Patent Publication Number: US-10326951-B2

Title: Image processing apparatus, image processing method, image capturing apparatus and image processing program

Description:
TECHNICAL FIELD 
     The present invention relates to an image processing technique of performing a noise reduction on an image. 
     BACKGROUND ART 
     In order to achieve a high image quality of an image produced by image capturing of an object space, it is important to reduce noise in the image. Typically, intensity of information of the object space included in the image is lower at a higher frequency, but intensity of the noise in the image is substantially constant irrespective of the frequency. Thus, a region with a higher frequency has a higher fraction of the noise included in an original signal of the image. For this reason, a high frequency component of the image is weakened to reduce the noise in a widely performed noise reduction. 
     As such a noise reduction disclosed is a method of reducing noise in an image while maintaining edge information of the object space by using a local characteristic of a signal of the image. Patent Document 1 discloses a method of categorizing a local region of an image into an edge part, a flat part and a gradation part and changing a noise reduction parameter depending on these categories. This method reduces the noise in the image while maintaining edge sharpness, by applying a weaker noise reduction in the edge part and a stronger noise reduction in the flat part where the noise is easily noticeable. 
     CITATION LIST 
     Patent Literature 
     [PLT1] Japanese Patent Laid-open No. 2010-109834 
     SUMMARY OF INVENTION 
     Technical Problem 
     However, the method disclosed in Patent Document 1 does not take into consideration an optical characteristic of an image capturing system (including an image capturing optical system and an image sensor, for example) that has produced an image that has noise to be reduced. 
     The image capturing system has a degree of freedom in an F-number and a focus position, and further in a focal length and the like when the image capturing optical system is a zoom lens. A characteristic of a produced image differs in accordance with the optical characteristic depending on the degree of freedom. Thus, a noise reduction without taking into consideration the optical characteristic of the image capturing system cannot efficiently reduce noise, and furthermore is likely to cause an increased loss in the information of the object space. 
     The present invention provides an image processing apparatus and the like that are capable of performing a favorable noise reduction on an image produced by image capturing. 
     Solution to Problem 
     The present invention provides as an aspect thereof an image processing apparatus including a processor configured to perform a noise reduction on at least part of an input image produced by image capturing using an image capturing system, and an acquirer configured to acquire first information on an optical characteristic of the image capturing system, the optical characteristic indicating a factor that degrades information of an object space in the image capturing of the input image. The processor is configured to change a process of the noise reduction depending on the first information. 
     The present invention provides as another aspect thereof an image capturing apparatus including the above image processing apparatus and at least part of the image capturing system. 
     The present invention provides as still another aspect thereof an image processing method of performing a noise reduction on at least part of an input image produced by image capturing using an image capturing system. The method includes preparing first information on an optical characteristic of the image capturing system, the optical characteristic indicating a factor that degrades information of an object space in the image capturing of the input image, and changing a process of the noise reduction depending on the first information. 
     The present invention provides as yet another aspect thereof an image processing program as a computer program that causes a computer to perform a noise reduction on at least part of an input image produced by image capturing using an image capturing system. The program causes the computer to acquire first information on an optical characteristic of the image capturing system, the optical characteristic indicating a factor that degrades information of an object space in the image capturing of the input image and to change a process of the noise reduction depending on the first information. 
     Further features and aspects of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
     Advantageous Effects of Invention 
     The present invention changes the process of the noise reduction on the input image produced by the image capturing, depending on the information on the optical characteristic of the image capturing system, thereby performing a highly accurate noise reduction on the input image. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram of a configuration of an image capturing apparatus that is Embodiment 1 of the present invention. 
         FIG. 2  is an exterior diagram of the image capturing apparatus of Embodiment 1. 
         FIG. 3  is a flowchart showing a noise reduction process in Embodiment 1. 
         FIGS. 4A and 4B  are explanatory diagrams of an optical characteristic in Embodiments 1 to 3. 
         FIG. 5  is a block diagram of a configuration of an image processing system that is Embodiment 2 of the present invention. 
         FIG. 6  is an exterior diagram of the image processing system of Embodiment 2. 
         FIG. 7  is an arrangement diagram of an imaging optical system in Embodiment 2. 
         FIG. 8  is a flowchart showing a noise reduction process in Embodiments 2 and 3. 
         FIG. 9  illustrates a relation between a defocus amount and a spread of an image thereof in Embodiments 2 and 3. 
         FIG. 10  illustrates an exemplary image capturing scene in Embodiments 2 and 3. 
         FIG. 11  illustrates an exemplary image produced by image capturing in Embodiments 2 and 3. 
         FIG. 12  illustrates a defocus characteristic region in Embodiments 2 and 3. 
         FIG. 13  is a block diagram of a configuration of an image capturing system that is Embodiment 3. 
         FIG. 14  is an exterior diagram of the image capturing system of Embodiment 3. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Exemplary embodiments of the present invention will be described below with reference to the accompanied drawings. 
     An imaging optical system used for image capturing has a degree of freedom in an F-number and a focus position, and further in a focal length and others when the optical system is a zoom lens. A characteristic of a produced image differs with an optical characteristic of the optical system depending on the degree of freedom. For example, a larger F-number increases an influence of diffraction, which restricts frequency information of an object space, which is acquirable from an image produced by image capturing to only a low frequency component. Therefore, performing on the image a stronger noise reduction than that in case of a smaller F-number does not cause a loss in the information of the object space included in the image. Thus, taking into consideration the optical characteristic of the imaging optical system used for image capturing, a noise reduction can efficiently reduce noise only while preventing the loss in the information of the object space. Embodiments will describe later a configuration and a method to achieve such a highly accurate noise reduction. 
