supplied from the continuity setting unit 17002. Further the model generating unit 17011 generates a function serving as a relation model modeling the relation between the pixel values of each of the pixels within the processing region and the actual world 1 signals, according to the pixels making up the processing region in the input image, and the continuity of actual world 1 signals corresponding to the image data of the processing region, and supplies this to the equation generating unit 17012.
The equation generating unit 17012 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 17001, and substitutes the pixel values of each of the pixels of the input image making up the processing region into the function serving as the relation model which is supplied from the model generating unit 17011, thereby generating an equation for obtaining an approximation function approximating the actual world 1 signals, which is supplied to the actual world waveform estimating unit 17013.
Note that here, a spline function is employed as an approximation function, as described above.
The actual world waveform estimating unit 17003 estimates the waveform of the actual world 1 signals by solving the equation supplied from the equation generating unit 17012. That is, the actual world waveform estimating unit 17013 obtains the approximation function serving as an approximation model modeling the actual world 1 signals by solving the equation supplied from the equation generating unit 17012, and supplies the approximation function to the image generating unit 17004.
Note that with the actual world estimating unit 17013, in the event that assisting information has been supplied from the user I/F 10006 in the immediately-preceding step S17305, at the model generating unit 17011 and equation generating unit 17012, processing is performed using that assisting information.
Following processing of step S17308, the flow proceeds to step S17309, where the image generating unit 17004 generates signals closer approximating the actual world 1 signals based on the approximation function supplied from (the actual world waveform estimating unit 17013 of) the actual world estimating unit 17003. That is to say, the image generating unit 17004 recognizes the processing region in the input image from the processing region information supplied from the processing region setting unit 17001, and with regard to this processing region, generates an approximation image which is image data closer approximating the image corresponding to the actual world 1 signals, based on the approximation function supplied from the actual world estimating unit 17003. Further the image generating unit 17004 generates, as an output image, an image wherein the portion of the processing region of the input image has been replaced with the approximation image, and supplies this to the image display unit 17005, and the flow proceeds from step S17309 to step S17310.
In step S17310, the image display unit 17005 substitutes the output image supplied from the image generating unit 17004 for the input image displayed in step S17301, or displays the output image supplied from the image generating unit 17004 along with the input image displayed in step S17301, the flow returns to step S17302, and hereafter, the same processing is repeated.
As described above, the processing region setting unit 17001, continuity setting unit 17002, and actual world estimating unit 17003 can obtain an image having higher image quality, in the event of performing processing using the assisting information to be input by the user operating the user I/F 17006.
That is to say, with the image display unit 17005, for example, in the event that an input image or output image on which a moving object is reflected is displayed, the user who views the image can determine a region where movement blurring occurs, for example, based on the memory of a real object (actual world 1) which the user has actually viewed. Accordingly, as shown in FIG. 153, information or the like representing the position subjected to pointing is supplied to the processing region setting unit 17001 as assisting information by prompting the user to subject a region where movement blurring occurs in the image displayed on the image display unit 17005 to pointing or the like by operating the user I/F 17006, whereby the processing region setting unit 17001 can easily identify the portion where movement blurring occurs based on the assisting information. Further, the processing region setting unit 17001 can set the processing region including a portion where movement blurring occurs in a sure manner, and accordingly, the movement blurring occurring on the input image can be removed precisely by the subsequent stage blocks subjecting such a processing region to processing.
Also, operating the user I/F 17006 can prompt the user to input information relating to the movement amount of an object displayed on the image. In this case, it is possible to prompt the user to directly input the movement amount of the object, but in general, it is difficult for the user to directly input the movement amount of the object. To this end, for example, the user I/F 17006 comprises a joystick, mouse, or the like, and operating the joystick can prompt the user to input the movement amount, and further, the direction of the movement as necessary. In this case, the user I/F 17006 supplies the operating amount and operating direction of the joystick to the continuity setting unit 17002 as assisting information, and the continuity setting unit 17002 sets the movement vector of the object based on the operating amount and operating direction of the joystick. That is to say, the continuity setting unit 17002 sets the movement amount of the object based on the operating amount of the joystick, and also sets the movement direction of the object based on the operating direction of the joystick. The subsequent stage blocks of the continuity setting unit 17002 perform processing based on the continuity information representing the movement vector set at the continuity setting unit 17002.
In this case, it is difficult to accurately input the movement vector of the object from the beginning by the user operating the joystick. However, for example, in the event of repeating that while changing the movement vector of the object in increments of one pixel based on operations of the joystick by the user, and the image display unit 17005 displays an output image obtained regarding the movement vector in real time, the user can recognize change in the image quality of the output image to be displayed on the image display unit 17005 according to operations of the joystick. Accordingly, as shown in FIG. 153, the user can obtain an output image having a high image quality, i.e., here, an image wherein movement blurring is removed from the input image by operating the joystick while viewing the output image displayed on the image display unit 17005.
Note that when an image wherein movement blurring is removed from the input image is obtained, the movement vector set at the continuity setting unit 17002 represents the movement of the object precisely.
Next, FIG. 154 illustrates a configuration example of a device equivalent to the signal processing device 4 in FIG. 113 in the event of performing, for example, removal of movement blurring as distortion caused on the image data due to the integration effects of the image sensor 2 serving as an image sensor based on user input.
The input image acquiring unit 17301 acquires the input image, and supplies this to the movement blurring removal processing unit 17303 and the output image synthesizing unit 17304. Here, let us say that the input image is, as described above, an image on which movement blurring is caused due to time mixture, which can be obtained by imaging, with an image sensor, a scene in which an object such as an automobile is moving in the horizontal direction at a constant speed.
The user input information acquiring unit 17302 acquires user input information (user input) supplied from the user I/F 17006 by the user operating the user I/F 17006, and supplies this to the movement blurring removal processing unit 17303 and the output image synthesizing unit 17304 as assisting information as necessary.
Here, examples of the user input information include information representing the processing region, information representing the movement amount v of the object in the input image, an end instruction for instructing end of the processing, and further, information representing the weight W1 and weight W2 introduced in the above Expression (199).
The movement blurring removal processing unit 17303 performs movement blurring removal processing for removing movement blurring caused on the image using the input image supplied from the input image acquiring unit 17301, and the assisting information supplied from the user input information acquiring unit 17302, and supplies the result of the movement blurring removal processing to the output image synthesizing unit 17304.
The output image synthesizing unit 17304 synthesizes the input image supplied from the input image acquiring unit 17301, and an approximation image serving as a result of the movement blurring removal processing supplied from the movement blurring removal processing unit 17303 based on the assisting information supplied from the user input information acquiring unit 17302, and supplies an output image obtained as a result thereof to the output unit 17305.
Here, a portion comprising the above input image acquiring unit 17301, user input information acquiring unit 17302, movement blurring removal processing unit 17303, and output image synthesizing unit 17304 corresponds to a portion comprising the processing region setting unit 17001, continuity setting unit 17002, actual world estimating unit 17003, and image generating unit 17004 in FIG. 113.
The output unit 17305 displays an image supplied from the output image synthesizing unit 17304.
The portion comprising the output unit 17305 corresponds to the portion comprising the image display unit 17005 in FIG. 113.
Next, the processing of the device shown in FIG. 154 will be described with reference to the flowchart in FIG. 155.
First of all, in step S17331, the input image acquiring unit 17301 acquires the input image, and supplies this to the movement blurring removal processing unit 17303 and the output image synthesizing unit 17304, and the flow proceeds to step S17332.
In step S17332, the user input information acquiring unit 17302 determines regarding whether or not the user input information has been supplied by the user operating the user I/F 17006, and in the event that determination is made that the user input information has not been supplied, the flow returns to step S17332.
Subsequently, in step S17332, in the event that determination is made that the user input information has been supplied from the user I/F 17006, the flow proceeds to step S17334, where the user input information acquiring unit 17302 acquires the user input information supplied from the user I/F 17006, and the flow proceeds to step S17333.
