Abstract:
A method of 3-dimensional structure estimation of the invention, making use of a plurality of stereo-pictures, repeats, for each pixel of a first picture, a step of extracting corresponding small regions ( 4 ) corresponding to the concerning pixel according to a depth estimation ( 68 ); a step of calculating a neighboring correspondence value for each of the corresponding small regions representing correspondence among neighboring corresponding small regions of picures taken by neighboring cameras; a step of obtaining a sum ( 61 ) of the neighboring correspondence values; and selecting a value of the depth estimation ( 68 ) which gives a singular value of the sum ( 61 ) representing correspondence among the corresponding small regions.

Description:
This application is a divisional of application Ser. No. 08/950,599, filed Oct. 15, 1997. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to a method of and an apparatus for 3-dimensional structure estimation which is used for obtaining 3-dimensional information of an object from 2-dimensional image data of the object, and more particularly to those based on triangular surveying making use of multiple sets of 2-dimensional image data of an object taken from multiple viewing positions. 
     There is a 3-dimensional structure estimation technique called stereo-method, which estimates 3-dimansional structure of an object based on the triangular surveying from multiple sets of 2-dimensional image data taken from multiple viewing positions. A conventional example of the stereo-method is described in a paper entitled “A Multiple-Baseline Stereo” by Okutomi et al, IEEE Transaction on Pattern Analysis and Machine Intelligence, pp. 353-363, Vol. 15, No. 4, April 1993. 
     First, principle of the stereo-method is described referring to a schematic diagram of FIG.  6 . 
     Suppose a first camera  10 - 1 , with a lens having a focal distance F, which is positioned on an X-Y plane, perpendicular to the sheet of FIG. 6, so that center of the lens is at coordinates (X 1 ,  0 ) and optical axis is perpendicular to the X-Y plane, and a second camera  10 - 2 , with its lens having the same focal distance F, which is positioned parallel to the first camera  10 - 1  so that center of its lens is at coordinates (X 2 ,  0 ). 
     Defining the coordinates (X 1 ,  0 ) and (X 2 ,  0 ) as viewing positions of the first camera  10 - 1  and the second camera  10 - 2 , respectively, a distance B =X 2 −X 1  between the two viewing positions is hereafter called the baseline B of the first and the second camera  10 - 1  and  10 - 2 . 
     When a first and a second picture of an object  1  are taken by the first and the second camera  10 - 1  and  10 - 2  having the baseline B, and a position P of the object  1  is projected at points p 1  and p 2  of the first and the second picture, that is, on focal planes of the first and the second camera  10 - 1  and  10 - 2 , respectively, a disparity d between the points p 1  and p 2  is represented as follows: 
     
       
           d=x   2   −x   1   =BF/z,   (1) 
       
     
     where x 1  and x 2  are x-components of coordinates of the points p 1  and p 2  on x-y planes having their origins on the centers of the first and the second picture, respectively, and z is a depth, that is, a distance to the X-Y plane of the position P of the object  1 . 
     Therefore, information of  3 -dimensional structure of the object  1  can be estimated from the disparity d if each point p 1  of the first picture is known to correspond to which point p 2  of the second picture. 
     In general, the stereo-method is performed according to an algorithm wherein a depth z at an interesting point p 1  of the first picture is estimated by retrieving a point p 2  of the second picture having correspondence to the interesting point p 1 , and by repeating above procedure for each point p 1  of the first picture, depth of each position P of the object  1  is estimated on the first picture taken by the first camera  10 - 1 . 
     In many algorithms, the correspondence is discriminated when an evaluation value such as brightness difference between the concerning two points p 1  and p 2 , or sum of brightness differences between two small regions around the concerning two points p 1  and p 2  becomes minimum in a retrieving range defined as follows. When a possible depth z to be obtained is between z min  to z max , the disparity d should be between d min =BF/z max  to d max =BF/z min  from the equation (1). 
     Therefore, the corresponding point P 2  should be retrieved in a range x 1 +d min≦x   2 ≦x 1 +d max . 
     In some algorithms, points in the retrieving range showing the evaluation value, brightness difference for example, within a threshold value are selected as candidates of the corresponding point, and one of the candidates which gives the most smooth variation of the depth z is determined as the corresponding point. Further, when there is known an obstacle  2  as illustrated in FIG. 7 in front of the object  1 , correspondence retrieved in a range where the obstacle  2  should exists are rejected in many algorithms as correspondence physically impossible. 
