Patent Publication Number: US-9894252-B2

Title: Image processing apparatus, image pickup apparatus, image processing method, and storage medium for reducing noise of an image obtained by combining parallax images

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an image processing apparatus which reconstructs an input image to generate a plurality of output images with different focus positions. 
     Description of the Related Art 
     Recently, an image pickup apparatus is provided which outputs various images by performing calculation on data obtained by an image pickup element and performing a digital image process corresponding thereto. Ren Ng, et al., “Light Field Photography with A Hand-held Plenoptic CAMERA”, 2005 COMPUTER Science Technical Report CTSR, and Todor Georgiev, et al., “Superresolution with Plenoptic 2.0 CAMERA”, 2009 Optical Society OF America disclose an image pickup apparatus which simultaneously obtains two-dimensional intensity distribution of light in an object space and angle information of a light beam, that is, parallax information, using “Light Field Photography”. The two-dimensional intensity distribution of light and the angle information of a light beam are collectively called light field, and it is possible to obtain three-dimensional information of the object space by obtaining the light field. By performing a reconstruction process of an image using the obtained light field, it is possible to perform refocusing such as changing a focus position of an image, changing an imaging viewpoint, and adjusting a depth of field. 
     Meanwhile, the image pickup apparatus is required to have further high image quality according to advance of a display device. For high image quality, it is important to reduce noise of an image. Japanese Patent Laid-open No. H06-86332 discloses a method of reducing noise by combining images obtained through a plurality of image pickup optical systems. 
     However, in the noise reducing method disclosed in Japanese Patent Laid-Open No. H06-86332, pixels that image the same object are simply combined. In this case, when the noise follows Poisson distribution, N pixels are combined such that the noise is reduced by N −1/2  times by averaging. However, according to the advance of the display device, the image is required to have further high quality, and thus the noise reducing method disclosed in Japanese Patent Laid-Open No. H06-86332 is insufficient. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides an image processing apparatus, an image pickup apparatus, an image processing method, and an image processing program that effectively reduce noise of an image obtained by combining parallax images. 
     An image processing apparatus as one aspect of the present invention is capable of generating a plurality of output images having different focus positions by reconstructing an input image, includes a storage unit configured to store image pickup condition information of the input image, and an image processing unit configured to generate the output image from the input image using the image pickup condition information, and the image processing unit is configured to obtain the input image that is information of an object space viewed from a plurality of viewpoints that is obtained via an imaging optical system and an image pickup element having a plurality of pixels, calculate an average pixel value of a pixel group of the input image of the same region of the object space, and substitute each pixel value of the pixel group by the average pixel value, and perform combination such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image. 
     An image pickup apparatus as another aspect of the present invention is capable of generating a plurality of output images having different focus positions by reconstructing an input image, includes an imaging optical system, an image pickup element including a plurality of pixels, a lens array configured to cause a light beam from the same position of an object plane to enter pixels of the image pickup element different from each other in accordance with a pupil region of the imaging optical system through which the light beam passes, and an image processing unit configured to generate the output image from the input image obtained by the image pickup element, and the image processing unit is configured to obtain the input image that is information of an object space viewed from a plurality of viewpoints that is obtained via the imaging optical system, the image pickup element, and the lens array, calculate an average pixel value of a pixel group of the input image of the same region of the object space, and substitute each pixel value of the pixel group by the average pixel value, and perform combination such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image. 
     An image pickup apparatus as another aspect of the present invention is capable of generating a plurality of output images having different focus positions by reconstructing an input image, includes an imaging optical system including a plurality of optical systems having a positive refractive power, at least one image pickup element including a plurality of pixels, and an image processing unit configured to generate the output image from the input image obtained by the image pickup element, when a pupil of the imaging optical system is a pupil formed by combining pupils of the plurality of optical systems, the plurality of optical systems are arranged such that a light beam from the same position of an object plane enters pixels of the image pickup element different from each other in accordance with the a pupil region of the imaging optical system through which the light beam passes, and the image processing unit is configured to obtain the input image that is information of an object space viewed from a plurality of viewpoints that is obtained via the imaging optical system and the image pickup element, calculate an average pixel value of a pixel group of the input image of the same region of the object space, and substitute each pixel value of the pixel group by the average pixel value, and perform combination such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image. 
     An image processing method as another aspect of the present invention is capable of generating a plurality of output images having different focus positions by reconstructing an input image, the method includes the steps of obtaining the input image that is information of an object space viewed from a plurality of viewpoints that is obtained via an imaging optical system and an image pickup element having a plurality of pixels, calculating an average pixel value of a pixel group of the input image of the same region of the object space, and substituting each pixel value of the pixel group by the average pixel value, and performing combination such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image. 
     A non-transitory computer-readable storage medium as another aspect of the present invention stores an image processing program capable of generating a plurality of output images having different focus positions by reconstructing an input image, the image processing program being configured to cause an information processing apparatus to execute the steps of obtaining the input image that is information of an object space viewed from a plurality of viewpoints that is obtained via an imaging optical system and an image pickup element having a plurality of pixels, calculating an average pixel value of a pixel group of the input image of the same region of the object space, and substituting each pixel value of the pixel group by the average pixel value, and performing combination such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image. 
     Further features and aspects of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic configuration diagram of an image pickup optical system in Embodiment 1. 
         FIG. 2  is a schematic configuration diagram of an image pickup optical system in Embodiment 2. 
         FIG. 3  is a schematic configuration diagram of an image pickup optical system in Embodiment 2. 
         FIG. 4  is a schematic configuration diagram of an image pickup optical system in Embodiment 3. 
         FIG. 5  is a block diagram of an image pickup apparatus in Embodiment 1. 
         FIG. 6  is a cross-sectional view of an image pickup optical system in Embodiment 1. 
         FIGS. 7A and 7B  are diagrams illustrating refocus image generation in Embodiment 1. 
         FIG. 8  is a diagram illustrating refocus range in Embodiment 1. 
         FIG. 9  is a diagram illustrating a relation of an image pickup optical system and an object distance in Embodiment 1. 
         FIG. 10  is a diagram illustrating a relation of an image pickup element and a lens array in Embodiment 1. 
         FIG. 11  is a diagram illustrating an example of an imaging scene in Embodiment 1. 
         FIGS. 12A to 12D  are diagrams illustrating examples of parallax images in Embodiment 1. 
         FIGS. 13A and 13B  are diagrams illustrating examples of refocus images in Embodiment 1. 
         FIG. 14  is a flowchart of an image processing method in Embodiment 1. 
         FIG. 15  is a block diagram of an image processing system in Embodiment 2. 
         FIG. 16  is a cross-sectional view of an image pickup optical system in Embodiment 2. 
         FIGS. 17A and 17B  are diagrams illustrating refocus image generation in Embodiment 2. 
         FIG. 18  is a diagram illustrating a refocus range in Embodiment 2. 
         FIG. 19  is a block diagram of an image pickup apparatus in Embodiment 3. 
         FIG. 20  is a schematic configuration diagram of an image pickup optical system in Embodiment 3. 
         FIG. 21  is a cross-sectional view of an optical system in Embodiment 3. 
         FIGS. 22A and 22B  are diagrams illustrating refocus image generation in Embodiment 3. 
         FIG. 23  is a diagram illustrating a refocus range in Embodiment 3. 
         FIG. 24  is a flowchart of an image processing method in each of Embodiments 2 and 3. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Exemplary embodiments of the present invention will be described below with reference to the accompanied drawings. In each of the drawings, the same elements will be denoted by the same reference numerals and a duplicate description will be omitted. 
     An image processing method of the embodiment is capable of generating a plurality of output images having different focus positions by reconstructing an input image. The input image is an image (a parallax image) imaging an object space from different viewpoints to obtain a light field, and is obtained by the following image pickup apparatus. That is, the image pickup apparatus is configured to obtain the light field by arranging a plurality of optical systems having a positive refractive power or by disposing a lens array on an image side of an imaging optical system. 