In step S17333, the user input information acquiring unit 17302 determines regarding whether or not the user input information is the end instruction for instructing end of the processing. In step S17333, in the event that determination is made that the user input information is not the end instruction for instructing end of the processing, i.e., in the event that the user input information is, for example, the assisting information for assisting the movement blurring removal processing by the movement blurring removal processing unit 17303 such as information representing the processing region, information representing the movement amount v of the object in the input image, and information representing the weight W1 and weight W2 in Expression (199), the flow proceeds to step S17334, where the user input information acquiring unit 17302 supplies the user input information to the movement blurring removal processing unit 17303, and further to the output image synthesizing unit 17304 as necessary as assisting information, and the flow proceeds to step S17335.
In step S17335, the movement blurring removal processing unit 17303 performs movement blurring removal processing for removing movement blurring caused on the image using the input image supplied from the input image acquiring unit 17301, and the assisting information supplied from the user input information acquiring unit 17302, and supplies the result of the movement blurring removal processing to the output image synthesizing unit 17304, and the flow proceeds to step S17336.
In step S17336, the output image synthesizing unit 17304 replaces the image of the processing region to be identified with the information representing the processing region as the assisting information supplied from the user input information acquiring unit 17302 of the input image supplied from the input image acquiring unit 17301, with an approximation image serving as a result of the movement blurring removal processing supplied from the movement blurring removal processing unit 17303, and thus, synthesizes the input image and the approximation image, supplies an output image obtained as a result thereof to the output unit 17305, and the flow proceeds to step S17337.
In step S17337, the output unit 17305 displays the output image supplied from the output image synthesizing unit 17304, the flow returns to step S17332, and hereafter, the above processing of steps S17332 through S17337 is repeated.
Subsequently, in step S17333, in the event that determination is made that the user input information is the end instruction for instructing end of the processing, i.e., for example, in the event that an output image having an image quality satisfied by the user (here, image of which movement blurring is sufficiently removed) is displayed on the output unit 17305 by the processing of steps S17332 through S17337 being repeated, and the user operates the user I/F 17006 so as to end the processing, the flow proceeds to step S17338, where the output unit 17305 stores the output image displayed at that time, and the processing ends.
Next, FIG. 156 illustrates a configuration example of the movement blurring removal processing unit 17303 in FIG. 154. Note that in the drawings, the portions which correspond to those in the case of the actual processing unit 17100 in FIG. 144 are denoted with the same reference numerals, and hereafter the description thereof will be omitted as appropriate. That is to say, the movement blurring removal processing unit 17303 in FIG. 156 is configured as with the actual processing unit 17100 in FIG. 144.
Accordingly, with the movement blurring removal processing unit 17303 in FIG. 156, the spline function which approximates the actual world 1 light signals regarding the input image can be obtained using the N+1 equations shown in Expression (166) through Expression (170) to be obtained based on the physical model shown in FIG. 125, thereby generating an image (approximation image) having a desired resolution and no movement blurring.
However, with the actual processing unit 17100 in FIG. 144, the processing region information and the continuity information representing the movement amount v have been arranged to be supplied as the parameters necessary for the actual processing, but with the movement blurring removal processing unit 17303 in FIG. 156, the processing region information and the continuity information representing the movement amount v are arranged to be supplied as the assisting information via the user input information acquiring unit 17302 by the user operating the user I/F 17006.
Next, description will be made regarding the processing of the movement blurring removal processing unit 17303 in FIG. 156 with reference to the flowchart in FIG. 157.
First of all, in step S17351, the modeling unit 17061 acquires the processing region information supplied from the user input information acquiring unit 17032 in FIG. 154 as the assisting information, and the movement amount v serving as the continuity information, also the pre-processing unit 17101 acquires the processing region information supplied from the user input information acquiring unit 17032 in FIG. 154 as the assisting information, and the flow proceeds to step S17352. In step S17352, the pre-processing unit 17101 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the simultaneous equation acquiring unit 17063 of the physical model adapting unit 17051.
Subsequently, the flow proceeds to step S17353 from step S17352, where the modeling unit 17061 subjects the actual world 1 light signal projected on the processing region represented with the processing region information acquired in step S17351 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17061 recognizes the number of pixels making up each horizontal line of the processing region based on the processing region information supplied from the user input information acquiring unit 17032. Further, the modeling unit 17061 obtains the physical model information in FIG. 125 from the number of pixels making up each horizontal line of the processing region, and the movement amount v acquired in step S17351, and supplies the physical model information to the equation creating unit 17062, and the flow proceeds to step S17354 from step S17353.
In step S17354, the equation creating unit 17062 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17061, supplies these to the simultaneous equation acquiring unit 17063, and the flow proceeds to step S17355.
Note that the processing in steps S17353 and S17354 is performed regarding all of the horizontal lines of the processing region represented with the processing region information.
In step S17355, the simultaneous equation acquiring unit 17063 selects a horizontal line which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region represented with the processing region information as the horizontal line of interest, acquires the pixel values Yk of the pixels of the horizontal line of interest from the pixel values of the processing region supplied from the pre-processing unit 17101, and the flow proceeds to step S17356. In step S17356, the simultaneous equation acquiring unit 17063 substitutes the pixel values Yk of the pixels of the horizontal line of interest for the equations of Expression (166) through Expression (170) regarding the horizontal line of interest supplied from the equation creating unit 17062, and thus, acquires simultaneous equations for the same amount as the number of pixels of the horizontal line of interest, and supplies these to the physical model value acquiring unit 17052.
Subsequently, the flow proceeds to step S17357 from step S17356, the simultaneous equation computing unit 17064 of the physical model value acquiring unit 17052 computes (solves) the simultaneous equation regarding the horizontal line of interest supplied from the simultaneous equation acquiring unit 17063, and thus, obtains the spline functions in Expression (137) and Expression (138) which approximate the actual world 1 signals projected on the horizontal line of interest, supplies these to the remixing unit 17053, and the flow proceeds to step S17358.
In step S17358, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the simultaneous equation computing unit 17064. That is to say, as for the spline function regarding the horizontal line of interest supplied from the simultaneous equation computing unit 17064, the remixing unit 17053 obtains pixel values having no movement blurring regarding the horizontal line of interest by integrating a curved surface to be obtained by assuming that the spline function thereof does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width or the 1⁄2 width in the x direction of the pixel #k of the processing region, and the flow proceeds to step S17359 from step S17358. Note that adjusting the unit of integration (integration range) in step S17358 enables the resolution of an image obtained by the integration thereof to be changed, as described above. This integration unit may be set beforehand, or may be input by the user operating the user I/F 17006.
Here, in step S17358, in the event that the integration in the x direction is, for example, performed in increments of the width in the x direction of the pixel #k, the pixel values Xk having no movement blurring can be obtained in accordance with Expression (171) through Expression (173). Also, in step S17358, in the event that the integration in the x direction is, for example, performed in increments of the 1⁄2 width in the x direction of the pixel #k, the pixel values Xk having no movement blurring can be obtained in accordance with Expression (174) through Expression (179).
In step S17359, the simultaneous equation acquiring unit 17063 determines regarding whether or not all of the horizontal lines of the processing region represented with the processing region information have been taken as the horizontal line of interest, and in the event that determination is made that all of the horizontal lines have not been taken as the horizontal line of interest, the flow returns to step S17355. In this case, in step S17355, the simultaneous equation acquiring unit 17063 newly selects a processing region as the horizontal line of interest, which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region, and hereafter, the same processing is repeated.
Also, in step S17359, in the event that determination is made that all of the horizontal lines of the processing region have been taken as the horizontal line of interest, i.e., in the event that pixels having no movement blurring are obtained regarding all of the horizontal lines of the processing region, the flow proceeds to step S17360, where the remixing unit 17053 outputs the pixel values having no movement blurring obtained regarding all of the horizontal lines of the processing region, i.e., the image of the processing region having no movement blurring, and the processing ends.
As described above, the movement blurring removal processing unit 17303 in FIG. 156 can obtain an image from which movement blurring is removed, having an improved resolution as necessary, as with the case in the actual processing unit 17100 in FIG. 144.
Next, FIG. 158 illustrates another configuration example of the movement blurring removal processing unit 17303 in FIG. 154. Note that in the drawings, the portions which correspond to those in the case of the actual processing unit 17100 in FIG. 146 are denoted with the same reference numerals, and hereafter the description thereof will be omitted as appropriate. That is to say, the movement blurring removal processing unit 17303 in FIG. 158 is configured as with the actual processing unit 17100 in FIG. 146.