     Returning to the equation (1), the disparity d is in proportion to the baseline B for the same depth z, and preciseness of the disparity d is limited according to the picture resolution. Therefore, the larger disparity d gives the higher precision of the estimated depth z, and the longer baseline B is preferable for the purpose. However, a longer baseline B gives a wider retrieving range as above described, causing a greater possibility of a false correspondence. 
     Therefore, there is a tradeoff between precision and false frequency of the estimation. 
     Techniques for dealing with this tradeoff can be classified into two methods. In one method, a coarse estimation is performed by retrieving correspondence between a pair of low resolution images, then a precise estimation is performed with a pair of high resolution images eliminating false correspondence inconsistent with the coarse estimation. Another approach is a method (hereafter called the multi-baseline stereo method) wherein multiple images of an object taken from multiple viewing positions having different baselines are used so that the evaluation value varies greatly according to whether there is correspondence or not. 
     In the prior paper beforehand mentioned of Okutomi et al., the latter approach, namely, the multi-baseline stereo method is applied. 
     Now, the multi-baseline stereo-method in the prior paper is described referring to a schematic diagram of FIG.  8 . 
     In FIG. 8, n pictures of an object  1  are taken by a first to n-th cameras  10 - 1  to  10 -n, each having a lens with a focal distance F and positioned at each of viewing positions (X 1 ,  0 ) to (X n ,  0 ) on an X-Y plane so as to have optical axis thereof perpendicular to the X-Y plane, n being a positive integer. Each of baselines B 1,2  to B 1,n  is that between the first camera  10 - 1  and each of the other cameras  10 - 2  to  10 -n. A position P having a depth z of the object  1  is projected at points p 1  to p n  of the n pictures, x 1  to x n  being distances of the points p 1  to p n  in X-direction to centers of the n pictures. 
     Here, n−1 disparities d 1,2  to d 1,n  between n−1 pairs of points p 1  and p 2  to p 1  and p n  are obtained as follows:                        d     1   ,   2       =         x   2     -     x   1       =       B     1   ,   2          F        /        z                     d     1   ,   3       =         x   3     -     x   1       =       B     1   ,   3          F        /        z                 ⋮               d     1   ,   n       =         x   n     -     x   1       =       B     1   ,   n          F        /        z               }           (   2   )                                
     Therefore, for a depth estimation z of a position P, correspondence between n−1 pairs of points represented by the above equations (2) can be checked, enabling to improve the estimation precision making use of long baselines and reducing false correspondence at the same time. 
     In the algorithm of the multi-baseline stereo method, a similar step to the algorithm with two cameras described in connection with FIG. 6 of retrieving a corresponding point to an interesting point p 1  of the first picture is performed for each of the other pictures taken by the second to the n-th cameras  10 - 2  to  10 -n, and above procedure is repeated for each point of the first picture. 
     In the algorithm with two cameras, the retrieving range is defined concerning the disparity d. However, in the multi-baseline stereo-method of the prior paper, the retrieving range is defined with an inverse distance 1/z, namely a reciprocal of the depth z, and the corresponding point giving a minimum of an evaluation value is retrieved in each of the other pictures according to the equations (2) by varying the inverse distance from  1 /z max  to  1 /z min . 
     As to the evaluation value, sum of the sums of squared-difference values between small regions of each pair of pictures is applied in the prior paper. 
     FIG. 9 is a schematic diagram illustrating the small regions  115 - 1  to  115 -n of n pictures of a rectangular solid  3  corresponding to left-upper front corner thereof taken with the first to the n-th cameras  10 - 1  to  10 -n. The sum of squared-difference values between the first small region  115 - 1  and each of the other small regions  115 - 2  to  115 -n is calculated for the first. Then, a value of the inverse distance  1 /z which makes minimum the total value of n−1 sums thus calculated is retrieved between  1 /z max  to  1 /z min . This procedure is performed for every point of the first picture take by the first camera  10 - 1 . 
     Thus, the multi-baseline stereo-method of the prior paper is performed. 
     However, when there is a large disparity, there may arise an extreme difference between a pair of small regions, such as the pair of the small regions  115 - 1  and  115 -n of FIG. 9, although both representing the same corner. In such a case, the calculated value of the inverse distance  1 /z may be shifted by the extreme difference, in the multi-baseline stereo-method of the prior paper. 