     Next, description will be made of the optical characteristic of the image capturing system in the embodiments before specific description of the embodiments is made. The image capturing system in the embodiments mainly includes an imaging optical system (image capturing optical system) and an image sensor. The image capturing system causes light from the object space to form an optical image and photoelectrically converts the optical image into an analog electric signal (that is, performs sampling). 
     Factors that degrade the information of the object space include diffraction, aberration and defocus in the imaging optical system, and blur produced during exposure of the image sensor due to a displacement of the image capturing system or a movement of an object. The embodiments describe, among these factors, the diffraction, the aberration and the defocus which are design values of the imaging optical system or values previously acquirable by measurement, and collectively refer to these characteristics as “an optical characteristic”. A later description will be made of a noise reduction taking information on the optical characteristic into consideration. However, the optical characteristic may include as its component all or part of the diffraction, aberration and defocus. This is because the diffraction, aberration and defocus have different causes, and magnitudes of their influences depend on an image capturing scene. 
     In the embodiments, the noise reduction takes into consideration a pixel pitch and a Nyquist frequency of the image sensor that are information on the sampling performed by the image sensor. 
     EXAMPLE 1 
     A first embodiment (Embodiment 1) of the present invention will describe a case in which the components of the optical characteristic of the image capturing system (imaging optical system) are the diffraction and the aberration.  FIG. 1  illustrates a basic configuration of an image capturing apparatus  100  according to Embodiment 1, and  FIG. 2  is an external diagram of the image capturing apparatus  100 . 
     Light entering an imaging optical system  101  from the object space (not illustrated) forms an optical image on the image sensor  102  by an imaging effect of the imaging optical system  101 . The image sensor  102  is a photoelectric conversion element constituted by, for example, a CCD (charge coupled device) sensor or a CMOS (complementary metal-oxide semiconductor) sensor. The image sensor  102  photoelectrically converts the optical image into an analog electric signal. This analog signal is converted into a digital signal by an A/D converter  103  and then input to an image processor  104 . 
     The imaging optical system  101  may be detachably attachable to the image capturing apparatus  100  including the image sensor  102 . In other words, the image capturing apparatus  100  only needs to include at least part (that is, the image sensor  102 ) of the image capturing system. 
     The image processor  104  as an image processing apparatus performs typical image processes on the input digital signal to produce an input image as image data. In addition, the image processor  104  performs a noise reduction (noise reduction process), which is a process to reduce noise, on the input image. This noise reduction uses information (first information; hereinafter referred to as “optical characteristic information”) on the optical characteristic of the imaging optical system  101  stored in a memory  105 , which will be described in detail later. 
     An output image obtained through the above-described image processes and the noise reduction at the image processor  104  is stored in a predetermined format in an image recording medium  106 . The image recording medium  106  may store, together with the output image, information (hereinafter referred to as “image capturing condition information”) on an image capturing condition. The image capturing condition information includes a state of an aperture stop and a focus state of the imaging optical system  101  at image capturing to produce the input image, and further includes a focal length and others when the imaging optical system  101  is a zoom lens. A state detector  107  may obtain the image capturing condition information from a system controller  108  or an optical controller  109 . 
     Alternatively, the image processor  104  may read an image previously stored in the image recording medium  106  as the input image and acquire the optical characteristic information from the memory  105  with reference to the image capturing condition information for the input image. Then, the image processor  104  may perform, on the input image, the noise reduction using the optical characteristic information. 
     The image stored in the image recording medium  106  is displayed on a display unit  110  constituted by, for example, a liquid crystal display. 
     The system controller  108  controls the above-described constituent components of the image capturing apparatus  100 . An optical controller  109  controls mechanical drive of a focus lens, the aperture stop, a magnification-varying lens and others of the imaging optical system  101 , in response to instructions from the system controller  108 . 
     Next, a detailed description will be made of the noise reduction process (image processing method) performed by the image processor  104  with reference to a flowchart in  FIG. 3  and  FIGS. 4A and 4B . The image processor  104  as an image processing computer executes this process according to an image processing program as a computer program. The image processor  104  serves as an acquirer and a processor. 
     At step S 101 , the image processor  104  acquires an input image. The input image includes, together with the information of the object space, shot noise generated at the image sensor  102  and others. 
     At step S 102 , the image processor  104  acquires information (second information; hereinafter referred to as “sampling information”) on sampling performed by the image capturing system (image sensor  102 ). The sampling information is, as described above, information on conditions of the sampling such as the pixel pitch indicating an interval of the sampling at the image sensor  102  and the Nyquist frequency as half of a frequency (sampling frequency) of the sampling. When the image sensor  102  includes multiple color channels for acquiring different colors and polarized lights, the image processor  104  acquires the sampling information corresponding to each color channel. For example, when a pixel array of the image sensor  102  is a Bayer array of RGB (red, green and blue), the sampling information for G and the sampling information for R and B are different from each other. 
     At step S 103 , the image processor  104  acquires a partial region in which the noise reduction is to be performed in this routine, from a noise reduction target region in the input image (that is, from at least part of the input image). 