       FIGS. 1 to 4  are examples of an image pickup optical system constituting such an image pickup apparatus. The image pickup optical system is configured to include an imaging optical system and an image pickup element. When a lens array is provided, the image pickup optical system is configured to include the lens array. In addition, as a method of obtaining another light field, a method of performing imaging many times while changing a position of an image pickup apparatus using the image pickup apparatus of obtaining two-dimensional intensity distribution of light of an object space is conceivable. In this case, the light field (the parallax image) is obtained by imaging an object space at times different from each other. For this reason, when a moving object is present in the object space, it is difficult to obtain correct information (parallax information). Accordingly, as illustrated in  FIGS. 1 to 4 , it is preferable that the image pickup optical system have a configuration capable of simultaneously obtaining parallax images (a plurality of parallax images). 
     A person or an object may not be necessarily present on an object plane  201  illustrated in  FIGS. 1 to 4 . This is because it is possible to focus on a person and an object present behind or in front of the object plane  201  after the imaging by a reconstruction process. In addition, for convenience, description of the following embodiments is performed using a one-dimensional system, but the same discussion is achieved about a two-dimensional system. 
     Embodiment 1 
     First, a configuration of an image pickup apparatus in Embodiment 1 of the invention will be described with reference to  FIG. 5 .  FIG. 5  is a block diagram of the image pickup apparatus of the embodiment. An image processing method of the embodiment is performed by an image processing unit  105  of the image pickup apparatus. 
     An image pickup element  103  is a two-dimensional image pickup element such as CCD (Charge Coupled DEVICE) or CMOS (Complementary Metal-Oxide Semiconductor), and is provided with a plurality of pixels. Energy of a light beam entering the image pickup element  103  via an imaging optical system  101  (a main lens unit) and a lens array  102  becomes an electric signal (an analog signal), and is converted into a digital signal by an A/D converter  104 . The digital signal is subjected to a predetermined process in the image processing unit  105 , and is stored in an image recording medium  110  such as a semiconductor memory in a predetermined format. In this case, image pickup condition information of the image pickup apparatus obtained from a state detecting unit  108  is also stored. The image pickup condition information is an imaging distance, an aperture, a focal length in a zoom lens, and the like. The state detecting unit  108  may directly obtain the image pickup condition information from a system controller  111 , and may obtain information about the image pickup optical system from an optical system controller  107 . 
     When the image stored in the image recording medium  110  is displayed on a display unit  106 , a reconstruction process is performed based on the image pickup condition information by the image processing unit  105 . As a result, an image reconstructed at a desired viewpoint, at a focus position, and in a depth of field is displayed on the display unit  106 . In addition, for a high speed, desired image settings (a viewpoint, a focus, and a depth of field) may be stored in a storage unit  109  in advance, and a reconstructed image may be directly displayed on the display unit  106  without the image recording medium  110 . In addition, the image recorded in the image recording medium  110  may be an image after reconstruction. A series of controls described above is performed by the system controller  111 , and mechanical driving of the image pickup optical system is performed by the optical system controller  107  by an instruction of the system controller  111 . 
     Next, a configuration of the image pickup optical system in the embodiment will be described with reference to  FIGS. 1 and 6 .  FIG. 1  is a schematic configuration diagram of the image pickup optical system.  FIG. 6  is a cross-sectional view of the image pickup optical system. The image pickup optical system is configured to include the imaging optical system  101 , the lens array  102 , and the image pickup element  103 . In the embodiment, the lens array  102  is configured using a plurality of lenses (small lenses), and the small lenses are configured by solid lenses. However, the embodiment is not limited thereto, and the lens array  102  may be configured using a liquid lens, a liquid crystal lens, or a diffraction optical element. Surfaces of both sides of the small lenses constituting the lens array  102  have a convex shape. However, the embodiment is not limited thereto, and a surface of one side may be a flat surface and a surface of the other side may have a convex shape. 
     The lens array  102  is disposed on an image-side conjugate plane with respect to the object plane  201  of the imaging optical system  101 . In addition, the lens array  102  is configured such that an exit pupil of the imaging optical system  101  and the image pickup element  103  are substantially in a conjugate relation. A light beam from the same position on the object plane  201  passes through the imaging optical system  101  and the lens array  102 , and then enters pixels of the image pickup element  103  different from each other according to a position and an angle of the light beam on the object plane  201 , to obtain a light field. Here, the lens array  102  serves to prevent the light beam passing through different positions on the object plane  201  from entering the same pixel. As a result, in the image pickup element  103 , an image in which the pixel groups obtained by imaging the same region on the object plane  201  from a plurality of viewpoints are arranged is obtained. In the configuration illustrated in  FIG. 1 , the same position on the object plane  201  is imaged by three pixels (nine pixels on two dimensions). For this reason, in the image pickup optical system of the embodiment, two-dimensional space resolution is reduced by 1/9 in the image pickup optical system which obtains only two-dimensional intensity distribution of light. This is qualitatively the same even when the number of pixels imaging the same position on the object plane  201  is changed. 
     In addition, it is preferable that a surface of an image side (the image pickup element  103  side) of the small lenses constituting the lens array  102  have a convex shape. Accordingly, astigmatism of the lens array  102  is reduced, and an image obtained on the image pickup element  103  becomes sharp. On the contrary, when the surface of the image side is not the convex shape, the astigmatism is increased, and a peripheral portion of an image formed by each small lens is blurred. When the image-blurred portion is used in the reconstruction process, it is difficult to obtain a sharp reconstructed image. In addition, it is further preferable that a surface of an object side (the imaging optical system  101  side) of the small lens have a flat or convex shape. Accordingly, a curvature of the small lens becomes low, aberration is reduced, and it is possible to further improve sharpness of the image. 
     Subsequently, refocus processing in the embodiment will be described. The refocus processing is described in “Fourier Slice Photography” (Ren Ng, 2005 ACM Trans. Graph. 24, 735-744), and thus will be briefly described herein. An example of a method of generating a refocus image will be described with reference to  FIG. 7 .  FIGS. 7A and 7B  are diagrams specifically illustrating a part of the lens array  102  and the image pickup element  103  in the image pickup optical system illustrated in  FIG. 1 . A chain line in  FIGS. 7A and 7B  is obtained by extending a center of each pixel and a path of a light beam passing through an image-side principal point of the small lens corresponding to the pixel. A virtual imaging plane  203  is an image-side conjugate plane of the imaging optical system  101  with respect to the object-side plane to be focused by refocus. However, in the embodiment, when the image-side conjugate plane is positioned closer to the image side than an object-side principal plane of the lens array  102 , a plane obtained by moving the image-side conjugate plane to the image side by a principal plane distance of the lens array  102  is the virtual imaging plane  203 . A pixel value obtained by the image pickup element  103  is moved in parallel to the virtual imaging plane  203  along a chain line and is combined, and thus it is possible to generate a refocus image at a desired focus position. 
     For example, in order to generate an image focused on the object plane  201  of  FIG. 1 , as illustrated in  FIG. 7B , the virtual imaging plane  203  may be set on a conjugate plane, that is, the principal plane (the image-side principal plane) of the lens array  102  through the object plane  201  and the imaging optical system  101 . In  FIGS. 7A and 7B , the pixel moved in parallel at the time of generating the refocus image is represented by a broken line, and is illustrated by sliding without overlapping to be easily seen. As illustrated in  FIGS. 7A and 7B , at the time of generating an arbitrary refocus image, when the pupil region of the imaging optical system  101  through which light flux entering the pixel passes is the same, it is understood that such a pixel has the same parallel movement amount. Accordingly, an operation of the pixel at the time of generating the refocus image is determined depending on the pupil region of the imaging optical system  101  through which the light flux entering the pixel passes. 
     Next, a refocusable range will be described. Since an opening size of the imaging optical system  101  is finite, an angle component of the light field obtained by the image pickup element  103 , that is, parallax information is also finite. Accordingly, the refocusable range is limited to a finite range. Here, two-dimensional intensity distribution of light is called a space component of the light field. In this case, the refocus range is determined by a sampling pitch Δy of the space component and a sampling pitch Δu of the angle component, and a coefficient α ±  thereof is given as the following Expression (1). 
     