     In a Japanese patent application laid open as a Provisional Publication No. 329481/&#39;92 entitled “A Method of and an Apparatus for Obtaining 3-Dimensional Data”, there is disclosed a method of estimating 3-dimensional structure to be applied even when there is a large disparity between a pair of stereo pictures. 
     In this prior art, variation of a correlation value between two small regions is calculated varying the disparity. When there can not be found a clear singular point in the correlation value, revision of size and scope of the small regions or distortion of one of the small regions, for example, is performed according to pattern of variation curve of the correlation value. 
     In the examples heretofore described, a sum of squared-difference of pixel brightness or a correlation value between small regions is used as the evaluation value for discriminating corresponding points in the stereo pictures. Beside these values, there are known stereo-methods making use of difference of edge lines or texture information as the evaluation value. 
     Problems in these proir arts are as follows. 
     First, in methods to compare small regions of pictures taken by a pair of cameras, correspondence of the small regions may not be discriminated correctly because of the large difference of viewing angle, when the baseline of the pair of cameras is large. In the method disclosed in the Japanese patent application Provisional Publication No. 329481/&#39;92, revision of size and scope of the small regions or distortion of one of the small regions is performed for dealing with this problem. However, the revision or the distortion requires somewhat ad hoc technique and it is very difficult to establish rules for the revision or distortion widely applicable. Therefore, it can be said that there was a limit of the baseline with the conventional methods for discriminating correspondence referring the small regions. 
     Second, difference of brightness because of variation of reflectivity according to difference of viewing angle is not considered in the prior arts. 
     When pictures of an object are taken by cameras from different viewing position, brightness of a point of the object differs generally in each picture owing to difference of viewing angle as illustrated in FIG.  10 . In FIG. 10, brightness of a point P of an object  1  illuminated by a light  7  becomes highest in a direction symmetric to the light  7  for the normal line of the point P, and varies according to viewing direction, that is, angle to the viewing position. Therefore, when the corresponding points is discriminated by evaluating simply the sum of squared-difference of pixel brightness between small regions, it is easily affected with the above variation of reflectivity, and so, does not become sufficiently small even at the corresponding point, resulting in an increase of the estimation errors. 
     The effect of the reflectivity variation may be reduced by applying the correlation value, or the difference of edge lines or texture information as the evaluation value. However, these values should be calculated from the small regions, and so, are not free from the first problem which limits the baseline length, and accordingly, the estimation precision. 
     SUMMARY OF THE INVENTION 
     Therefore, a primary object of the present invention is to provide a method of and an apparatus for 3-dimensional structure estimation wherein a high estimation precision and a high estimation reliability are both realized at the same time. 
     In order to achieve the object, a method of 3-dimensional structure estimation of the invention for estimating a 3-dimensional structure of an object from image data of a plurality of pictures of the object each taken from each viewing position ranged on a straight line by a camera with an optical axis parallel to a direction perpendicular to the straight line has a step of performing, for each pixel of image data of a first of the plurality of pictures, steps of: 
     extracting corresponding small regions, having a size of at least one pixel, each from the image data of each of the plurality of pictures, a position of each of the corresponding small regions in corresponding each of the plurality of pictures being defined by a focal distance of the camera, a distance between a viewing position wherefrom the corresponding each of the plurality of pictures is taken and a viewing position wherefrom the first of the plurality of pictures is taken, a position of a concerning pixel of image data of the first of the plurality of pictures, and a variable representing a depth of a point of the object corresponding to the concerning pixel; 
     calculating a neighboring correspondence value for each of the corresponding small regions, the neighboring correspondence value representing correspondence among the corresponding small regions of neighboring certain of the plurality of pictures, viewing positions wherefrom the neighboring certain are taken being ranged within a predetermined distance from a viewing position wherefrom a picture including said each of the corresponding small regions is taken; 
     obtaining a sum of the neighboring correspondence value of all of the corresponding small regions; and 
     selecting an estimation value in a predetermined range of the variable which gives a singular value of the sum of the neighboring correspondence value, and outputting the estimation value as an estimation of the depth of the point corresponding to the concerning pixel. 