     At step S 104 , the image processor  104  acquires (provides) the optical characteristic information for a position of the partial region acquired at step S 103  in the input image. The optical characteristic information indicates the optical characteristic of the imaging optical system  101  at image capturing to produce the input image; the optical characteristic information includes an optical transfer function (OTF) and a point spread function (PSF). Alternatively, the optical characteristic information may be simply a spot diameter as a spread amount of a point image, for example. However, the optical transfer function and the point spread function are desirably acquired to perform the noise reduction with a higher accuracy. 
     Description will be made of parameters for determining the optical characteristic information. As described above, in this embodiment, the optical characteristic information includes the diffraction and the aberration as its components. A second embodiment (Embodiment 2) of the present invention will later give description about the defocus. 
     The diffraction is substantially constant irrespective of an image height. Thus, when only the diffraction is considered, the optical characteristic information depends on a state (shape and size) of a pupil of the imaging optical system  101  and does not depend on the position of the partial region acquired at step S 103 . In this case, the noise reduction may be performed for the entire input image as a single process, not only for the partial region acquired at step S 103 . 
     In contrast, the aberration changes with the image height. Thus, an acquirable threshold frequency of the object space changes with the image height. Consequently, the optical characteristic information changes with the position of the partial region acquired at step S 103 , that is, with the image height. In addition, the aberration also changes with the F-number and the focus position of the imaging optical system  101  and the focal length of the imaging optical system  101  as the zoom lens. Thus, these values are information needed to determine the optical characteristic information for the partial region. 
     Furthermore, the aberration also changes with a wavelength. Thus, when the image sensor  102  includes the multiple color channels, the wavelength is needed to determine the optical characteristic information. The aberration also changes with a defocus amount in the partial region, which is a difference between the focus position of the imaging optical system  101  and a depth of the partial region. Thus, the information to determine the optical characteristic information may include the depth of the partial region. 
     The optical characteristic includes both of the diffraction and the aberration in this embodiment, but may include only one of them as necessary. The optical characteristic may include the aberration only in a case of, for example, a large-aperture lens because performance degradation due to the aberration is dominant over that due to the diffraction. Alternatively, when the aperture stop is narrowed to set the F-number to an extremely large value, the optical characteristic may include the diffraction only because the aberration is extremely small but the influence of the diffraction is large in this case. 
     However, when an influence of vignetting of the imaging optical system  101  is large and the optical characteristic includes the diffraction only, the position of the partial region is needed as a parameter to determine the optical characteristic information. This is because a diffraction limit changes with the image height. On the other hand, when the optical characteristic includes as its component the aberration only, not all parameters such as the focus position and the image height are needed to be taken into consideration. For example, when performance degradation due to spherical aberration is dominant over that due to off-axis aberration as in a telephoto lens, performance fluctuation with the image height can be ignored, and only a parameter largely related to an aberration change may be used. 
     At step S 105 , the image processor  104  determines a process of the noise reduction depending on the optical characteristic information and the sampling information thus acquired. In other words, the image processor  104  changes the process of the noise reduction depending on the optical characteristic information and the sampling information. The determination or change of “the process of the noise reduction” includes determination or change of a parameter that changes (controls) strength of the noise reduction and selection or change of a method of the noise reduction. In this embodiment, the image processor  104  determines or changes the process of the noise reduction such that the strength of the noise reduction (in other words, a noise reduction effect) is stronger as a frequency component acquirable by the imaging optical system  101  is smaller. This is described below with reference to  FIGS. 4A and 4B . 
       FIGS. 4A and 4B  each illustrate an MTF (modulation transfer function) of the imaging optical system  101  obtained from the optical characteristic information. In  FIGS. 4A and 4B , a horizontal axis represents a frequency q, and q N  represents the Nyquist frequency of the image sensor  102  acquired from the sampling information. To simplify the description, the MTF is taken to be one-dimensional, and a negative frequency component is omitted. However, the following description is applicable to a case in which the MTF is two-dimensional. 
       FIG. 4A  and  FIG. 4B  illustrate two types of the MTFs. The MTF illustrated in  FIG. 4B  shows that an acquirable frequency component is smaller than that shown by the MTF illustrated in  FIG. 4A . This difference between the MTFs originates from, for example, a difference of the F-numbers with respect to the diffraction, and from a difference of the image heights with respect to the aberration. An image acquired with the optical characteristic illustrated in  FIG. 4B  has the information of the object space up to a lower frequency range than that of an image acquired with the optical characteristic illustrated in  FIG. 4A . In  FIG. 4B , q 0  represents a frequency at which the MTF has a zero value. In other words, any frequency component higher than the frequency q 0  in the image is determined to be noise. This suggests that a stronger process of the noise reduction than that in  FIG. 4A  can be selected for the optical characteristic corresponding to the MTF illustrated in  FIG. 4B . 
     Next, description will be made of a method using, as an exemplary reference to determine the process of the noise reduction, a frequency at which an MTF is equal to or smaller than a predetermined value. When q dn  represents a frequency at which the MTF is equal to or smaller than a predetermined threshold r thr , q dn  is equal to q dn1  in  FIG. 4A , and q dn  is equal to q dn2  in  FIG. 4B . This frequency is used as the reference to determine the process of the noise reduction. A case of using a step function for the noise reduction and determining a parameter of the step function will be described as a simplest example. In this case, a Fourier transform of the partial region acquired from the input image is multiplied with a value of Expression (1) below to calculate an inverse Fourier transform of the multiplication. 
     