       
         
           
             
               
                 
                   
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                     1 
                     
                       1 
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                         Δ 
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                           y 
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                           Δ 
                         
                         ⁢ 
                         
                             
                         
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                         u 
                       
                     
                   
                 
               
               
                 
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     The refocus range α + s 2  to α − s 2  of the image side represented by Expression (1) and the range conjugate with respect to the imaging optical system  101  are the refocus range of the object side. Here, s 2  is a distance between the image-side principal plane of the imaging optical system  101  and the image-side conjugate plane of the imaging optical system  101  with respect to the object plane  201 . 
       FIG. 8  is a diagram of a refocus range. In a configuration example illustrated in  FIG. 8 , a one-dimensional cycle of the lens array  102  is three pixels, and thus the sampling pitch Δy of the space component is three times the pixel pitch Δu of the image pickup element  103 . The sampling pitch of the angle component is ⅓ of an exit pupil diameter since the exit pupil of the imaging optical system  101  is divided into three (divided into nine on two dimensions). When it is over the refocus range represented by Expression (1), information is insufficient in the obtained light field, and it is difficult to generate a correct refocus image. Expression (1) may be approximated as the following Expression (2) since a pixel pitch Δ of the image pickup element  103  is sufficiently smaller than an exit pupil distance P of the imaging optical system  101 .
 
α ±   s   2   =s   2   ∓NFΔy=s   2   ∓NFΔ   LA   (2)
 