     Therefore, the first problem of the prior arts beforehand described that the correspondence of the small regions may not be discriminated correctly because of the extreme difference thereof due to large difference of viewing angle can be eliminated in the invention, enabling to obtain still higher estimation precision by enlarging the baseline length. 
     Further, the neighboring correspondence value is so calculated as to represent relative differential of concerning pixel values, such as a variance, for example, of pixel values in the corresponding small regions of the neighboring certain of the plurality of pictures. 
     Therefore, the second problem of the prior arts that the correspondence estimation is easily affected with the variation of reflectivity owing to difference of viewing angles can be also reduced greatly in the invention, resulting in still higher estimation reliability. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing, further objects, features, and advantages of this invention will become apparent from a consideration of the following description, the appended claims, and the accompanying drawings wherein the same numerals indicate the same or the corresponding parts. 
     In the drawings: 
     FIG. 1 is a block diagram illustrating an apparatus for 3-dimensional structure estimation according to a first embodiment of the invention; 
     FIG. 2 is a block diagram illustrating an apparatus for 3-dimensional structure estimation according to a second embodiment; 
     FIG. 3 is a block diagram illustrating an apparatus for 3-dimensional structure estimation according to a third embodiment; 
     FIG. 4 is a block diagram illustrating an apparatus for 3-dimensional structure estimation according to a fourth embodiment; 
     FIG. 5 is a schematic diagram illustrating, by way of example, the second average brightness  117 - 2  represented by the second small region average signal  17 - 2  output from the second neighboring small region average calculation means  16 - 2  of FIG. 1; 
     FIG. 6 is a schematic diagram illustrating principle of a stereo-method; 
     FIG. 7 illustrates an obstacle  2  in front of the object  1 ; 
     FIG. 8 is a schematic diagram illustrating a multi-baseline stereo-method; 
     FIG. 9 is a schematic diagram illustrating the small regions  115 - 1  to  115 -n of n pictures of a rectangular solid  3  corresponding to left-upper front corner thereof taken with the first to the n-th cameras  10 - 1  to  10 -n; and 
     FIG. 10 illustrates variation of brightness of a point P of the object owing to difference of viewing angle. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Now, embodiments of the present invention will be described in connection with the drawings. 
     FIG. 1 is a block diagram illustrating an apparatus for 3-dimensional structure estimation according to a first embodiment of the invention for estimating a 3-dimensional structure of an object from pictures taken by a first to an n-th camera  10 - 1  to  10 -n such ranged at n viewing position as described in connection with FIG. 8, n being an integer more than one. 
     The apparatus of FIG. 1 comprises; 
     first small region extraction means  14 - 1  for outputting a first corresponding small region signal, the first small region extraction means  14 - 1  being supplied with a reference pixel position signal  66  together with a first image signal  11 - 1 , a first viewing position signal  12 - 1  and a first focal distance signal  13 - 1  supplied from the first camera  10 - 1 , second to n-th small region extraction means  14 - 2  to  14 -n, each of the second to the n-th small region extraction means  14 - 2  to  14 -n being supplied with the reference pixel position signal  66  and a depth signal  68  together with corresponding each of a second to an n-th image signal  11 - 2  to  11 -n, corresponding each of a second to an n-th viewing position signal  12 - 2  to  12 -n and corresponding each of a second to an n-th focal distance signal  13 - 2  to  13 -n supplied from corresponding each of the second to the n-th cameras  10 - 2  to  10 -n, for outputting each of a second to an n-th corresponding small region signal, respectively, first to n-th neighboring small region average calculation means  16 - 1  to  16 -n each for outputting a first to an n-th neighboring small region average signal, respectively, supplied with a small region signal set  4  consisting of the first to the n-th corresponding small region signal and a viewing position signal set  5  consisting of the first to the n viewing position signal  12 - 1  to  12 -n, 
     first to n-th differential calculation means  18 - 1  to  18 -n, each of the first to the n-th differential calculation means  18 - 1  to  18 -n being supplied with corresponding each of the first to the n-th corresponding small region signal and corresponding each of the first to the n-th neighboring small region average signal for outputting each of a first to an n-th differential signal, 
     sum calculation means  60  for outputting a differential sum signal  61  supplied with the first to the n-th differential signal, 
     minimum cost depth selection means  62  for outputting a 3-dimensional signal  63  and a count signal  64 , supplied with the differential sum signal  61 , the reference pixel position signal  66  and the depth signal  68 , 
     reference pixel position counting means  65  for outputting the reference pixel position signal  66  supplied with the count signal  64 , and depth counting means  67  for outputting the depth signal  68  supplied with the reference pixel position signal  66 . 