Accordingly, with the movement blurring removal processing unit 17303 in FIG. 158, the spline function which approximates the actual world 1 light signals regarding the input image can be obtained using the 2 (N−1) constraint condition expressions shown in Expression (186) and Expression (187), which describe a constraint condition, as well as the N+1 equations shown in Expression (166) through Expression (170) to be obtained based on the physical model shown in FIG. 125, thereby generating an image (approximation image) having a desired resolution and no movement blurring.
However, with the actual processing unit 17100 in FIG. 146, the processing region information, the continuity information representing the movement amount v, and the weight W1 and weight W2 in Expression (201) introduced in Expression (199) have been arranged to be supplied via the user input information acquiring unit 17032 as the assisting information by the user operating the user I/F 17006.
Next, description will be made regarding the processing of the movement blurring removal processing unit 17303 in FIG. 158 with reference to the flowchart in FIG. 159.
First of all, in step S17381, the modeling unit 17091 acquires the processing region information supplied from the user input information acquiring unit 17032 in FIG. 154 as the assisting information, and the movement amount v serving as the continuity information, also the pre-processing unit 17101 acquires the processing region information supplied from the user input information acquiring unit 17032 in FIG. 154 as the assisting information. Further, in step S17381, the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 acquires the weight W1 and weight W2 supplied from the user input information acquiring unit 17302 in FIG. 154 as the assisting information, and the flow proceeds to step S17382. In step S17382, the pre-processing unit 17101 recognizes the processing region from the processing region information, extracts the pixel values of pixels making up the processing region from the input image, and supplies these to the least-square method adapting unit 17093 of the physical model value acquiring unit 17083.
Subsequently, the flow proceeds to step S17383 from step S17382, where the modeling unit 17091 subjects the actual world 1 light signal projected on the horizontal line of the processing region represented with the processing region information acquired in step S17381 to modeling after the physical model shown in FIG. 125.
That is to say, the modeling unit 17091 recognizes the number of pixels making up each horizontal line of the processing region based on the processing region information supplied from the user input information acquiring unit 17302. Further, the modeling unit 17091 obtains the physical model information in FIG. 125 from the number of pixels making up each horizontal line of the processing region, and the movement amount v acquired in step S17381, and supplies the physical model information to the in-pixel constraining-equation creating unit 17082 and the equation creating unit 17092, and the flow proceeds to step S17384 from step S17383.
In step S17384, the equation creating unit 17092 creates the equations shown in Expression (166) through Expression (170) from the physical model information supplied from the modeling unit 17091, supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17385.
In step S17385, the in-pixel constraining-equation creating unit 17082 creates the constraint condition expressions shown in Expression (186) and Expression (187), supplies these to the physical model value acquiring unit 17083, and the flow proceeds to step S17386.
Note that the processing in steps S17383 through S17385 is performed regarding all of the horizontal lines of the processing region.
In step S17386, the least-square method adapting unit 17093 of the physical model value acquiring unit 17083 selects a horizontal line which has not been taken as the horizontal line of interest, of the horizontal lines of the processing region as the horizontal line of interest, acquires the pixel values Yk of the pixels of the horizontal line of interest from the pixel values of the processing region supplied from the pre-processing unit 17101, and the flow proceeds to step S17387.
In step S17387, the least-square method adapting unit 17093 acquires the normal equation of Expression (201) by substituting the pixel values Yk of the pixels of the horizontal line of interest for the equations of Expression (166) through Expression (170) regarding the horizontal line of interest supplied from the equation creating unit 17092, and the constraint condition expressions shown in Expression (186) and Expression (187) supplied from the in-pixel constraining-equation creating unit 17082, and further formulating the normal equation of Expression (201) using the weight W1 and weight W2, and the flow proceeds to step S17388.
In step S17388, the least-square method adapting unit 17093 obtains (the variables yk which define) the spline function of Expression (137) regarding the horizontal line of interest by solving the normal equations obtained regarding the horizontal line of interest, i.e., obtains the spline functions of Expression (137) and Expression (138) which approximate the actual world 1 signals, and supplies these to the remixing unit 17053, and the flow proceeds to step S17389.
In step S17389, the remixing unit 17053 performs remixing (reintegration) using the spline functions supplied from the least-square method adapting unit 17093. That is to say, as for each of the spline functions obtained regarding the horizontal line of interest supplied from the least-square method adapting unit 17093, the remixing unit 17093 obtains pixel values having no movement blurring regarding the horizontal line of interest by integrating a curved surface to be obtained by assuming that the spline function thereof does not move from the position at the time of start of exposure during exposure time, in the time direction during exposure time alone, and also integrating (reintegrating) this in the x direction, for example, in predetermined increments such as the width or 1⁄2 thereof in the x direction of the pixel #k of the processing region, and the flow proceeds to step S17390 from step S17389. Note that adjusting the unit of integration (integration range) in step S17389 enables the resolution of an image obtained by the integration thereof to be changed, as described above. This integration unit may be set beforehand, or may be input by the user operating the user I/F 17006.
Here, in step S17389, in the event that the integration in the x direction is, for example, performed in increments of the width in the x direction of the pixel #k, the pixel values Xk having no movement blurring can be obtained in accordance with Expression (171) through Expression (173). Also, in step S17389, in the event that the integration in the x direction is, for example, performed in increments of the 1⁄2 width in the x direction of the pixel #k, the pixel values Xk having no movement blurring can be obtained in accordance with Expression (174) through Expression (179).
In step S17390, the least-square method adapting unit 17093 determines regarding whether or not all of the horizontal lines of the processing region have been taken as the horizontal line of interest, and in the event that determination is made that all of the horizontal lines have not been taken as the horizontal line of interest, the flow returns to step S17386. In this case, in step S17386, the least-square method adapting unit 17093 newly selects a horizontal line as the horizontal line of interest, which has not been taken as the horizontal line of interest, of the processing region, and hereafter, the same processing is repeated.
Also, in step S17390, in the event that determination is made that all of the horizontal lines of the processing region have been taken as the horizontal line of interest, i.e., in the event that pixel values having no movement blurring are obtained regarding all of the horizontal lines of the processing region, the flow proceeds to step S17391, where the remixing unit 17053 outputs the pixel values having no movement blurring obtained regarding all of the horizontal lines of the processing region, i.e., the image of the processing region having no movement blurring, and the processing ends.
As described above, the movement blurring removal processing unit 17303 in FIG. 158 can also obtain an image from which movement blurring is removed, having an improved resolution as necessary, as with the case in the actual processing unit 17100 in FIG. 146.
As described above, in the event that a processing region within image data wherein the actual world 1 light signals are projected on a plurality of pixels each having time-space integration effects, and part of the actual world light signal 1 continuity is lost is set, the movement amount of the object within the image data, which is the real world light signal continuity lost in the image data, is set, and the light signal function F(x) is estimated assuming that the pixel value of each pixel corresponding to a position in the x direction of the time-space directions of the image data within the processing region is a pixel value acquired by the light signal function (actual world function) F(x) corresponding to the actual world 1 light signal approximated with the spline function integrating a model moving while phase-shifting in the time direction according to the movement amount in the x direction and in the time direction, the processing region, movement amount, weight W1 and weight W2, and so forth are set according to user input. Accordingly, the light signal function F(x) may be estimated precisely by the user adjusting the processing region, movement amount, weight W1 and weight W2, and so forth while viewing an image generated from the estimated result of the light signal function F(x), and as a result, the user can ultimately obtain an image having a high image quality.
Note that in the above case, an arrangement has been made wherein when a moving object is displayed on the input image, the object is moving in the horizontal direction (from left to right direction) at a constant speed, i.e., the movement direction of the object is fixed to the horizontal direction, and the movement amount serving as the magnitude of the movement is employed as the continuity information, but as the continuity information, movement vector having directional information as well as the magnitude of the movement may be employed. In this case, as for an input image of which the movement of an object (continuity) is represented with movement vector, the physical model in FIG. 125, for example, may be adapted by taking the movement direction shown with movement vector as the x direction.
Also, in the above case, a still image has been employed as an input image, but a moving image may be employed as an input image as well. In this case, the signal processing device 4 performs processing of a moving image in increments of frame or field, for example.
Further, as for a processing region, an arbitrary shape other than a rectangle may be employed.
Next, with the continuity setting unit 17002 in FIG. 113, movement serving as the continuity information may be set not only based on user operations but also by detecting movement from the input image.