       
         
           
             
               
                 
                   
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     When q dn  is larger than q N , a signal of the object space cannot be distinguished from noise. Thus, the process of the noise reduction may be changed depending on q dn  and q N , which respectively are the optical characteristic information and the sampling information (that is, depending on a relation between the optical characteristic information and the sampling information). Although this description is made by using the Fourier transform of the image, a discrete cosine transform or a wavelet transform may be used, for example. 
     At step S 106 , the image processor  104  performs the noise reduction for the partial region acquired at step S 103  by the process determined at step S 105 . The method of the noise reduction may be a smoothing filter such as a bilateral filter, an NLM (non-local means) filter, or the step function in Expression (1), for example. 
     At step S 107 , the image processor  104  determines whether or not the noise reduction has completed for the partial regions acquired from the entire noise reduction target region in the input image. If this noise reduction has completed, the image processor  104  ends this noise reduction process. If the noise reduction has not yet completed, the image processor  104  returns to step S 103  to acquire a new partial region from the noise reduction target region and repeats the processes at steps S 103  to S 107 . 
     This embodiment provides the image capturing apparatus  100  including the image processor  104  capable of performing a highly accurate noise reduction with taken into consideration the optical characteristic (diffraction and aberration) of the image capturing system and the conditions (pixel pitch and Nyquist frequency) of the sampling. 
     EXAMPLE 2 
     Next, description will be made of an image processing system that is a second embodiment (Embodiment 2) of the present invention to which the above-described image processing method is applied. This embodiment describes the defocus as the component of the optical characteristic of the image capturing system. Embodiment 1 describes the case in which the image processing apparatus (image processor  104 ) is built in the image capturing apparatus  100 . In this embodiment, as illustrated in a system configuration diagram of  FIG. 5  and a system exterior diagram of  FIG. 6 , an image capturing apparatus  201  and the image processing apparatus  202  that performs the noise reduction are separately provided. 
     An input image produced by image capturing through the image capturing apparatus  201  is input to the image processing apparatus  202  through a communication unit  203  provided in the image processing apparatus  202 . The image capturing apparatus  201  is configured to acquire multiple parallax images having parallaxes therebetween (described in detail later). 
     The image processing apparatus  202  acquires (produces), from information on the parallaxes, information on a depth of an object space at each position (coordinates) in the input image, in other words, a depth map as information on a distribution of the depth in the input image. The image processing apparatus  202  then stores the depth map in a memory  204 . The image processing apparatus  202  also acquires optical characteristic information of the image capturing apparatus (image capturing system)  201  used for image capturing to produce the input image, from the image capturing apparatus  201  or from a set of information associated with the input image. The image processing apparatus  202  then stores the optical characteristic information on the memory  204 . 
     A noise reducer  205  as an acquirer and a processor included in the image processing apparatus  202  performs a noise reduction on the input image acquired through the communication unit  203 . An output image after the noise reduction is output through the communication unit  203  to at least one of a display apparatus  206 , a recording medium  207  and an output apparatus  208 . The display apparatus  206  is constituted by a liquid crystal display or a projector, for example, and displays the output image. The recording medium  207  is a semiconductor memory, a hard disk, or a server on a network, for example, and stores the output image. The output apparatus  208  is constituted by a printer that prints the output image, for example. The image processing apparatus  202  may have functions to perform a development process and other image processes as necessary. 
       FIG. 7  illustrates a configuration of the image capturing apparatus  201 . The image capturing apparatus  201  includes a multi-lens imaging optical system constituted by imaging optical systems  211   a  to  211   p  two-dimensionally disposed. Each of the imaging optical systems  211   a  to  211   p  includes an image sensor (not illustrated) on its image plane side. This configuration allows the image capturing apparatus  201  to produce multiple parallax images having parallaxes therebetween through image capturing from multiple viewpoints and to obtain information of the parallaxes of the object space from these parallax images. The image sensors may be replaced with a single image sensor that can receive all optical images formed by the imaging optical systems  211   a  to  211   p . The number of pixels may differ between the image sensors corresponding to the imaging optical systems. 
     The imaging optical systems  211   a  to  211   p  include multiple types of imaging optical systems whose focal lengths are mutually different. The imaging optical systems  211   a  to  211   d  are wide-angle lenses, and the imaging optical systems  211   e  to  211   h  are normal lenses. The imaging optical systems  211   i  to  211   l  are semi-telephoto lenses, and the imaging optical systems  211   m  to  211   p  are telephoto lenses. The types of the imaging optical systems and the number and arrangement thereof for each type are not limited to the configuration illustrated in  FIG. 7 . The image capturing apparatus  201  does not necessarily need to include the multi-lens imaging optical system, but may be a plenoptic camera, for example. The image capturing apparatus  201  may include a single-lens imaging optical system when information on the distribution of the depth of the object space is acquirable from other than parallax images. The information on the distribution of the depth may be acquired by using a TOF (time of flight) method and structured illumination. 
     Next, detailed description will be made of a noise reduction process (image processing method) performed by the image processing apparatus  202  (noise reducer  205 ) with reference to a flowchart in  FIG. 8  and  FIGS. 9 to 11 . The image processing apparatus  202  as an image processing computer executes this process according to an image processing program as a computer program. 