     Now, operation of the first embodiment of FIG. 1 is described. 
     The reference pixel position counting means  65  output the reference pixel position signal  66  indicating coordinates (x k , y k ) of a reference pixel p k  in first image data taken by the first camera  10 - 1  represented by the first image signal  11 - 1 . 
     The first small region extraction means  14 - 1  outputs the corresponding small region signal indicating data of 5×5 pixels around the reference pixel p k  extracted from the first image signal  11 - 1  taken by the first camera  10 - 1 . 
     The second small region extraction means  14 - 2  output the second corresponding small region signal indicating data of 5×5 pixels around a second corresponding pixel position (x 2 , y 2 ) extracted from the second image signal  11 - 2  taken by the second camera  10 - 2 , where the second corresponding pixel position (x 2 , y 2 ) of the second image signal  11 - 2  is calculated as follows, according to the equations (2) beforehand described, from a baseline B 1,2  indicated by the second viewing position signal  12 - 2 , a focal distance F indicated by the second focal distance signal  13 - 2  and a depth z indicated by the depth signal  68 : 
     x 2 =B 1,2 F/z+x k , 
     y 2 =y k . 
     In the same way, the i-th (i being each integer from three to n) small region extraction means  14 -i outputs the i-th corresponding small region signal indicating data of  5 × 5  pixels around an i-th corresponding pixel position (x i =B 1,i F/z+x k , y k ) extracted from the i-th image signal  11 -i talen by the i-th camera  10 -i. 
     All of the first to the n-th corresponding small region signal thus obtained are supplied to every of the first to the n-th neighboring small region average calculation means  16 - 1  to  16 -n as the small region signal set  4 , marked with a light hatched allow in FIG. 1, together with the viewing position signal set  5  marked with a deep hatched allow consisting of the first to the n viewing position signal  12 - 1  to  12 -n. 
     The first neighboring small region average calculation means  16 - 1  select neighboring cameras  10 -j, difference of viewing position |X j -X 1 |to each thereof smaller than a predetermined value C, and output the first neighboring small region average signal according to an average brightness value of pixels included in each of the corresponding small region signals corresponding to the neighboring cameras  10 -j, calculated as follows:            the                 average                 brightness     =       1     25        N   1                ∑     j   ∈         arg   j                 X   j     -     X   1              &lt;   C                         g     x   ,   y     j           ,                          
     where N 1 =Σ jεarg     j     |x     j     −x     1     |&lt;C    1  is a number of the neighboring cameras  10 -j concerning the first camera  10 - 1  and g x,   j   y  is brightness of a pixel at relative coordinates (x, y) of 5×5 pixel plane of each of the corresponding small region signals. 
     In the same way, the i-th (i being each integer from two to n) neighboring small region average calculation means  16 -i output the i-th neighboring small region average signal by calculating an i-th average brightness as follows:                  i        -        th                 average                 brightness     =       1     25        N   i                ∑     j   ∈         arg   j                 X   j     -     X   i              &lt;   C                         g     x   ,   y     j           ,           (   3   )                                
     where N i =Σ j⊖arg     j     |x     j     -x     i     &lt;C    1  is a number of the neighboring cameras  10 -j concerning the i-th camera. 
     Each of the first to the n-th neighboring small region average signal thus obtained is supplied to corresponding each of the first to the n-th differential calculation means  18 - 1  to  18 -n together with corresponding each of the first to the n-th corresponding small region signal. 
     Each (i-th, for example, i being each integer from one to n) of the first to the n-th differential calculation means  18 - 1  to  18 -n calculate an i-th square sum of difference of every pixel brightness of the i-th corresponding small region signal to the i-th average brightness indicated by the i-th neighboring small region average signal, as follows, to be output to the sum calculation means  60  as each of the first to the n-th differential signal:                i        -        th                 square                 sum     =       ∑   x                       ∑   y                         (       g     x   ,   y     j     -       1     25        N   i                ∑     j   ∈         arg   j                 X   j     -     X   i              &lt;   C                         g     x   ,   y     j           )     2     .                 (   4   )                                
     The sum calculation means  60  calculate a sum of each of the first to the n-th square sum according to the first to the n-th differential signal, which is supplied to the minimum cost depth selection means  62  as the differential sum signal  61 . 