Now, description will be made regarding a method for detecting movement in the continuity setting unit 17002.
In the event that a certain object is moving in an input image, as for a method for detecting movement vector serving as the movement of the object for example, the so-called block matching method has been known.
However, with the block matching method, matching is performed between the frame of interest and the frames before and after the frame of interest, so that movements cannot be detected easily with the frame of interest alone.
To this end, the continuity setting unit 17002 is configured so as to detect movements from an input image having one frame alone.
That is to say, FIG. 160 illustrates a configuration example of the continuity setting unit 17002.
With the continuity setting unit 17002 of which the configuration is shown in FIG. 160, the movement direction of an object in the processing region of the an input image is detected, and the input image is corrected such that the movement direction becomes the horizontal direction. Subsequently, the features subjected to the one-dimensional differentiation in the movement direction of the object in the input image, which are the differential value of the pixel values of pixels adjacent in the movement direction, are detected.
Further, the correlation is detected between the features of the pixel of interest and the features of the corresponding pixel with a predetermined distance in the movement direction, and the movement amount of the object is detected according to the distance between the corresponding pixel and the pixel of interest, which exhibits the maximum detected correlation.
That is to say, the continuity setting unit 17002 of which the configuration is shown in FIG. 160 includes a movement direction detecting unit 11201, a movement direction correcting unit 11202, a features detecting unit 11203, and a movement amount detecting unit 11204.
Further, the movement direction detecting unit 11201 includes an activity computing unit 11211, and an activity evaluating unit 11212. The movement direction correcting unit 11202 includes an affine transformation unit 11213.
The features detecting unit 11203 includes a difference computing unit 11214, a difference evaluating unit 11215, an intermediate image creating unit 11216, an intermediate image creating unit 11217, frame memory 11218, a sign inverting unit 11219, and frame memory 11220.
Further, the movement amount detecting unit 11204 includes a correlation detecting unit 11221, and a correlation evaluating unit 11222.
With the continuity setting unit 17002 of which configuration is shown in FIG. 160, the input image is supplied to the movement direction detecting unit 11201 and the movement direction correcting unit 11202. Further, the processing region information that is output from the processing region setting unit 17001 is also supplied to the movement direction detecting unit 11201 and the movement direction correcting unit 11202.
The movement direction detecting unit 11201 acquires the input image and the processing region information, and detects the movement direction in the processing region from the acquired input image.
When capturing a moving object, movement blurring occurs on the image of the object. This is caused by actions of the image sensor of a camera or video camera serving as the sensor 2 for capturing the image of an object.
That is to say, an image sensor such as a CCD (Charge Coupled Device) or CMOS (Complementary Metal-Oxide Semiconductor) sensor consecutively converts the incident light into electric charge for each pixel during exposure time (shutter time), and further converts the electric charge into one pixel value. When an object to be captured is in a stationary state, the image (light) of the same portion of the object is converted into one pixel value during exposure time. The image thus captured includes no movement blurring.
On the other hand, when an object is moving, the image of the portion of the object to be cast into one pixel changes during exposure time, and the images of different portions of the object are converted into one pixel value by accident. Speaking inversely, the image of one portion of the object is cast into multiple pixel values, which is movement blurring.
Movement blurring occurs in the movement direction of the object.
Upon focusing on the pixel values of pixels arrayed in the movement direction of the portion where movement blurring occurs (region including movement blurring), the image of generally the same range portion of the object is projected to the pixel values of the pixels arrayed in the movement direction. Accordingly, we can say that change in the pixel values of the pixels arrayed in the movement direction at the portion where movement blurring occurs is further reduced.
The movement direction detecting unit 11201 detects a movement direction based on such change, i.e., activity in the pixel value of a pixel in the processing region of an input image.
More specifically, the activity computing unit 11211 of the movement direction detecting unit 11201 computes change (activity) in the pixel values of pixels arrayed in various directions for each predetermined direction. For example, the activity computing unit 11211 computes the difference between the pixel values of the pixels positioned corresponding to each direction for each predetermine direction as activity. The activity computing unit 11211 supplies information indicating change in the computed pixel values to the activity evaluating unit 11212.
The activity evaluating unit 11212 selects the minimum change in the pixel value, of change in the pixel values of the pixels for each predetermined direction supplied from the activity computing unit 11211, and takes the direction corresponding to the selected change in the pixel value as the movement direction.
The movement direction detecting unit 11201 supplies movement direction information indicating the movement direction thus detected to the movement direction correcting unit 11202.
The movement direction correcting unit 11202 is supplied with processing region information as well. The movement direction correcting unit 11202 converts the image data within the processing region in the input image based on the movement direction information supplied from the movement direction detecting unit 11201 such that the movement direction becomes the horizontal direction of the image.
For example, the affine transformation unit 11213 of the movement direction correcting unit 11202 subjects the image data within the processing region in the input image to affine transformation based on the movement direction information supplied from the movement direction detecting unit 11201 such that the movement direction shown in the movement direction information becomes the horizontal direction of the image.
The movement direction correcting unit 11202 supplies the image data within the processing region in the input image converted such that the movement direction becomes the horizontal direction of the image to the features detecting unit 11203.
The features detecting unit 11203 detects the features of the image supplied from the movement direction correcting unit 11202.
That is to say, the difference computing unit 11214 of the features detecting unit 11203 sets a pixel selected by selecting one pixel from the pixels in the processing region of the input image, as a pixel of interest. Subsequently, the difference computing unit 11214 of the features detecting unit 11203 obtains a difference value by subtracting the pixel value of the pixel adjacent to the pixel of interest on the right side from the pixel value of the pixel of interest.
The difference computing unit 11214 obtains difference values by taking the pixels in the processing region of the input image as a pixel of interest in order. That is to say, the difference computing unit 11214 obtains difference values regarding all of the pixels in the processing region of the input image. The difference computing unit 11214 supplies the difference values thus computed to the difference evaluating unit 11215 along with information indicating the position of the pixel of interest corresponding to each obtained difference value (positional information indicating the position on the screen of each difference value).
The difference evaluating unit 11215 determines regarding whether or not the difference values are 0 or more, supplies the difference values equal to or greater than 0 to the intermediate image creating unit 11216 along with the positional information indicating the position on the screen of each difference value, and supplies the difference values less than 0 to the intermediate image creating unit 11217 along with the positional information indicating the position on the screen of each difference value.
The intermediate image creating unit 11216 creates, based on the difference values equal to or greater than 0 supplied from the difference evaluating unit 11215 along with the positional information indicating the position on the screen of the difference values, an intermediate image made up of each difference value. That is to say, the intermediate image creating unit 11216 creates an intermediate image by setting the difference values equal to or greater than 0 supplied from the difference evaluating unit 11215 to the pixels at the positions on the screen indicated by the positional information, and setting 0 to the pixels at the positions where no difference value is supplied from the difference evaluating unit 11215. The intermediate image creating unit 11216 supplies the intermediate image thus created (hereafter, referred to as non-inverted intermediate image) to the frame memory 11218.
The intermediate image creating unit 11217 creates, based on the difference values less than 0 (negative values) supplied from the difference evaluating unit 11215 along with the positional information indicating the positions on the screen of the difference values, an intermediate image made up of the difference values. That is to say, the intermediate image creating unit 11217 creates an intermediate image by setting the difference values less than 0 supplied from the difference evaluating unit 11215 to the pixels at the positions on the screen indicated by the positional information, and setting 0 to the pixels at the positions where no difference value is supplied from the difference evaluating unit 11215. The intermediate image creating unit 11216 supplies the intermediate image thus created to the sign inverting unit 11219.
The sign inverting unit 11219 inverts the signs of the difference values less than 0 set to the pixels of the intermediate image supplied from the intermediate image creating unit 11217. The signs of the value 0 set to the pixels of the intermediate image are not inverted. That is to say, the sign inverting unit 11219 selects the difference values less than 0 set to the pixels of the intermediate image supplied from the intermediate image creating unit 11217, and converts the selected difference values less than 0 into the values greater than 0 having the same absolute values as the difference values. For example, the difference value, which is −15, is converted into 15 by inverting the sign thereof. The sign inverting unit 11219 supplies the intermediate image thus sign-inverted (hereafter referred to as inverted intermediate image) to the frame memory 11220.