     Here, the exit pupil distance P of the imaging optical system  101  is a distance between the exit pupil plane of the imaging optical system  101  and the image-side conjugate plane of the imaging optical system  101  with respect to the object plane  201 . In addition, N is the number of one-dimensional divisions of the pupil of the imaging optical system  101 , and F is an F number of the imaging optical system  101 , and Δ LA  is a pitch of the lens array  102 . When the pixel group corresponding to any small lens is moved in parallel along a chain line of  FIG. 7 , it is over the maximum refocus amount of Expression (2), the distance of the pixels becomes larger than Δy, and a region with lacked information occurs. In this case, it is difficult to generate the correct refocus image. 
     Next, a noise reducing process (an image processing method) in the embodiment will be described. First, a noise reducing effect according to the conventional reconstruction method will be described. For easily understanding, the number of one-dimensional pupil divisions of the imaging optical system  101  is two in the configuration of  FIG. 1 , and a case of a configuration illustrated in  FIG. 9  is considered.  FIG. 9  is a relational diagram between the image pickup optical system and the object distance in the embodiment. However, the following discussion is not limited thereto. 
       FIG. 10  is a relational diagram between the image pickup element  103  of  FIG. 9  and (the pitch of) the lens array  102 . In  FIG. 10 , a rectangle represented by a solid line represents a pixel of the image pickup element  103 . In addition, a distance between centers of two most adjacent circles (two adjacent circles) represents a pitch of the lens array  102 . Here, a circle represented by a broken line represents a region which a light beam passing through one small lens enters. This region is represented by a circular shape in  FIG. 10 , but is changed according to a pupil shape of the imaging optical system  101 . In the configuration of  FIG. 9 , the number of pupil divisions is two-dimensionally four, and thus the number of pixels corresponding to one small lens is four as illustrated in  FIG. 10 . In this case, when only the pixels at the same position with respect to the center of each circle are extracted, it is possible to obtain an image imaged from the same viewpoint. In addition, in  FIG. 10 , a region outside the circle drawn by a broken line is a region which a light beam does not enter, and is called a dead zone. 
     Here, in the configuration of  FIG. 9 , a case of imaging an object space illustrated in  FIG. 11  is considered.  FIG. 11  is a diagram illustrating an example of an imaging scene in the embodiment. In the object space illustrated in  FIG. 11 , an object A is positioned on the object plane  201 , an object B is positioned far away therefrom, and an object C is positioned farther away. A chain line in  FIG. 11  represents an angle of view of the image pickup apparatus  10  in a horizontal direction. 
       FIGS. 12A to 12D  are diagrams illustrating an example of the parallax image in the embodiment, and illustrates an image obtained by extracting a pixel corresponding to each viewpoint from the image obtained from the image pickup element  103 .  FIGS. 12A to 12D  are images as viewing the object space from each region of the pupil of the imaging optical system  101  divided into four. Here, the image of each viewpoint is configured by 18×12 pixels, but the number of pixels is not limited thereto. As known from  FIG. 9 , since an object point on the object plane  201  is imaged at the same position of the lens array  102  without depending on the viewpoint, the parallax does not occur. For this reason, the object A is imaged at the same position of  FIGS. 12A to 12D . Meanwhile, parallax occurs for the object B present at another object distance. For this reason, as illustrated in  FIGS. 12A to 12D , the object B is imaged at each shifted position. 
       FIGS. 13A and 13B  are diagrams illustrating an example of the refocus image in the embodiment. When the images of  FIGS. 12A to 12D  are combined to completely overlap the object A, the refocus image focused on the object plane  201  is generated as illustrated in  FIG. 13A . In this case, the object positioned other than the object plane  201  is combined to be shifted, and thus is blurred similarly to the object B of  FIG. 13A . The size of the blurring corresponds to the F number of the imaging optical system  101 . A method of generating the refocus image illustrated in  FIG. 13A  corresponds to  FIG. 7B . 
     The object A illustrated in  FIG. 13A  is obtained by combining four images. For this reason, when it is assumed that a noise component of the image follows Poisson distribution, the noise is reduced by ½ by averaging. In addition, the object B is blurred, that is, resolution is lowered, and thus the noise is reduced. The reducing of the resolution corresponds to sampling at a pitch larger than a pitch of a pixel of an image. For example, when the image of the pixel pitch Δ is sampled by a pitch 2Δ, the resolution is lowered, but the noise is reduced by ½. By the refocus of the object B or the like, the blurring region reduces the noise corresponding thereto. Accordingly, in the combined image of  FIG. 13A , the noise is further reduced than the images illustrated in  FIGS. 12A to 12D . The noise reducing effect is obtained similarly even in the refocused image in addition to the object plane  201 . For example, when  FIGS. 12A to 12D  are combined to overlap the object B, it is possible to obtain the image illustrated in  FIG. 13B . In this case, the noise of the object B is reduced by about ½ by averaging, the object A is blurred (the resolution is lowered), and the noise is reduced. 
     Next, the noise reducing process of the embodiment will be described. Here, it is assumed that a surface of an object present in the object space is a uniform diffusion surface. Each of the pixels of a region surrounded by the broken lines of  FIGS. 12A to 12D  images the same region of the object space. An edge portion of the object A is excluded because the edge portion is likely to be influenced by a background having parallax. However, when the edge portion is rarely influenced, the edge portion may be included in the region. 
     Here, since the object is the uniform diffusion surface, the signal value of each pixel has the same value when excluding the noise component. For example, four pixels with diagonal lines in  FIGS. 12A to 12D  image the same region of the object space, and thus has the same signal value when excluding the noise. For this reason, an average pixel value of four pixels is obtained, and the pixel value of the original diagonal line portion is substituted by the average pixel value. This is performed on all the pixels covered with the broken line, and thus the noise component of the region covered with the broken line of  FIGS. 12A to 12D  is reduced by about ½. 
     Here, the average pixel value may be a value obtained by averaging the pixel values by the same weight, and may be a value calculated by different weights. In the case of the latter, a method is conceivable in which the average pixel value is calculated first by the uniform weight, and the weight of the pixel close to the average pixel value in the original pixel values is increased. Next, the images of  FIGS. 12A  to  12 D in which the noise of the broken line portion is reduced are combined to generate an output image. In this case, when the parallax image is combined to completely overlap the broken line portion, that is, is refocused on the object plane  201 , it is the same as the conventional reconstruction as a result, and it is difficult to obtain the noise reducing effect more than that. However, when an image refocused other than the object plane  201  is generated, the pixel in which the noise is reduced by substitution by the average pixel value is combined with the pixel having the more different pixel value, and thus the noise is further reduced. Accordingly, for example, in the image refocused on the object B as illustrated in  FIG. 13B , the noise in the vicinity of the blurred object A is reduced more than that of the case of using the conventional reconstruction method. In the conventional refocus processing, the noise of the region focused by the refocus is reduced by averaging of a plurality of pixels in which only the noise components are different. Then, in the region blurred by the refocus, the resolution of the region is lowered as compared with each parallax image, and the noise is reduced. However, in the noise reducing method of the embodiment, substitution by the average pixel value is performed in the region blurred by the refocus in addition to the conventional refocus processing. That is, in the region, the averaging of the pixels in which only the noises are different is performed in addition to the lowering of the resolution, and thus it is possible to further obtain the noise reducing effect. 
     Since the description hitherto is made in connection with a case in which the pixel substituted by the average pixel value is limited to the pixel imaging the object plane  201 , for the simplification. However, the pixel may be pixels which image at different distances on the object space as long as the pixel images the same region of the object space.  FIG. 9  is a diagram in which the pixels  1031  to  1034  are projected to the object space through the lens array  102  and the imaging optical system  101 . From  FIG. 9 , it is understood that the pixel  1031  and the pixel  1034  image the same region at the object distance  204   a . Similarly, the pixel  1032  and the pixel  1033  image the same region at the object distance  204   b.    