     A sequence of processes above described is performed for each value of the depth z between z min  and z max  of the depth signal  68  generated by the depth counting means  67 . 
     The minimum cost depth selection means  62  select a depth estimation z(x k , y k ) giving a minimum value of the differential sum signal  61  among values of the depth z between z min  and z max , and revise the count signal  64  for shifting the reference pixel P k . 
     Repeating above procedure by assigning each pixel of the first image data taken by the first camera  10 - 1  to the reference pixel P k  according to the count signal  64 , the 3-dimensional signal  63  is obtained, which represents information z(x, y) of a 3-dimensiona structure of the object indicating the depth estimation at each coordinates (x, y) on a plane of the first image data. 
     Thus operates the apparatus for 3-dimensional structure estimation according to the first embodiment. 
     As heretofore described, average brightnesses each defined by the equation (3) of the small regions in the image data taken by neighboring cameras are calculated by the first to the n-th neighboring small region average calculation means  16 - 1  to  16 -n to be considered, in the embodiment. 
     FIG. 5 is a schematic diagram illustrating, by way of example, the second average brightness  117 - 2  represented by the second neighboring small region average signal output from the second neighboring small region average calculation means  16 - 2 , which is obtained by averaging a first corresponding small region  115 - 1  represented by the first corresponding small region signal to a third corresponding small region  115 - 3  represented by the third corresponding small region signal, for example, wherein is no extreme difference. 
     Therefore, the first problem of the prior arts beforehand described that the correspondence of the small regions may not be discriminated correctly because of the extreme difference thereof due to large difference of viewing angle can be eliminated in the embodiment, enabling to obtain still higher estimation precision by enlarging the baseline length. 
     Further, the sum of the square sums each defined by the equation (4) indicating a differential value is calculated by the sum calculation means  60  according to the first to the n-th differential signal to be made use of as the evaluation value, in the embodiment. 
     Therefore, the second problem of the prior arts that the correspondence estimation is easily affected with the variation of reflectivity owing to difference of viewing angles can be also reduced greatly in the embodiment, resulting in still higher estimation reliability. Heretofore, the present invention is described in connection with the first embodiment of FIG.  1 . However, the scope of the invention is not limited in the first embodiment. 
     For example, in the embodiment of FIG. 1, the size of the corresponding small regions is described to have 5×5 pixels. However it may be any appropriate size. 
     Further, the first camera  10 - 1  is illustrated to be positioned most left in FIG.  8 . However, any other camera may be assigned to the first camera. 
     Further, the average brightnesses of corresponding small regions are calculated according to the equation (3), and the square sums of difference of every pixel brightness thereof to the average brightnesses are calculated according to the equation (4), in the embodiment, as values representing correspondence of the corresponding small regions of pictures taken by the neighboring cameras. However, they may be calculated according to any other equations appropriate for representing the correspondence among corresponding small regions corresponding to the neighboring cameras. 
     Still further, each of the first to the n-th image signal  11 - 1  to  11 -n is described to be supplied from each of the first to the n-th camera. However, each of them may be supplied sequentially from a camera which is shifted to each of the viewing positions sequentially. 
     Now, a second embodiment of the invention is described referring to a block diagram of FIG. 2 illustrating an apparatus for 3-dimensional structure estimation according to the second embodiment, wherein a size of 1×1 pixel of the small regions is applied. 
     In the second embodiment having a similar configuration to the first embodiment of FIG. 1, the first to the n-th small region extraction means  14 - 1  to  14 -n of FIG. 1 are replaced with a first to an n-th corresponding pixel extraction means  24 - 1  to  24 -n each extracting a value of a pixel corresponding to the reference pixel P k  according to the equation (2) from corresponding each of the first to the n-th image signal  11 - 1  to  11 -n for outputting as each of a first to an n-th corresponding pixel signal. 
     All of the first to the n-th corresponding pixel signal are supplied to every of a first to an n-th neighboring pixel average calculation means  26 - 1  to  26 -n, each replacing each of the first to the n-th neighboring small region average calculation means  16 - 1  to  16 -n of FIG. 1, as a pixel signal set  6  marked with a light hatched allow in FIG. 2, together with the viewing position signal set  5  marked with a deep hatched allow consisting of the first to the n-th viewing position signal  12 - 1  to  12 -n. 