The frame memory 11218 supplies the non-inverted intermediate image made up of the difference values equal to or greater than 0 and 0 to the movement amount detecting unit 11204 as features. The frame memory 11220 supplies the inverted intermediate image made up of the difference values greater than 0 of which the signs are inverted and 0 to the movement amount detecting unit 11204 as features.
The movement detecting unit 11204 detects movements based on the features supplied from the features detecting unit 11203. That is to say, the movement detecting unit 11204 detects the correlation between the features of at least the pixel of interest, of the pixels of the image of the object in the processing region of the input image, and the features of the corresponding pixel allocated in the movement direction as to the pixel of interest, and detects the movement amount of the image of the object in the processing region of the input image according to the detected correlation.
The correlation detecting unit 11221 of the movement amount detecting unit 11204 detects the correlation between the non-inverted intermediate image serving as features supplied from the frame memory 11218 of the features detecting unit 11203, and the inverted intermediate image serving as features supplied from the frame memory 11220 of the features detecting unit 11203. The correlation detecting unit 11221 supplies the detected correlation to the correlation evaluating unit 11222.
More specifically describing, for example, the correlation detecting unit 11221 of the movement amount detecting unit 11204 moves (shifts) the inverted intermediate image made up of the difference values of which the signs are inverted so as to be greater than 0, and 0 supplied from the frame memory 11220 of the features detecting unit 11203, in the horizontal direction of the screen in units of pixel as to the non-inverted intermediate image made up of the difference values equal to or greater than 0, and 0 supplied from the frame memory 11218 of the features detecting unit 11203. That is to say, the correlation detecting unit 11221 moves the positions on the screen of the pixels making up the inverted intermediate image in the horizontal direction.
The positional relation on the screen between the pixels of the non-inverted intermediate image and the pixels of the inverted intermediate image changes by moving (the pixels of) the inverted intermediate image in the horizontal direction on the screen. For example, the corresponding pixel of the inverted intermediate image positioned on the screen corresponding to the pixel of interest of the non-inverted intermediate image before movement results in departing from the position corresponding to the pixel of interest of the non-inverted intermediate image by the movement distance after movement. More specifically, when the non-inverted intermediate image is moved to the right by 20 pixels, the corresponding pixel of the inverted intermediate image departs from the position corresponding to the pixel of interest of the non-inverted intermediate image to the right by 20 pixels. Speaking inversely, the corresponding pixel of the inverted intermediate image positioned on the screen corresponding to the pixel of interest of the non-inverted intermediate image after movement departs from the position corresponding to the pixel of interest by the movement distance before movement.
The correlation detecting unit 11221 computes the difference between the pixel values of the pixels corresponding to the non-inverted intermediate image and the inverted intermediate image moved, and takes the sum of the differential absolute values as a correlation value.
For example, the correlation detecting unit 11221 moves (shifts) the inverted intermediate image in the horizontal direction of the screen in increments of one pixel in a range of 70 pixels in the left direction of the screen through 70 pixels in the right direction of the screen as to the non-inverted intermediate image, computes the difference between the pixel values of the pixels to be positioned at the same position on the screen regarding the non-inverted intermediate image and the inverted intermediate image moved for each moved position (each movement distance), and takes the sum of the differential absolute values as a correlation value.
For example, when the inverted intermediate image is moved to the left direction of the screen as to the non-inverted intermediate image, the movement distance is represented with a negative (minus). When the inverted intermediate image is moved to the right direction of the screen as to the non-inverted intermediate image, the movement distance is represented with a positive (plus). The correlation detecting unit 11221 computes the difference between the pixel values of the pixels to be positioned at the same position on the screen regarding the non-inverted intermediate image and the inverted intermediate image moved for each movement distance of −70 pixels through +70 pixels, and takes the sum of the differential absolute values as a correlation value.
The correlation detecting unit 11221 supplies the correlation value corresponding to the movement distance to the correlation evaluating unit 11222. That is to say, the correlation detecting unit 11221 supplies a pair of the movement distance and the correlation value to the correlation evaluating unit 11222.
The correlation evaluating unit 11222 detects the movement amount of the image of the object in the processing region of the input image according to the correlation. More specifically, the correlation evaluating unit 11222 takes, of the correlations supplied from the correlation detecting unit 11221, the movement distance corresponding to the maximum (strongest) correlation as a movement amount.
For example, the correlation evaluating unit 11222 selects the minimum value, of the sum of the differential absolute values serving as the correlation value supplied from the correlation detecting unit 11221, and sets the movement distance corresponding to the selected minimum value to the movement amount.
The correlation evaluating unit 11222 outputs the detected movement amount.
FIG. 161 through FIG. 163 are diagrams for describing the principle for detecting movements by the continuity setting unit 17002 in FIG. 160.
Now, let us say that a white foreground object serving as an object to be captured is disposed in front of a black background object serving as another object to be captured, and is moving from the left side to the right side, and a camera having an image sensor such as a CCD or CMOS sensor captures the foreground object along with the background object with a predetermined exposure time (shutter time).
In this case, upon focusing on one frame of the image to be output from the camera, the background object is black, so that the camera outputs, for example, a pixel value 0 as to the background object image. The foreground object is white, so that the camera outputs, for example, a pixel value 255 as to the foreground object image. Here, let us say that the camera outputs a pixel value in a range of 0 through 28−1.
The diagram in the upper side of FIG. 161 is a diagram illustrating the pixel values of the image to be output by the camera when the foreground object is in a stationary state at the position at the moment that the shutter of the camera opens (moment of starting exposure).
The diagram in the lower side of FIG. 161 is a diagram illustrating the pixel values of the image to be output by the camera when the foreground object is in a stationary state at the position at the moment that the shutter of the camera closes (moment of ending exposure).
As shown in FIG. 161, the movement amount of the image of the foreground object is a distance wherein the image of the foreground object moves from the moment that the shutter of the camera opens until the moment that the shutter of the camera closes.
FIG. 162 is a diagram illustrating the pixel values of the image to be output from the camera when the foreground object moving in front of the background object is captured by the camera. The image sensor of the camera consecutively converts the image (light) of the object into electric charge during exposure time (shutter time) for each pixel, and further converts the electric charge into one pixel value, and accordingly, the image of the foreground object 11251 is projected into the pixel values of the multiple pixels. The maximum pixel value of the image shown in FIG. 162 is small as compared with the maximum pixel value of the image shown in FIG. 161.
The slope width of the pixel values shown in FIG. 162 corresponds to the width of the image of the background object.
Upon the difference value as to the adjacent pixel on the right side being computed, and set to the pixel regarding each pixel of the image shown in FIG. 162, the image made up of the difference values shown in FIG. 163 is obtained.
That is to say, one pixel is selected from the pixels of the image shown in FIG. 162, and set to as a pixel of interest to which attention is paid. Subsequently, the difference value is obtained by subtracting the pixel value of the pixel adjacent to the pixel of interest on the right side from the pixel value of the pixel of interest. The difference value is set to the pixel at the position corresponding to the pixel of interest. The pixels of the image shown in FIG. 162 are taken as a pixel of interest in order, and the image made up of the difference values shown in FIG. 163 is obtained.
The difference value having a negative (minus) sign emerges on the one-pixel left side as to the position of the foreground object at the moment that the shutter of the camera opens shown in the diagram on the upper side of FIG. 161, and the difference value having a positive (plus) sign emerges on the one-pixel left side as to the position of the foreground object at the moment that the shutter of the camera closes shown in the diagram on the lower side of FIG. 161.
Accordingly, upon matching being performed between a value obtained by inverting the sign of the difference value having a negative (minus) sign and the difference value having a positive (plus) sign shown in FIG. 163, the movement distance of the value obtained by inverting the sign of the difference value having a negative (minus) sign is the same as the movement amount on the basis of the difference value having a positive (plus) sign when performing matching, for example.
For example, on the basis of the difference value having a positive (plus) sign, the value obtained by inverting the sign of the difference value having a negative (minus) sign is moved in the horizontal direction, the correlation between the value obtained by inverting the negative difference value and the positive difference value is detected for each movement distance thereof, thereby detecting the maximum (strongest) correlation. The movement distance when the maximum correlation is detected is the same as the movement amount.