     When the object present at such an object distance is imaged, the pixels imaging the object have the same signal value except for the noise. For this reason, by calculating and substituting the average pixel value, it is possible to obtain the noise reducing effect described above. In this case, when the pixels substituted by the same average pixel value are combined to completely overlap, it is difficult to obtain the improved noise reducing effect as described above. For this reason, the combining of the parallax images is performed such that the pixels substituted by the same average pixel value does not coincide, and thus it is possible to always improve the noise reducing effect as compared with the convention method. 
     More preferably, the shift amount of the combined pixels to each other is non-integral multiple of the pixel pitch. This corresponds to that the parallax images are combined to be shifted by a unit of sub-pixels to each other. Accordingly, in addition to the noise reducing effect, it is possible to achieve high resolution based on super-resolution by pixel shift. 
     In the case of  FIG. 1 , a pixel imaging constantly the same region is present on the object plane  201 . Meanwhile, in the configuration of  FIGS. 2 to 4 , the pixel imaging the same region is not necessarily present. However, similarly, even in the configuration of  FIGS. 2 to 4 , it is possible to obtain the pixel imaging the same region and the object distance thereof by projecting the pixel to the object space. 
     In addition, it is not necessary that the pixel substituted by the average pixel value necessarily image completely the same region. Light intensity distribution of an object space is continuous except for an edge portion of the object. That is, when the regions imaged by the pixels substantially coincide with each other except for the edge portion, it can be considered that such pixel values are substantially the same except for noise. For example, when two pixels projected to the object space are overlapped with each other more than a half of the region of the projection pixel, the pixels may be considered as the pixels imaging substantially the same region. For this reason, when two pixels do not image the edge portion of the object, the average pixel value may be calculated and the pixel value may be substituted. 
     Next, an image processing method of generating an output image from an input image will be described with reference to  FIG. 14 .  FIG. 14  is a flowchart of the image processing method of generating the output image from the input image. In  FIG. 14 , Steps S 102  and S 103  correspond to the substitution process, and Step S 106  corresponds to a combining process. In addition, the steps of  FIG. 14  are performed by the image processing unit  105  based on an instruction of the system controller  111 . 
     First, in Step S 101 , the image processing unit  105  obtains an input image obtained (imaged) through the image pickup optical system illustrated in  FIG. 6 . A method of reserving the light field included in the input image is changed according to the configuration of the image pickup optical system. However, in the embodiment, the pixel groups obtained by imaging the same region on the object plane  201  from a plurality of viewpoints are arranged in the image. In addition, the input image may be an image imaged by the same image pickup optical system stored in the image recording medium  110 . 
     Subsequently, in Step S 102 , the image processing unit  105  extracts pixels imaging the same region of the object space from the input image. Such pixel extraction is performed, for example, using the following method. From the configuration of the image pickup apparatus recorded in the input image, as illustrated in  FIG. 9 , when the pixel is projected to the object space, it is possible to calculate an object distance in which different pixels are overlapped with each other and the overlapped pixels. In addition, it is possible to calculate a distance of the object space from parallax information of the input image. For this reason, by combining them, it is possible to obtain pixels to be extracted from the input image. In addition, there is a method of, first, generating an image of each viewpoint, obtaining a correspondence point of each image by using a block matching method or the like, and extracting the pixel by assuming that the same region is imaged when a difference of the pixel values of the corresponding pixels is equal to or less than a predetermined threshold value. 
     Then, in step S 103 , the image processing unit  105  calculates the average pixel value of the extracted pixel, and substitutes the pixel value of each extracted pixel by the average pixel value. Subsequently, in Step S 104 , the image processing unit  105  designates conditions of the output image. Here, the conditions of the output image are a focus position of the output image, a size of blurring, a viewpoint, a brightness, an image size, and the like, but are not limited thereto. In addition, among the plurality of conditions, the user designates only a predetermined condition, prescribed values of the other conditions are preset, and the prescribed values may be used. 
     Then, in Step S 105 , when the output image is generated under the designated condition, the image processing unit  105  determines whether the pixels (the pixel group) substituted by the same average pixel value are combined without coinciding with each other, that is, whether the substituted pixels are combined to be shifted from each other. When the substituted pixels do not coincide, that is, when the substituted pixels are combined to shift, it is possible to obtain the noise reducing effect by the substitution of the average pixel value, and thus process proceeds to Step S 106 . Meanwhile, when the substituted pixels coincide, the process proceeds to Step S 107 . As the determination method, for example, there is a method in which a condition that the pixels substituted by the same average pixel value coincide at the time of combining is calculated from information about the configuration of the image pickup optical system, and is compared with a designated condition. In addition, a condition for coinciding may be calculated in advance, and the condition may not be designated in Step S 104 . In this case, Steps S 105  and S 107  are unnecessary. 
     In Step S 105 , when the substituted pixels do not coincide, the image processing unit  105  combines the parallax images (the input images) to generate the output image in Step S 106 . At the time of combining the parallax images, as described above, the same operation (parallel movement or the like) is performed on the pixel of the input image corresponding to the pixel of the image pickup element  103  which the light beam passing through the same pupil region of the imaging optical system  101  enters. In this case, the pixels of the parallax images may be combined by different weights using the distance information of the object space. By setting appropriate weight to each pixel, aliasing is reduced, and it is possible to obtain a high-quality output image. 
     In Step S 105 , when the substituted pixels coincide, the image processing unit  105  changes the condition of the output image to obtain the noise reducing effect by the substitution of the average pixel value in Step S 107 . In this case, when the condition of the output image is drastically changed from the condition of the output image designated in Step S 104 , the output image is drastically separated from the designated condition. For this reason, when the focus position designated in Step S 104  is the first focus position and the focus position of the generated output image is the second focus position, it is preferable that a difference between the first focus position and the second focus position is within the range of the depth of focus of the imaging optical system  101 . That is, when the first focus position is designated, it is preferable that the image processing unit  105  generates the output image focused on the second focus position in which the difference from the first focus position is within the range of the depth of focus of the imaging optical system  101 . Accordingly, the output image becomes close to the condition of the output image designated by the user. 
     The depth of focus of the imaging optical system  101  is represented approximately by ±Fε when a diameter of a permissible confusion circle is ε and an F number of the imaging optical system  101  is F. Here, the diameter ε is a value determined according to performance necessary for the image pickup apparatus. As a method of determining the diameter ε, there is a method of setting a difference between a width of a point image in the depth of focus and a width of a point image at the focus position to a range imperceptible for the user. For example, the diameter is given about five times the pixel pitch of the image pickup element  103 . In addition, at the first focus position, when the pixels substituted by the same average pixel value do not coincide at the time of combining, the first focus position and the second focus position may not be the same as each other. 
     In addition, as necessary, another noise reducing process may be used together. For example, when a change amount of pixel values of adjacent pixels is small, a coring process of removing the small amount as noise, a bilateral filter, or a median filter may be used. Such a noise reducing process may be performed on the image of each viewpoint, or may be performed on the output image after combining. 