     At step S 201 , the noise reducer  205  acquires an input image through the communication unit  203  from the image capturing apparatus  201 . The input image may be multiple parallax images obtained by the image capturing apparatus  201  as described above, or may be one viewpoint image among the parallax images. Alternatively, the input image may be a combined image obtained by combining these parallax images. In this case, however, when optical characteristics of the imaging optical systems corresponding to the respective parallax images are mutually different (for example, when image capturing is performed with the imaging optical systems  211   a  to  211   d  whose F-numbers are mutually different), the following problem occurs. 
     A noise reduction for such a combined image requires calculation of an optical characteristic at each position in the combined image, which is difficult. Thus, when the input image is the combined image obtained by combining multiple parallax images corresponding to the respective imaging optical systems having mutually different optical characteristics, a noise reduction described below is desirably performed on the parallax images before being combined. Description below will be made of a case where multiple parallax images are obtained as the input images. 
     At step S 202 , the noise reducer  205  acquires (produces) the depth map of the input image. In this embodiment, because information on the parallaxes of the object space is acquirable from the multiple parallax images as the input images, the depth map is acquired by, for example, a stereo method. Although the depth can be estimated only in an edge part of an image in which a feature point exists, the depth in a non-edge region such as a gradation region can be calculated by interpolation with the depth in the edge part. 
     At step S 203 , the noise reducer  205  acquires sampling information of the image sensor corresponding to each parallax image as the input image among the multiple image sensors provided to the image capturing apparatus  201 . 
     At step S 204 , the noise reducer  205  acquires a partial region in which the noise reduction is to be performed in this routine, in a noise reduction target region that is the entire input image or part thereof. 
     At step S 205 , the noise reducer  205  acquires the optical characteristic information at a position of the partial region acquired at step S 204  in the parallax image. The optical characteristic information in this embodiment is a defocus characteristic of the imaging optical system corresponding to the parallax image. Performance degradation due to defocus is larger as the depth of the partial region acquired at step S 204  is further away from a focus position (that is, an in-focus plane) of the imaging optical system, in other words, as a defocus amount is larger. In addition, a degree of the performance degradation for the same defocus amount still changes with the focal length and the F-number of the imaging optical system. Thus, determination of the optical characteristic information requires the F-number, the focus position and the focal length (in the zoom lens) of the imaging optical system and the position (that is, the depth) of the partial region. Although the defocus characteristic changes with the wavelength, a large absolute value of the defocus amount gives a small difference between defocus characteristics for different wavelengths, and thus determination of whether or not to take the defocus characteristic into consideration for each wavelength may depend on the defocus amount. 
     As described above, the information on the depth of the object space is needed to take the defocus into consideration as the optical characteristic. However, because objects typically exist at various depth positions, a change in an acquirable frequency due to the defocus is larger than those due to the aberration and the diffraction described in Embodiment 1. Thus, performing the noise reduction with the defocus taken into consideration as the optical characteristic as in this embodiment provides a noise reduction effect with a higher accuracy than that obtained in Embodiment 1. 
     Processes of steps S 206  to S 208  are the same as the processes of steps S 105  to S 107  in Embodiment 1 ( FIG. 3 ). Specifically, the noise reducer  205  determines the process of the noise reduction depending on the optical characteristic information and the sampling information at step S 206  and performs the noise reduction by the determined process on the partial region at step S 207 . Then, the processes of steps S 204  to S 207  are repeated until it is determined that the noise reduction has completed for the entire noise reduction target region in the input image (parallax image) at step S 208 . 
     This embodiment can achieve the image processing apparatus  202  and the image processing system that are capable of performing a highly accurate noise reduction with the optical characteristic (defocus) of the image capturing system and the conditions of the sampling taken into consideration. 
     Next, description will be made of a desirable condition to achieve a higher accuracy of the noise reduction in this embodiment. 
     The partial region is desirably acquired (extracted) from the input image at step S 204  in the following manner. First, the depth map is divided such that a division pitch is larger as a division position is further away from the image capturing system (image capturing apparatus  201 ) in a direction corresponding to the depth (in other words, a depth direction). This division provides multiple defocus characteristic regions whose defocus characteristics are mutually different. In other words, the division provides multiple defocus characteristic regions in each of which a range of the defocus characteristic (defocus characteristic range) can be regarded as a range of an identical defocus characteristic and whose defocus characteristic ranges are mutually different. Then, the partial region is acquired from one (single) defocus characteristic region among the multiple defocus characteristic regions. 
     If any multiple regions whose depths are discontinuous exist on a boundary between multiple objects in the partial region, completely different defocus characteristics exist in the partial region, which leads to a reduced effect of this embodiment. Thus, the partial region is desirably acquired from a single defocus characteristic region whose defocus characteristic range can be regarded as an identical defocus characteristic. 
     Description will be made of a reason why the division pitch of the defocus characteristic regions is larger as the division position is further away from the image capturing apparatus  201 . To simplify the description, the imaging optical system is approximated to a thin system. In this case, an imaging equation is given by Expression (2) below. 
     