More specifically, for example, on the basis of the difference value having a positive (plus) sign, the value obtained by inverting the sign of the difference value having a negative (minus) sign is moved in the horizontal direction, as the correlation between the value obtained by inverting the negative difference value and the positive difference value for each movement distance thereof, the positive difference value is subtracted from the inverted value for each pixel. Subsequently, the minimum value within the subtracted results, i.e., the maximum correlation is detected. The movement distance corresponding to the detected maximum correlation is the same as the movement amount.
As described above, the movement amount, which is the amount wherein the image of the object moves, can be detected from one frame of the image during exposure time (shutter time).
That is to say, the difference computing unit 11214 of the features detecting unit 11203 selects one pixel from pixels in the processing region of the input image, sets this as a pixel of interest, and subtracts the pixel value of the pixel adjacent to the pixel of interest on the right side from the pixel value of the pixel of interest, thereby computing the difference values shown in FIG. 163, for example. The difference evaluating unit 11215 classifies the difference values into the positive difference values and the negative difference values based on the signs of the difference values.
The intermediate image creating unit 11216 creates, from the classified positive difference values, a non-inverted intermediate image made up of the positive difference values thereof. The intermediate image creating unit 11217 creates, from the classified negative difference values, a intermediate image made up of the negative difference values thereof. The sign inverting unit 11219 creates a non-inverted intermediate image by inverting the signs of the negative pixel values of the intermediate image made up of the negative difference values.
The movement amount detecting unit 11204 obtains the movement distance of the non-inverted intermediate image and the inverted intermediate image, which have the strongest correlation, and takes the obtained movement distance as the movement amount.
When the features detecting unit 11203 detects the image of the moving object, and detects the features of the image of the moving object, the movement amount detecting unit 11204 detects a correlation based on the features, and detects the movement amount of the image of the object within the input image according to the detected correlation.
Also, when the features amount detecting unit 11203 selects the pixel of interest to which attention is paid from the pixels belonged to the image of the moving object, and detects the features of the pixel of interest, the movement amount detecting unit 11204 detects the correlation between the features of the pixel of interest and the features of the corresponding pixel to be allocated in the movement direction as to the pixel of interest, and detects the movement amount of the image of the object in the processing region of the input image according to the detected correlation.
FIG. 164 is a flowchart for describing the processing for detecting a movement amount by the continuity setting unit 17002 in FIG. 160.
In step S11201, the movement direction detecting unit 11201 and the movement direction correcting unit 11202 acquire the input image and the processing region information, and the flow proceeds to step S11202.
In step S11202, the activity computing unit 11211 of the movement direction detecting unit 112011 computes activity regarding the pixels of the processing region in the input image acquired in the processing in step S11201, and the flow proceeds to step S11203.
For example, the activity computing unit 11211 selects the pixel of interest to which attention is paid, of the pixels of the processing region in the input image. The activity computing unit 11211 extracts a predetermined number of perimeter pixels in the vicinity of the pixel of interest. For example, the activity computing unit 11211 extracts perimeter pixels made up of 5×5 pixels (5 pixels by 5 pixels) centered on the pixel of interest.
Subsequently, the activity computing unit 11211 detects activity corresponding to the predetermined direction on the image from the extracted perimeter pixels.
With the following description, a pixel array in the horizontal direction is referred to as a row, and a pixel array in the vertical direction is referred to as a column.
Regarding 5×5 perimeter pixels for example, the activity computing unit 11211 detects activity as to the angle of 90 degrees (vertical direction of the screen) on the basis of the horizontal direction of the screen by computing the differences between the pixel values of the adjacent pixels in the up-and-down (vertical) direction on the screen, dividing the sum of the differential absolute values computed by the number of differences, and taking the result as activity.
For example, the difference of pixel values is computed regarding the two pixels adjacent in the up-to-down direction on the screen of 20 pairs, the sum of the differential absolute values computed is divided by 20, and the result (quotient) is set to the activity as to the angle of 90 degrees.
Regarding 5×5 perimeter pixels for example, the activity computing unit 11211 detects activity as to the angle of 76 degrees (tan−1(4/1)) on the basis of the horizontal direction of the screen by computing the differences between the respective pixel values of the leftmost pixel through the fourth pixel from the left in the lowest row, and the respective pixel values of the pixels on the four-pixel upper side and also on one-pixel right side as to the respective pixels, dividing the sum of the differential absolute values computed by the number of differences, and taking the result as activity.
For example, the difference of pixel values is computed regarding the two pixels in the upper right direction having a distance of four pixels in the vertical direction, and one pixel in the horizontal direction of four pairs, the sum of the differential absolute values computed is divided by four, and the result (quotient) is set to the activity as to the angle of 76 degrees.
The activity computing unit 11211 detects activity as to the angle in a range of 90 degrees through 180 degrees on the basis of the horizontal direction of the screen with the same processing. In the event of detecting activity as to the angle in a range of 90 degrees through 180 degrees, activity is calculated based on the difference of the pixel values of the pixels positioned in the upper left direction.
The activity thus detected is taken as the activity as to the pixel of interest.
Note that the detected activity may be the activity as to the perimeter pixels.
Also, description has been made that the perimeter pixels are made up of 5×5 pixels (5 pixels by 5 pixels), but pixels having a desired range may be employed regardless of 5×5 pixels. In the event of employing a great number of perimeter pixels, angular resolution improves.
The activity computing unit 11211 supplies information indicating activity corresponding to multiple directions to the activity evaluating unit 11212.
Returning to FIG. 164, in step S11203, the activity evaluating unit 11212 obtains the movement direction by selecting the minimum activity based on the activity corresponding to a predetermined direction calculated in the processing in step S11202, and taking the selected direction as the movement direction, and the flow proceeds to step S11204.
In step S11204, the movement direction correcting unit 11202 converts the image data in the processing region of the input image based on the movement direction obtained in the processing in step S11203 such that the movement direction becomes the horizontal direction of the image, and the flow proceeds to step S11205. For example, in step S11204, the affine transformation unit 11213 of the movement direction correcting unit 11202 subjects the image data in the processing region of the input image to affine transformation based on the movement direction obtained in the processing in step S11203 such that the movement direction becomes the horizontal direction of the image. More specifically, for example, the affine transformation unit 11213 subjects the image data in the processing region of the input image to affine transformation so as to rotate 18 degrees in the clockwise direction on the basis of the horizontal direction of the screen when the movement direction is the angle of 18 degrees.
In step S11205, the difference computing unit 11214 of the features detecting unit 11203 computes the difference value of the pixel value as to the pixel adjacent in the horizontal direction regarding each pixel in the processing region of the input image converted such that the movement direction becomes the horizontal direction of the screen in the processing in step S11204, and the flow proceeds to step S11206.
For example, in step S11205, the difference computing unit 11214 sets a pixel of interest to which attention is paid by selecting one pixel from the pixels in the processing region of the input image. Subsequently, the difference computing unit 11214 obtains the difference value by subtracting the pixel value of the pixel adjacent to the pixel of interest on the right side from the pixel value of the pixel of interest.
In step S11206, the difference evaluating unit 11215 of the features detecting unit 11203 allocates the difference values based on the signs of the difference values, and the flow proceeds to step S11207. That is to say, the difference evaluating unit 11215 supplies the difference values equal to or greater than 0 to the intermediate image creating unit 11216, and supplies the difference values less than 0 to the intermediate image creating unit 11217. In this case, the difference evaluating unit 11215 supplies the difference values to the intermediate image creating unit 11216 or the intermediate image creating unit 11217 along with the positional information indicating the position of each difference value on the screen.
In step S11207, the intermediate image creating unit 11216 of the features detecting unit 11203 creates an intermediate image made up of the positive difference values based on the difference values equal to or greater than 0 (positive difference values) allocated in the processing in step S11206, and the flow proceeds to step S11208. That is to say, in step S11207, the intermediate image creating unit 11216 creates an intermediate image by setting the positive difference values to the pixels at the positions on the screen indicated with the positional information, and setting 0 to the pixels at the positions where no difference value was supplied.
Thus, a non-inverted intermediate image is created in the processing in step S11207.