     As described above, the image processing unit  105  obtains the input image that is the information of the object space viewed from the plurality of viewpoints and that is obtained via the imaging optical system  101  and the image pickup element  103  having the plurality of pixels (Step S 101 ). In addition, the image processing unit  105  calculates the average pixel value of the pixel group of the input image (the image pickup element  103 ) of the same region of the object space, and substitutes each pixel value of the pixel group by the average pixel value (Steps S 102  and S 103 ). The image processing unit  105  performs combining such that the pixels of the pixel group substituted by the average pixel value are shifted from each other to generate the output image (Step S 106 ). 
     According to the embodiment, it is possible to provide the image processing apparatus, the image pickup apparatus, the image processing method, and the image processing program to effectively reduce the noise of the image obtained by combining the parallax images. 
     Embodiment 2 
     Next, Embodiment 2 of the invention will be described. In the embodiment, an image processing apparatus (an image processing system) embodying the image processing method described above will be described.  FIG. 15  is a block diagram of the image processing system of the embodiment. As illustrated in  FIG. 15 , the image processing system includes an image pickup apparatus  301 . The image pickup apparatus  301  has an image pickup optical system having the configuration of  FIG. 2 . The lens array  102  of  FIG. 2  is disposed such that the image-side conjugate plane  202  of the imaging optical system  101  with respect to the object plane  201  and the image pickup element  103  are conjugate to each other. 
     The image processing apparatus  302  is a computer apparatus (an information processing apparatus) performing the image reconstruction described above. The image processing apparatus  302  includes a storage unit  307  that stores image pickup condition information (information about a configuration of the image pickup optical system and distance information of an input image) of the input image obtained by the image pickup apparatus  301 . The image pickup condition information stored in the storage unit  307  is used for generation (a substitution process and a combining process) of the output image. The image processing apparatus  302  performs a noise reducing process and a predetermined reconstruction process on the input image, and outputs the process result (the output image) to any one or a plurality of an output device  305 , a display device  304 , and a recording medium  303 . As described above, the image processing apparatus  302  is an image processing unit that generates the output image from the input image using the image pickup condition information. 
     The recording medium  303  is, for example, a semiconductor memory, a hard disk, or a server on a network. The display device  304  is, for example, a liquid crystal display or a projector. The output device  305  is, for example, a printer. The display device  304  is connected to the image processing apparatus  302 , and the reconstructed image is input to the display device  304 . The user can perform work while confirming the image reconstructed through the display device  304 . An image processing software  306  (an image processing program) performs the noise reducing process described above and the reconstruction process (the image processing method), and performs a development process or the other image process as necessary. 
     However, the embodiment is not limited thereto. For example, the image processing software  306  (the image processing program) having the function of the embodiment may be provided (installed) to the image processing apparatus  302  or the like through a network or various recording mediums  308  such as a CD-ROM. In this case, the image processing apparatus  302  reads the installed image processing program, and causes a computer (the information processing apparatus) such as a CPU or an MPU in the image processing apparatus  302  to perform the image process of the embodiment. 
       FIG. 16  is a cross-sectional view of the image pickup optical system in the embodiment. In  FIG. 16 , the imaging optical system  101  is a zoom lens. In the small lens constituting the lens array  102 , an object-side surface is flat and an image-side surface has a convex shape, and an image is formed on the image pickup element  103  by viewing an image formed by the imaging optical system  101  as an imaginary object. The imaging optical system  101  includes, in order from the object side, a first lens unit L 1  having a positive refractive power, a second lens unit L 2  having a positive refractive power, a third lens unit L 3  having a negative refractive power, a fourth lens unit L 4  having a positive refractive power, and a fifth lens unit L 5  having a positive refractive power. At the timing of zooming, the first lens unit L 1  and the fifth lens unit L 5  are fixed, and the second lens unit L 2 , the third lens unit L 3 , and the fourth lens unit L 4  are moved on an optical axis. 
     The lens array  102  is disposed on the image-side conjugate plane of the imaging optical system  101  with respect to the object plane  201 . In addition, the lens array  102  is configured such that the exit pupil of the imaging optical system  101  and the image pickup element  103  are substantially in the conjugate relation. Here, generally, the conjugate relation is meaning not only indicating a strict conjugate relation but also including a relation evaluated substantially as the conjugate relation (in short, the conjugate relation). The light beam from the object plane  201  enters a plurality of pixels of the image pickup element  103  different from each other according to the position and the angle on the object plane  201  of the light beam through the imaging optical system  101  and the lens array  102 . By such a configuration, a light field is obtained. In the configurations of  FIGS. 2 and 3 , it is possible to obtain an image in which a plurality of small images with a different imaging viewpoint and imaging range by the image pickup element  103 . 
     The configuration of the image pickup optical system of  FIG. 3  is the same as the configuration of the image pickup optical system illustrated in  FIG. 2  except that the lens array  102  is disposed further to image side than the image-side conjugate plane  202 . A different from the configuration of  FIG. 2  is that the lens array  102  reimages on the image pickup element  103  by viewing the formed image of the imaging optical system  101  as an actual object. However, all the configurations of the image pickup optical systems illustrated in  FIGS. 2 and 3  are essentially the same since the lens array  102  views the image formed by the imaging optical system  101 , as an object, and the image is imaged on the image pickup element  103 . Accordingly, the following discussion is achieved similarly even with respect to the configuration of  FIG. 3 . 
     Next, a method of generating a refocus image in the embodiment will be described with reference to  FIGS. 17A and 17B .  FIGS. 17A and 17B  are specific diagrams of a part of the lens array  102  and the image pickup element  103  in the configuration of the image pickup optical system illustrated in  FIG. 2 . In the embodiment, the lens array  102  is configured by a small lens in which an object-side surface is flat and an image-side surface has a convex shape. However, similarly to Embodiment 1, the shape of the lens array  102  is not limited thereto. 
     Chain lines in  FIGS. 17A and 17B  represent an angle of view of each small lens. The pixel values obtained by the image pickup element  103  are projected to a virtual imaging plane  203  and are combined through the small lens corresponding to the pixel, and thus it is possible to generate a refocus image focused on the virtual imaging plane  203 . For example, in order to generate the image focused on the object plane  201  of  FIG. 2 , it is preferable to set the virtual imaging plane  203  to the image-side conjugate plane  202 . In  FIGS. 17A and 17B , the pixel projected at the time of generating the refocus image is represented by a broken line, and is illustrated to be shifted without overlapping to be easily understood. The generation of the refocus image may be a generating method of projecting the pixel described above, and a method of moving the pixels in parallel and combines the pixels to overlap the same pixel. In this case, when the regions of the lens array  102  through which the light beams entering the pixels pass are the same, the parallel movement amounts of such pixels are the same. As described above, the operation of the pixel at the time of generating the refocus image in the embodiment is determined according to the region of the lens array  102  through which the light beam entering the pixel passes. 
     Subsequently, a refocusable range will be described. The refocus range of the image pickup optical system in the embodiment is also represented by Expression (1) similarly to Embodiment 1. Relation thereof is as illustrated in  FIG. 18 .  FIG. 18  is a diagram of a refocus range in the embodiment. In the image pickup optical system of the embodiment, Δy=Δ|σ 1 /σ 2 | is satisfied. This is to reduce and image the image formed by the imaging optical system  101  by |σ 2 /σ 1  times on the image pickup element  103  by viewing the image as an imaginary object by the lens array  102 . Here, σ 1  is a distance (an interval) between the image-side conjugate plane  202  and the object-side principal plane of the lens array  102 , and σ 2  is a distance (an interval) between the image-side principal plane of the lens array  102  and the image pickup element  103 . σ 1  has a positive value when the image-side conjugate plane  202  is further to the object side than the object-side principal plane of the lens array  102 , and has a negative value when it is further to the image side. In addition, for Δu=P/(NF), Expression (1) may be rewritten as the following Expression (3) from Δ&lt;&lt;P.
 