       
         
           
             
               
                 
                   
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     In this expression, f represents a focal length of the imaging optical system, σ represents a distance from the imaging optical system to the image sensor, and s represents a distance from the imaging optical system to an in-focus plane (an object side plane conjugate with the image sensor with respect to the imaging optical system). An origin of a distance coordinate system is located at a position of the imaging optical system. Thus, s and σ have different signs when the imaging optical system forms a real image. 
     A spread of an image (hereinafter referred to as “an image spread”) due to the defocus on the image sensor is equal to δ at two imaging distances, which is given by Expression (3) below. 
     
       
         
           
             
               
                 
                   
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     In this expression, F represents an F-number of the imaging optical system. σ+Δσ i  represents two imaging distances at which the image spread due to the defocus is δ on the image sensor, where i is 1 or 2. Object distances s+Δs i  corresponding to the two imaging distances represented by Expression (3) are represented by Expression (4) below by using Expression (2). 
     
       
         
           
             
               
                 
                   
                     s 
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         s 
                         i 
                       
                     
                   
                   = 
                   
                     s 
                     + 
                     
                       
                         
                           
                             ( 
                             
                               f 
                               + 
                               s 
                             
                             ) 
                           
                           2 
                         
                         ⁢ 
                         
                           Δσ 
                           i 
                         
                       
                       
                         
                           f 
                           2 
                         
                         - 
                         
                           
                             ( 
                             
                               f 
                               + 
                               s 
                             
                             ) 
                           
                           ⁢ 
                           
                             Δσ 
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Expression (3) is approximately rewritten to Expression (5) below when f is sufficiently larger Fδ.
 
σ+Δσ i =σ+(−1) −i   Fδ   (5)
 
     Substituting Expression (5) into Expression (4) yields Expression (6) below. 
     