     Each, i-th for example, of the first to the n-th neighboring pixel average calculation means  26 - 1  to  26 -n output an i-th neighboring pixel average signal having an average of values indicated by the corresponding pixel signals corresponding to neighboring cameras  10 -j, by selecting the neighboring cameras  10 -j in the same way with the first embodiment of FIG.  1 . 
     Each, i-th for example of the first to the n-th differential calculation means  18 - 1  to  18 -n calculate an i-th square difference of the i-th corresponding pixel signal to the i-th neighboring pixel average signal in a similar way with the first embodiment of FIG. 1, as follows, to be output to the sum calculation means  60  as each of the first to the n-th differential signal:          i        -        th                 square                 difference     =         (       g   i     -       1     N   i              ∑     j   ∈         arg   j                 X   j     -     X   i              &lt;   C                         g   j           )     2     .                            
     where g i  being the pixel value of the i-th corresponding pixel signal. 
     Following processes are performed in the same way to the first embodiment of FIG.  1 . 
     That is, the sum calculation means  60  calculate a sum of the first to the n-th square difference according to the first to the n-th differential signal, which is supplied to the minimum cost depth selection means  62  as the differential sum signal  61 . The sequence of processes above described is performed for each value of the depth z between z min  and z max  of the depth signal  68  generated by the depth counting means  67 . The minimum cost depth selection means  62  select a depth estimation z(x k , y k ) giving a minimum value of the differential sum signal  61  among values of the depth z between z min  and z max , and revise the count signal  64  for shifting the reference pixel p k . Repeating above procedure by assigning each pixel of the first image data taken by the first camera  10 - 1  to the reference pixel p k  according to the count signal  64 , the 3-dimensional signal  63  is obtained, which represents information z(x, y) of a 3-dimensiona structure of the object indicating the depth estimation at each coordinates (x, y) on the plane of the first image data. 
     Thus operates the apparatus for 3-dimensional structure estimation according to the second embodiment. 
     In a third embodiment of the invention illustrated by a block diagram of FIG. 3, variances of the corresponding small regions of the pictures taken by neighboring cameras are calculated for representing the correspondence among them. 
     In the third embodiment having a similar configuration to the first embodiment of FIG. 1, each pair of the first to the n-th neighboring small region average calculation means  16 - 1  to  16 -n and the first to the n-th differential calculation means  18 - 1  to  18 -n of FIG. 1 is replaced with a first to an n-th neighboring small region variance calculation means  36 - 1  to  36 -n. Other components are the same with the first embodiment of FIG. 1, and so, duplicated description is omitted. 
     The small region signal set  4  and the viewing position signal set  5  are supplied to all of the first to the n-th neighboring small region variance calculation means  36 - 1  to  36 -n. 
     Each, i-th for example, of the first to the n-th neighboring small region variance calculation means  36 - 1  to  36 -n output an i-th variance signal defined by following equation (5) indicating a variance of pixel values indicated by the corresponding small region signals corresponding to neighboring cameras  10 -j, by selecting the neighboring cameras  10 -j in the same way with the first embodiment of FIG.  1 .                i   -     th                 variance       =       1     N   i              ∑   x                       ∑   y                       ∑     l   ∈         arg   l                 X   l     -     X   i              &lt;   C                             (       g     x   ,   y     l     -       1     25        N   i                ∑     j   ∈         arg   j                 X   j     -     X   i              &lt;   C                         g     x   ,   y     j           )     2     .                     (   5   )                                
     The sum calculation means  60  calculate a sum of the first to the n-th variance according to the first to the n-th variance signal, which is supplied to the minimum cost depth selection means  62  as a variance sum signal  69 , and the minimum cost depth selection means  62  outputs the 3-dimensional signal  63  in the same way with the first or the second embodiment. 
     In a fourth embodiment illustrated by a block diagram of FIG. 4, the 1×1 size of the corresponding small regions is applied to the third embodiment, in a similar way with the second embodiment of FIG. 2 wherein it is applied to the first embodiment, duplicated description being omitted. 
     Thus, the apparatus for 3-dimensional estimation according to the invention can realize a high estimation precision together with a high estimation reliability at the same time.