α ±   s   2   =s   2   ∓NFΔy=s   2   ∓NFΔ|σ   1 /σ 2 |  (3)
 
     Here, Δ is a pixel pitch of the image pickup element  103 . When it is over the range of Expression (3) similarly to Embodiment 1, it is difficult to generate a correct refocus image. 
     Next, an image processing method of generating an output image from an input image in the embodiment will be described with reference to  FIG. 24 .  FIG. 24  is a flowchart of the image processing method of generating the output image from the input image in the embodiment. Concerning  FIG. 24 , the description about the same portion as that of  FIG. 14  is omitted. Each step of  FIG. 24  is performed by the image processing apparatus  302 . 
     First, in Step S 201 , the image processing apparatus  302  obtains an image in which a plurality of small images with different imaging viewpoints and imaging ranges are arranged, as the input image, from the image pickup apparatus  301  (the image pickup element  103 ). Subsequently, in Step S 202 , the image processing apparatus  302  extracts pixels imaging the same region of the object space from the input image. As the extracting method, in addition to the method described in Embodiment 1, a method of reading information of the pixels imaging the same region recorded in the image pickup apparatus  301  may be used. In addition, when the distance information of the object space is recorded in the image pickup apparatus  301 , the distance information may be read and used. Subsequently, Steps S 203  and S 204  are the same as Steps S 103  and S 104  of  FIG. 14 , respectively. 
     Then, in Step S 205 , when the output image is generated under the designated condition, the image processing apparatus  302  determines whether the shift amount (the pixel shift) of the combined pixel is non-integral multiple of the pixel pitch. Here, the method of generating the output image is determined based on the configuration of the image pickup apparatus  301  recorded in the input image. When the image pickup apparatus  301  has the image pickup optical system illustrated in  FIG. 1 , the method of generating the refocus image described in Embodiment 1 is used. In the embodiment, the image pickup apparatus  301  has the image pickup optical system illustrated in  FIG. 2 . For this reason, the method of generating the refocus image illustrated in  FIG. 17  or the like is used. 
     Here, as illustrated in  FIG. 17A , when the pixel shift amount is non-integral multiple of the pitch of the projection pixel, the process proceeds to Step S 206 . Meanwhile, as illustrated in  FIG. 17B , when the pixel shift amount is integral multiple of the pitch of the projection pixel, the process proceeds to Step S 207 . As the determination method, in addition to the method described in Embodiment 1, a method of reading the condition of overlapping the combined pixels recorded in the image pickup apparatus  301  and determining may be used. 
     In Step S 205 , when the pixel shift is non-integral multiple of the pixel pitch, the image processing apparatus  302  combines the parallax images to generate the output image in Step S 206 . At the time of combining the parallax images, as described above, the same operation is performed on the pixel of the input image corresponding to the pixel of the image pickup element  103  which the light beam passing through the same region of the lens array  102  enters. 
     As described above, the image processing apparatus  302  obtains the input image that is the information of the object space viewed from the plurality of viewpoints and that is obtained via the imaging optical system  101  and the image pickup element  103  having the plurality of pixels (Step S 201 ). In addition, the image processing apparatus  302  calculates the average pixel value of the pixel group of the input image (the image pickup element  103 ) of the same region of the object space, and substitutes each pixel value of the pixel group by the average pixel value (Steps S 202  and S 203 ). The image processing apparatus  302  performs combining such that the shift amount of the pixel of the pixel group substituted by the average pixel value may be the non-integral multiple of the pixel to generate the output image (Step S 206 ). 
     According to the embodiment, it is possible to provide the image processing apparatus, the image pickup apparatus, the image processing method, and the image processing program to effectively reduce the noise of the image obtained by combining the parallax images, and to have high resolution based on super-resolution by the pixel shift. 
     Embodiment 3 
     Next, Embodiment 3 of the invention will be described.  FIG. 19  is a block diagram of an image pickup apparatus of the embodiment.  FIG. 20  is a schematic configuration diagram of an image pickup optical system in the embodiment, and is a diagram as viewing an imaging optical system  101  from an object side. In  FIG. 19 , a light beam from an object space (not illustrated) enters the imaging optical system  101 . The imaging optical system  101  is configured to include a plurality of optical systems  101   a  to  101   g  having a positive refractive power as illustrated in  FIG. 20 . The imaging optical system  101  has a configuration with six-times symmetry when the optical axis of the optical system  101   b  is a rotation axis. However, the configuration of the imaging optical system  101  is not limited thereto, and the number or arrangement of optical systems may be appropriately modified. Image pickup elements  103   a  to  103   g  are arranged on image sides of the optical systems  101   a  to  101   g , respectively. However, it is not essential to include the plurality of image pickup elements  103   a  to  103   g  in the embodiment, a singular image pickup element may be provided when it is possible to receive images formed by the optical systems  101   a  to  101   g . For this reason, the image pickup apparatus of the embodiment may have at least one image pickup element. 
       FIG. 4  is a schematic diagram as viewing the image pickup optical system of the embodiment from a cross section including the optical axes of the optical systems  101   a  to  101   c . The beams of light refracted by the optical system  101   a  to  101   c  are received by the corresponding image pickup elements  103   a  to  103   c , respectively. The plurality of images obtained by the image pickup elements  103   a  to  103   c  are parallax images obtained by observing the object space from different viewpoints. By matching such a plurality of images, it is possible to obtain two-dimensional intensity distribution and angle information of light in the object space, that is, a light field. In the embodiment, such a plurality of parallax images become the input images. 
       FIG. 21  is a cross-sectional view of the optical system in the embodiment, and illustrates cross sections of the optical system  101   a  and the image pickup element  103   a . Since the same is applied to the other optical systems  101   b  to  101   g  and the image pickup elements  103   b  to  103   g , the description thereof is omitted. However, configurations of optical systems may be different from each other. The optical system  101   a  illustrated in  FIG. 21  is a single-focus lens. As illustrated in  FIG. 4 , the light beam from the object plane  201  enters the other optical system constituting the imaging optical system  101  in accordance with the position and the angle of the light beam on the object plane  201 , and is received by a different pixel of the image pickup element, and thus it is possible to obtain a light field. 
     Next, a method of generating a refocus image in the embodiment will be described.  FIG. 22  is a diagram about refocus image generation, and is a specific diagram of the configuration of  FIG. 4 . The combined object-side principal plane of  FIG. 22  is defined as a plane passing through each object-side principal point of the optical systems  101   a  to  101   g . Similarly, the combined image-side principal plane is a plane passing through each image-side principal point of the optical systems  101   a  to  101   g . In the configuration of the embodiment, the object-side principal plane and the image-side principal plane of the imaging optical system  101  are represented by the combined object-side principal plane and the combined image-side principal plane, respectively. A chain line of  FIG. 22  represents an angle of view of each optical system. 
     When the focus position of the image side is matched with the virtual imaging plane  203 , it is preferable that the pixel values obtained by the image pickup elements  103   a  to  103   g  are projected to the object-side refocus plane  204  through the optical systems  101   a  to  101   g  corresponding to the image pickup elements  103   a  to  103   g  and combined. The object-side refocus plane  204  is a plane conjugate to the virtual imaging plane  203  via the optical systems  101   a  to  101   g . By moving the virtual imaging plane  203 , it is possible to generate the refocus image focused on an arbitrary position. 
     For example, in order to generate the image focused on the object plane  201  of  FIG. 4 , it is preferable to set the virtual imaging plane  203  on the image pickup elements  103   a  to  103   g . In this case, the object plane  201  and the object-side refocus plane  204  coincide. In  FIG. 22 , the pixel projected at the time of generating the refocus image is represented by a broken line, and is illustrated to be shifted without overlapping to be easily understood. The generation of the refocus image may be a generating method of projecting the pixel described above, and a method of moving the pixels in parallel and combines the pixels to overlap the same pixel. In this case, when the optical systems through which the beams of light input to the pixels pass are the same, the parallel movement amounts of such pixels are the same. As described above, the operation of the pixel at the time of generating the refocus image in the embodiment is determined in accordance with to the optical system through which the light beam entering the pixel passes. 
     Subsequently, a refocusable range will be described. The refocus range of the image pickup optical system in the embodiment is also represented by Expression (1) similarly to Embodiment 1, and relation thereof is as illustrated in  FIG. 23 .  FIG. 23  is a diagram of a refocus range in the embodiment. 
     In the image pickup optical system of the embodiment, Δy=Δ and Δu=P syn /(NF syn ) are satisfied, and Expression (1) may be approximated as the following Expression (4) from Δ&lt;&lt;P syn .
 