       
         
           
             
               
                 
                   
                     s 
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         s 
                         i 
                       
                     
                   
                   = 
                   
                     s 
                     + 
                     
                       
                         
                           
                             ( 
                             
                               - 
                               1 
                             
                             ) 
                           
                           i 
                         
                         ⁢ 
                         
                           
                             F 
                             ⁡ 
                             
                               ( 
                               
                                 f 
                                 + 
                                 s 
                               
                               ) 
                             
                           
                           2 
                         
                         ⁢ 
                         δ 
                       
                       
                         
                           f 
                           2 
                         
                         - 
                         
                           
                             
                               ( 
                               
                                 - 
                                 1 
                               
                               ) 
                             
                             i 
                           
                           ⁢ 
                           
                             F 
                             ⁡ 
                             
                               ( 
                               
                                 f 
                                 + 
                                 s 
                               
                               ) 
                             
                           
                           ⁢ 
                           δ 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Expression (6) is rewritten to yield Expression (7) below, which represents a relation between the image spread δ due to the defocus and the defocus amount Δs i  on an object space side. 
     
       
         
           
             
               
                 
                   δ 
                   = 
                   
                     
                       
                         
                           ( 
                           
                             - 
                             1 
                           
                           ) 
                         
                         i 
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                       ⁢ 
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         s 
                         i 
                       
                     
                     