In step S11208, the intermediate image creating unit 11217 of the features detecting unit 11203 creates an intermediate image made up of the negative difference values based on the difference values less than 0 (negative difference values) allocated in the processing in step S11206, and the flow proceeds to step S11209. That is to say, in step S11208, the intermediate image creating unit 11217 creates an intermediate image by setting the negative difference values to the pixels at the positions on the screen indicated with the positional information, and setting 0 to the pixels at the positions where no difference value was supplied.
In step S11209, the sign inverting unit 11219 of the features detecting unit 11203 inverts the signs of the negative difference values of the intermediate image made up of the negative difference values created in the processing in step S11208. That is to say, in step S11209, the negative difference values set to the pixels of the negative intermediate image are converted into the positive values having the same absolute values.
Thus, in step S11209, a non-inverted intermediate image is created, and then the flow proceeds to step S11210.
In step S11210, the movement amount detecting unit 11204 executes correlation detecting processing. The details of the processing in step S11210 will be described later with reference to the flowchart in FIG. 165.
In step S11211, the correlation evaluating unit 11222 selects the strongest correlation, of the correlations detected in the processing in step S11210, and the flow proceeds to step S11212. For example, in step S11211, of the correlation values serving as the sum of the differential absolute values of the pixel values, the minimum correlation value is selected.
In step S11212, the correlation evaluating unit 11222 sets the movement distance corresponding to the strongest correlation selected in the processing in step S11211 to the movement amount, and the flow proceeds to step S11213. For example, in step S11212, of the correlation values serving as the sum of the differential absolute values of the pixel values, the movement distance of the inverted intermediate image stored in the processing in step S11223 described later corresponding to the selected minimum correlation value is set to the movement amount.
In step S11213, the movement amount detecting unit 11204 outputs the movement amount detected in the processing in step S11210, and the processing ends.
FIG. 165 is a flowchart for describing correlation detecting processing corresponding to the processing in step S11210.
In step S11221, the correlation detecting unit 11221 of the movement amount detecting unit 11204 moves the positions of the pixels of the inverted intermediate image created in the processing in step S11209 in the horizontal direction in increments of pixel, and the flow proceeds to step S11222.
In step S11222, the correlation detecting unit 11221 detects the correlation between the non-inverted intermediate image and the inverted intermediate image of which the positions of the pixels are moved in the processing in step S11221, and the flow proceeds to step S11223. For example, in step S11222, the differences are computed between the pixel values of the pixels of the non-inverted intermediate image and the pixel values of the pixels of the inverted intermediate image at the corresponding positions on the screen, and the sum of the computed differential absolute values is detected as a correlation value. The correlation detecting unit 11221 supplies correlation information indicating the detected correlation to the correlation evaluating unit 11222 along with the movement distance of the pixels of the inverted intermediate image in the processing in step S11221.
In step S11223, the correlation evaluating unit 11222 stores the correlation detected in the processing in step S11222 along with the movement distance of the pixels of the inverted intermediate image in the processing in step S11221, and the flow proceeds to step S11224. For example, the correlation evaluating unit 11222 stores the correlation value serving as the sum of the differential absolute values of the pixel values along with the movement distance of the pixels of the inverted intermediate image in the processing in step S11221.
In step S11224, the correlation detecting unit 11221 determines regarding whether or not correlation as to all of the movement distances has been detected, and in the event that determination is made that correlation has not been detected with some movement distances, the flow returns to step S11221, where the processing for detecting correlation as to the next movement distance is repeated.
For example, in step S11224, the correlation detecting unit 11221 determines whether or not all correlations have been detected in a case of moving pixels of the inverted intermediate image in the range of 70 pixels in the left direction in the image through 70 pixels in the right direction in the image.
In the event that determination is made in step S11224 that the correlations for all movements amount have been detected, the processing ends (returns).
Thus, the correlation detecting unit 11221 can detect correlation.
As described above, the continuity setting unit 17002 of which the configuration is shown in FIG. 160 can detect movement amount from one frame in an image.
Now, while movement has been detected here with regard to a processing region, an arrangement may be made wherein movement over the entire screen due to hand shaking, for example, can be detected, by processing the entire screen.
Also, even in the event that there are a great amount of repetitive patterns of the same design in the input image, these can be detected in an accurate manner so long as the movement distance and movement direction of the processing region in the input image to be processed is constant.
While movement distance detection from one frame in an image has been described above, it is needless to say that an arrangement may be made wherein movement distance is detected from one field.
Also, an arrangement may be made wherein the movement amount is detected regarding only the perimeter of the selected pixel of interest.
Note that the above-described embodiments include, besides embodiments of the invention described in the Claims, embodiments regarding the first throughout fourteenth signal processing devices given below.
A first signal processing device comprises: processing region setting means for setting the processing region within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; movement vector setting means for setting movement vectors of an object within the image data corresponding to the continuity of the real world light signals of which a part of the continuity has been lost in the image data; and actual world estimating means for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data within the processing region is a pixel value obtained by the actual world function corresponding to the actual world light signal approximated with a spline function integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one dimensional direction and in the time direction, wherein at least one of the processing region setting means and the movement vector setting means sets a processing region or movement vector, according to user input.
A second signal processing device, which in addition to the features of the first signal processing device, further comprises: image generating means for generating an image by integrating a spline function which approximates the actual world function, which is the estimation result of the actual world function, in a predetermined one-dimensional direction and in the time direction in predetermined increments; and display means for displaying the image generated by the image generating means; wherein at least one of the processing region setting means and the movement vector setting means sets a processing region or movement vector, according to user input, following an image being displayed on the display means.
A third signal processing device, wherein, in addition to the features of the second signal processing device, the movement vector setting means set a plurality of movement vector, the actual world estimating means estimate a plurality of actual world functions according to the plurality of movement vectors, the image generating means generate a plurality of images according to the estimation results of the plurality of actual world functions, the display means display the plurality of images, and the movement vector setting means further sets one of the plurality of movement vectors according to user input for selecting any one of the plurality images.
A fourth signal processing device, wherein, in addition to the features of the first signal processing device, the actual world estimating means comprises: model generating means for generating a relation model modeling the relation between the pixel value of each pixel within the image data and the actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data within the processing region is a pixel value acquired by the actual world function corresponding to the real world light signals integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one dimensional direction and in the time direction; equation generating means for substituting the pixel value of each pixel within the image data for the relation model generated by the model generating means to generate an equation; and actual world waveform estimating means for estimating the actual world function corresponding to the real world light signals by computing the equation generated with the equation generating means.
A fifth signal processing device, wherein, in addition to the features of the fourth signal processing device, the model generating means generate a relation model assuming that the level of the actual world function outside of the processing region is a steady value.
A sixth signal processing device, which in addition to the features of the fourth signal processing device, further comprises image generating means for generating an image made up of pixel values wherein the movement blurring of the object within the image data is removed by integrating a spline function which approximates the actual world function, which is the estimation result of the actual world function, in a predetermined one-dimensional direction and in the time direction in predetermined increments.
A seventh signal processing device comprises: movement vector setting means for setting the movement vector of an object within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; and actual world estimating means for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data is a pixel value obtained by the actual world function corresponding to the real world light signal approximated with a spline function integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one dimensional direction and in the time direction.
A eighth signal processing device, wherein, in addition to the features of the seventh signal processing device, the actual world estimating means comprises: model generating means for generating a relation model modeling the relation between the pixel value of each pixel within the image data and the actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data is a pixel value acquired by the actual world function corresponding to the real world light signal approximated with a spline function integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one-dimensional direction and in the time direction; equation generating means for substituting the pixel value of each pixel within the image data for the relation model generated by the model generating means to generate an equation; and actual world waveform estimating means for estimating the actual world function corresponding to the real world light signals by computing the equations generated by the equation generating means.
A ninth signal processing device, wherein, in addition to the features of the eighth signal processing device, the model generating means generate a relation model assuming that the level of the actual world function outside of the image data region is a steady value.
A tenth signal processing device, which in addition to the features of the eighth signal processing device, further comprises image generating means for generating an image made up of pixel values wherein the movement blurring of the object within the image data is removed by integrating an approximation model which approximates the actual world function, which is the estimation result of the actual world function, in a predetermined one-dimensional direction and in the time direction in predetermined increments.