α ±   s   2   =s   2   ∓NF   syn   Δy=s   2   ∓NF   syn Δ  (4)
 
     Here, F syn  and P syn  are an F number and an exit pupil distance calculated from a combined pupil of the imaging optical system  101  obtained by combining pupils of the optical systems  101   a  to  101   g . A method of combining the pupils of the optical systems  101   a  to  101   g  may be a combination opening method or the like. The broken line of  FIG. 20  and the combined exit pupil plane of  FIG. 23  represent a concept of the combined pupil formed by the optical systems  101   a  to  101   g . In the configuration of the embodiment, the pupil of the imaging optical system  101  is the combined pupil obtained by combining the plurality of optical systems  101   a  to  101   g . Accordingly, the light beam from the same position on the object plane  201  passes through different pupil regions in the imaging optical system  101  according to an angle. Here, N is the number of divisions of the combined pupil in one-dimensional direction. In addition, when it is over the range of Expression (4) similarly to Embodiment 1, it is difficult to generate a correct refocus image. In addition, in the embodiment, the depth of focus of the imaging optical system  101  is calculated based on the combined pupil obtained by combining the pupils of the plurality of optical systems  101   a  to  101   g.    
     The image processing method of generating the output image from the input image in the embodiment is performed by the image processing unit  105  according to the flowchart illustrated in  FIG. 24 . In addition, in the embodiment, the description about the same portion as that of Embodiment 2 is omitted. 
     First, in Step S 201 , the image processing unit  105  obtains a plurality of parallax images obtained by the image pickup elements  103   a  to  103   g , as the input images. However, when the plurality of parallax information are obtained by a singular image pickup element, the input image is an image obtained by one image pickup element. The subsequent Steps S 202  to S 204  are the same as those of Embodiment 2. 
     Then, in Step S 205 , when the output image is generated under the designated condition, the image processing unit  105  determines whether the shift amount (the pixel shift) of the combined pixel is non-integral multiple of the pixel pitch. As illustrated in  FIG. 22A , when the pixel shift is non-integral multiple of the pitch of the projection pixel, the process proceeds to Step S 206 . Meanwhile, as illustrated in  FIG. 22B , when the pixel shift is integral multiple of the pitch of the projection pixel, the process proceeds to Step S 207 . 
     In Step S 205 , when the pixel shift is non-integral multiple of the pixel pitch, the image processing unit  105  combines the parallax images to generate the output image in Step S 206 . At the time of combining the parallax images, the same operation is performed on the pixel of the input image corresponding to the pixel of the image pickup element  103  which the light beam passing through the same optical system enters. 
     According to the embodiment, it is possible to provide the image processing apparatus, the image pickup apparatus, the image processing method, and the image processing program to effectively reduce the noise of the image obtained by combining the parallax images, and to have high resolution based on super-resolution by the pixel shift. 
     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. 2012-200117, filed on Sep. 12, 2012, which is hereby incorporated by reference herein in its entirety.