                       
                         F 
                         ⁡ 
                         
                           ( 
                           
                             f 
                             + 
                             s 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           f 
                           + 
                           s 
                           + 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               s 
                               i 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
       FIG. 9  illustrates graphs each showing the relation obtained using Expression (7) between defocus amount Δs i  and the image spread δ. In  FIG. 9 , f is 50 [mm], and s is −2500 [mm], and this relation is illustrated for a case of an F-number of 1.4 (shown by a solid line) and an F-number of 2.8 (shown by a dashed line). In  FIG. 9 , a horizontal axis represents the defocus amount Δs i  (s=−2500 at an origin thereof, and a point thereon closer to a positive side represents a position closer to the image capturing apparatus  201 ) on the object space, and a vertical axis represents the image spread δ due to the defocus (in other words, a spread of defocus blur) on the image sensor, the spread corresponding to the defocus amount. The spread δ may be expressed in an absolute value, but is here in a signed value to explicitly show a shape of the graph. 
     As understood from  FIG. 9 , as the distance from the image capturing apparatus  201  to the object becomes larger, a change in the spread of defocus blur becomes smaller. Thus, dividing the object space into regions such that the spreads of defocus blur are mutually approximately equal between the regions is equivalent to dividing the depth with a larger interval (pitch) as the division position is further away from the image capturing apparatus  201 . 
     A specific example of the division is described with reference to  FIGS. 10 to 12 .  FIG. 10  illustrates an exemplary scene (image capturing scene) of which image is captured by the image capturing apparatus  201 . In the image capturing scene, there are a first object  301 , a second object  302 , a third object  303  and a fourth object  304  in this order from the image capturing apparatus  201 .  FIG. 11  illustrates one of multiple parallax images produced by image capturing of the image capturing scene illustrated in  FIG. 10 . In reality, the imaging optical system of the image capturing apparatus  201  is focused on either object (in-focus plane) in the parallax image of  FIG. 11 , and the image has a larger defocus blur as a position is further away from the in-focus plane. In  FIG. 11 , however, image degradation due to this defocus is ignored. Dashed lines in  FIG. 10  represent the depths of the first to fourth objects  301  to  304  and an image capturing angle of view of the imaging optical system used in the image capturing to produce the parallax image of  FIG. 11 . 
     In  FIG. 10 , dashed-dotted lines divide the depth into regions in which the spreads of defocus blur in the object space are mutually equal. Each region between two dashed-dotted lines is a region whose defocus characteristic range can be regarded as a range of an identical defocus characteristic, in other words, a region having an identical defocus characteristic, which is one defocus characteristic region.  FIG. 10  illustrates four exemplary defocus characteristic regions  311  to  314 . However, there may be defocus characteristic regions on a front side (closer side) of the defocus characteristic region  311  and on a back side (farther side) of the defocus characteristic region  314 . 
       FIG. 12  illustrates the defocus characteristic regions  311  to  314  over the input image. In  FIG. 12 , different densities of dots correspond to different depths, and a region with identical densities represents one defocus characteristic region.  FIG. 12  illustrates a defocus characteristic region  315  on the farther side of the defocus characteristic region  314 , which is not illustrated in  FIG. 10 . Acquiring the partial region from a single defocus characteristic region can prevent degradation in the accuracy of the noise reduction. 
     The optical characteristic information corresponding to the partial region acquired at step S 204  is desirably set for an average value of the depth in the partial region. This provides appropriate (less erroneous) optical characteristic information for the depth that fluctuates in the partial region, which achieves a highly accurate noise reduction for the partial region. 
     In addition, it is desirable to acquire a map of a degree of depth reliability indicating an accuracy of the depth map for the input image and to determine (change) the process of the noise reduction depending on the degree of depth reliability. Since the depth map is calculated from parallax images in this embodiment, an accuracy of estimating the depth is reduced due to, for example, a small number of corresponding points among the parallax images. Similarly, when the depth is acquired by the TOF method and the structured illumination, any disturbance and a characteristic of an object surface may reduce an accuracy of the acquisition. Use of such an inaccurate depth acquired in this manner in the process reduces the accuracy of the noise reduction. For example, even though the depth is acquired by actually acquiring the information on the object space up to a high frequency range, a low accuracy (reliability) of the depth may result in a determination that the information is acquired only for a low frequency range, which leads to such an excessive noise reduction that the information of the object space is lost. Thus, it is desirable to change the process of the noise reduction depending on the degree of depth reliability. 
     For example, a threshold relating to the degree of depth reliability may be provided. The process of the noise reduction is selected which weakens the strength of the noise reduction (that is, the noise reduction effect) for a region where the degree of depth reliability is lower than the threshold, compared to that for a region that has the same depth value and where the degree of depth reliability is higher than the threshold. This can reduce a risk of losing the information of the object space due to the excessive noise reduction as described above. The strength of the noise reduction may be weakened by adjusting a parameter in the same method of the noise reduction, or by changing the method of the noise reduction itself. 
     Alternatively, when the depth is calculated from parallax images, the degree of depth reliability may be defined to be high in a partial area having a large number of corresponding points among the parallax images and in an edge area where the noise reduction is stronger. This is because a calculation accuracy of the depth is higher in the partial area having a larger number of corresponding points and in the edge area where the noise reduction is stronger. 
     In calculation of the depth from parallax images, defocus of each parallax image has such an influence that a target feature point (object) in the parallax images is more unlikely to be extracted when the target feature point is located further away from the in-focus plane, which reduces the degree of depth reliability for the feature point. In such a case, a specific depth for which an accuracy of extracting the feature point is equal to or lower than a predetermined value may be previously acquired. This specific depth (in other words, an optical characteristic for the specific depth) may be used to perform the noise reduction for a partial region having a depth for which the degree of depth reliability is low. This specific depth is a depth closer to the in-focus plane than an original depth of the partial region, which results in the noise reduction with a lower strength. 
     As the optical characteristic information in this embodiment, instead of using information based on the optical transfer function, the defocus characteristic may be obtained in a simplified manner from, for example, Expression (7) or the like by using the focal length and the F-number of the imaging optical system. To perform the process with a higher accuracy, the optical characteristic information based on the optical transfer function may be used. 
     EXAMPLE 3 
     Next, description will be made of an image capturing system that is a third embodiment (Embodiment 3) of the present invention. In Embodiment 3, as illustrated in a system configuration diagram in  FIG. 13  and a system exterior diagram in  FIG. 14 , an image capturing apparatus  401  sends an image (input image) produced by image capturing and a depth map to a server (computer)  403  as an image processing apparatus through wireless communication. The server  403  performs a noise reduction on the received input image using the received depth map. In this embodiment, similarly to Embodiment 2, an optical characteristic of the image capturing apparatus (image capturing system)  401  is the defocus. 
     The image capturing apparatus  401  includes an image sensor according to the TOF (time of flight) method and produces the input image by image capturing and the depth map thereof. The server  403  includes a communication unit  404  and is connected to be capable of communicating with the image capturing apparatus  401  through a network  402 . When the image capturing apparatus  401  performs image capturing, the input image produced by the image capturing and the depth map is sent to the server  403  automatically or in response to an instruction provided by a user of the image capturing apparatus  401 . The input image and the depth map are stored on a memory  405  in the server  403 . At the same time, the optical characteristic information and the sampling information of the image capturing apparatus  401  are sent from the image capturing apparatus  401  to the server  403  and stored on the memory  405 . 
     An image processor  406  in the server  403  performs the noise reduction described in Embodiment 2 ( FIG. 8 ) on the input image. The server  403  sends an output image obtained as a result of the noise reduction to the image capturing apparatus  401  and stores the output image on the memory  405 . 
     In the same image capturing system, the optical characteristic of the image capturing apparatus (image capturing system) may include the aberration and the diffraction. 
     This embodiment provides the server  403  and further the image capturing system which are capable of performing a highly accurate noise reduction with the optical characteristic of the image capturing apparatus  401  and the conditions of the sampling taken into consideration. 
     OTHER EXAMPLES 
     Embodiments of the present invention can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiments and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiments, and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiments and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiments. The computer may comprise one or more processors (e.g., central processor (CPU), micro processor (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2014-257239, filed on Dec. 19, 2014 which is hereby incorporated by reference herein in its entirety. 
     REFERENCE SIGNS LIST 
     
         
           101  imaging optical system 
           102  image sensor 
           104  image processor 
           202  image processing apparatus 
           403  server