An eleventh signal processing device comprises: movement vector setting means for setting the movement vector of an object within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; model generating means for generating a relation model modeling the relation between the pixel value of each pixel within the image data and the actual world function approximated with a spline function, assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data is a pixel value acquired by the actual world function corresponding to the real world light signal integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one-dimensional direction and in the time direction; equation generating means for substituting the pixel value of each pixel within the image data for the relation model generated by the model generating means to generate an equation, and also generating an equation for providing a constraint condition assuming that change in the pixel value within the pixel represented with the spline function which approximates the actual world function; and actual world waveform estimating means for estimating the actual world function corresponding to the real world light signals by computing the equation generated by the equation generating means.
A twelfth signal processing device, wherein, in addition to the features of the eleventh signal processing device, the equation generating means further generates an equation for providing a constraint condition assuming that the level of the actual world function outside of the region of the image data is a steady value.
A thirteenth signal processing device, which in addition to the features of the twelfth signal processing device, further comprises: weighting modifying means for modifying weighting as to an equation for a constraint condition assuming that change in the pixel value within the pixel represented with the spline function which approximates the actual world function, and as to an equation for providing a constraint condition assuming that the level of the actual world function outside of the region of the image data is a steady value, wherein the actual world waveform estimating means estimate the actual world function by computing the equations.
A fourteenth signal processing device, which in addition to the features of the thirteenth signal processing device, further comprises: image generating means for generating an image made up of pixel values wherein the movement blurring of the object within the image data is removed by integrating a spline function which approximates the actual world function, which is the estimation result of the actual world function, in a predetermined one-dimensional direction and in the time direction in predetermined increments; and display means for displaying the image generated by the image generating means, wherein the weighting modifying means modify weighting according to user input following an image being displayed on the display means.
The above-described embodiments also include embodiments regarding the first through third signal processing methods, programs, and recording mediums, given below.
A first signal processing method, program, and recording medium, comprise: a processing region setting step for setting the processing region within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; a movement vector setting step for setting movement vectors of an object within the image data which is the continuity of the real world light signals lost in the image data; and an actual world estimating step for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data within the processing region is a pixel value obtained by the actual world function corresponding to the real world light signal approximated with a spline function integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one dimensional direction and in the time direction, wherein at least one of the processing region setting step and the movement vector setting step sets a processing region or movement vector, according to user input.
A second signal processing method, program, and recording medium, comprise: a movement vector setting step for setting the movement vector of an object within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; and an actual world estimating step for estimating an actual world function assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data is a pixel value obtained by the actual world function corresponding to the actual world light signal approximated with a spline function integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one dimensional direction and in the time direction.
A third signal processing method, program, and recording medium, comprise: a movement vector setting means for setting the movement vector of an object within image data, wherein light signals of the real world have been projected on a plurality of pixels each having time-space integration effects and a part of the continuity of the real world light signals has been lost; a model generating step for generating a relation model modeling the relation between the pixel value of each pixel within the image data and the actual world function approximated with a spline function, assuming that the pixel value of each pixel corresponding to a position in a predetermined one-dimensional direction of the spatial direction of the image data is a pixel value acquired by the actual world function corresponding to the real world light signal integrating a model moving while phase-shifting in the time direction corresponding to the movement vector thereof, in the predetermined one-dimensional direction and in the time direction; an equation generating step for substituting the pixel value of each pixel within the image data for the relation model generated in the model generating step to generate an equation, and also generating an equation for providing a constraint condition assuming that change in the pixel value within the pixel represented with the spline function which approximates the actual world function; and an actual world waveform estimating step for estimating the actual world function corresponding to the real world light signals by computing the equation generated in the equation generating step.
INDUSTRIAL APPLICABILITY
As described above, according to the present invention, images and the like closer approximating real world signals can be obtained.

## Claims

1. A signal processing device comprising:
actual world estimating means for estimating an actual world function, the pixel value of each pixel corresponding to a position at least in one-dimensional direction of the time-space directions of image data wherein real world light signals are projected on a plurality of pixels each having the time-space integration effects, and part of the continuity of the real world light signals has been lost is a pixel value acquired by integrating the actual world function corresponding to said real world light signals approximated with a spline function at least in the one-dimensional direction; and
image generating means for generating an image by integrating said actual world function, approximated by the spline function shifting in the other one-dimensional direction different from said one-dimensional direction of said time-space directions, in two-dimensional directions.

2. The signal processing device according to claim 1, wherein the pixel of each pixel corresponding to a position in a one-dimensional direction of the spatial direction of said image data is a pixel value acquired by the one-dimensional actual world function approximated with a spline function integrating a model, which is moving in the time direction, in the two-dimensional directions.

3. The signal processing device according to claim 2, said actual world estimating means comprising:
model generating means for generating a relation model modeling the relation between the pixel value of each pixel within said image data and said actual world function based on the pixel value of each pixel corresponding to a position in a one-dimensional direction of the spatial direction of said image data is a pixel value acquired by the actual world function corresponding to said real world light signals integrating a model, which is moving in the time direction, in said one-dimensional direction and the time direction;
equation generating means for generating equations by substituting the pixel values of each of the pixels within said image data as to the relation model generated by said model generating means; and
actual world waveform estimating means for estimating said actual world function corresponding to said real world light signals by computing equations generated by said equation generating means.

4. The signal processing device according to claim 3, wherein said model generating means generates said relation model with the level of said actual world function outside of the region of said image data being a steady value.

5. A signal processing method comprising:
detecting a plurality of pixels with a hardware sensor;
estimating an actual world function based on the pixel value of each pixel corresponding to a position at least in one-dimensional direction of the time-space directions of image data wherein real world light signals are projected on the plurality of pixels each having the time-space integration effects, and part of the continuity of the real world light signals has been lost is a pixel value acquired by integrating the actual world function corresponding to said real world light signals approximated with a spline function at least in the one-dimensional direction; and
generating an image by integrating said actual world function, approximated by the spline function shifting in the other one-dimensional direction different from said one-dimensional direction of said time-space directions, in two-dimensional directions.

6. A recording medium storing a program for causing a computer to perform a method of predetermined signal processing, said method comprising:
detecting a plurality of pixels with a hardware sensor;
estimating said actual world function based on the pixel value of each pixel corresponding to a position at least in one-dimensional direction of the time-space directions of image data wherein real world light signals are projected on the plurality of pixels each having the time-space integration effects, and part of the continuity of the real world light signals has been lost is a pixel value acquired by integrating the actual world function corresponding to said real world light signals approximated with a spline function at least in the one-dimensional direction; and
generating an image by integrating said actual world function, approximated by the spline function shifting in the other one-dimensional direction different from said one-dimensional direction of said time-space directions, in two-dimensional directions.

7. A signal processing device comprising:
a hardware sensor configured to detect a plurality of pixels;
an actual world estimating unit configured to estimate an actual world function, the pixel value of each pixel corresponding to a position at least in one-dimensional direction of the time-space directions of image data wherein real world light signals are projected on the plurality of pixels each having the time-space integration effects, and part of the continuity of the real world light signals has been lost is a pixel value acquired by integrating the actual world function corresponding to said real world light signals approximated with a spline function at least in the one-dimensional direction; and
an image generating unit configured to generate an image by integrating said actual world function, approximated by the spline function shifting in the other one-dimensional direction different from said one-dimensional direction of said time-space directions, in two-dimensional directions.

8. The signal processing device according to claim 7, wherein the pixel of each pixel corresponding to a position in a one-dimensional direction of the spatial direction of said image data is a pixel value acquired by the one-dimensional actual world function approximated with a spline function integrating a model, which is moving in the time direction, in the two-dimensional directions.

9. The signal processing device according to claim 8, said actual world estimating unit comprising:
a model generating unit configured to generate a relation model modeling the relation between the pixel value of each pixel within said image data and said actual world function based on the pixel value of each pixel corresponding to a position in a one-dimensional direction of the spatial direction of said image data is a pixel value acquired by the actual world function corresponding to said real world light signals integrating a model, which is moving in the time direction, in said one-dimensional direction and the time direction;
an equation generating unit configured to generate equations by substituting the pixel values of each of the pixels within said image data as to the relation model generated by said model generating unit; and
an actual world waveform estimating unit configured to estimate said actual world function corresponding to said real world light signals by computing equations generated by said equation generating unit.

10. The signal processing device according to claim 9, wherein said model generating unit is configured to generate said relation model, with the level of said actual world function outside of the region of said image data being a steady value.