Patent Publication Number: US-2023133736-A1

Title: Image analyzing device and image analyzing method

Description:
TECHNICAL FIELD 
     This invention relates to an image analyzing device and an image analyzing method for performing image analysis. 
     BACKGROUND ART 
     Synthetic aperture radar (SAR) technology is a technology which can obtain an image equivalent to the image by an antenna having a large aperture, when a flying object such as artificial satellite, aircraft, or the like transmits and receives a radio wave while the flying object moves. The synthetic aperture radar is utilized, for example, for analyzing an elevation or a ground surface deformation by signal-processing reflected waves from the ground surface. When SAR technology is used, the image analyzing device takes time-series SAR images (SAR data) obtained by a synthetic aperture radar as input, and performs time-series analysis of the input SAR images. 
     Interferometric SAR analysis is an effective method for analyzing an elevation or a ground surface deformation. In the interferometric SAR analysis, the phase difference between radio signals of plural (for example, two) SAR images taken at different times is calculated. Then, a change in distance between the flying object and the ground that occurred during the shooting time period is detected. 
     When performing interferometric SAR analysis, a displacement and an elevation are generally assumed to vary linearly in time. For example, in the multi-temporal SAR analysis such as a method (Interferometry Stacking) stacking multiple (for example, three or more) SAR images to reduce noise, a linear displacement is often assumed. 
     Then, if a nonlinear displacement, etc. are large, an accurate analysis result might not be obtained. 
     A technique for SAR analysis with relatively high tolerance to a nonlinear displacement, etc. is described in patent literature 1. In the technique described in patent literature 1, coherence is calculated using a phase difference between close pixels. Points with valid displacement information are extracted, and the displacement velocity, etc. are determined based on phases on those points. 
     Non-patent literature 1 describes an interferometric SAR analysis using the multipath method. In the interferometric SAR analysis described in non-patent literature 1, a phase difference between neighboring pixels is calculated, and a displacement velocity and an elevation difference between neighboring pixels are calculated. Then, respective displacement velocities are merged. In addition, respective elevation differences are merged. Specifically, the evaluation function (evaluation formula of linear regression of phase) of equation (1) is optimized (in this case, maximized). 
     
       
         
           
             
               
                 
                                   
                   
                     [ 
                     
                       Math 
                       . 
                           
                       1 
                     
                     ] 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     ? 
                   
                   = 
                   
                     Re 
                     ⁢ 
                     
                       
                         { 
                         
                           
                             1 
                             M 
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 
                                   ( 
                                   
                                     k 
                                     , 
                                     l 
                                   
                                   ) 
                                 
                                 ∈ 
                                 S 
                               
                             
                             
                               
                                 Δ 
                                 
                                   x 
                                   
                                     ❘ 
                                     &#34;\[LeftBracketingBar]&#34; 
                                   
                                 
                               
                               ⁢ 
                               
                                 a 
                                 
                                   k 
                                   , 
                                   L 
                                 
                               
                               ⁢ 
                               exp 
                             
                           
                         
                       
                       
                                                  
                         
                           _ 
                           
                             Phase 
                             difference 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         
                           [ 
                           
                             
                               
                                 - 
                                 j 
                               
                               ⁢ 
                               
                                 
                                   4 
                                   ⁢ 
                                   π 
                                 
                                 λ 
                               
                               ⁢ 
                               
                                 Δ 
                                 
                                   x 
                                   
                                     ❘ 
                                     &#34;\[LeftBracketingBar]&#34; 
                                   
                                 
                               
                               ⁢ 
                               v 
                               ⁢ 
                               Δ 
                               ⁢ 
                               
                                 t 
                                 
                                   k 
                                   , 
                                   L 
                                 
                               
                             
                                             
                           
                           ] 
                         
                         
                           
                                               
                             
                               Displacement 
                               _ 
                             
                           
                                                  
                         
                       
                         
                     
                     ⁢ 
                     exp 
                     ⁢ 
                     
                       
                         
                           [ 
                           
                             
                               - 
                               j 
                             
                             ⁢ 
                             
                               
                                 4 
                                 ⁢ 
                                 π 
                               
                               λ 
                             
                             ⁢ 
                             
                               β 
                               
                                 k 
                                 , 
                                 L 
                               
                             
                             ⁢ 
                             
                               Δ 
                               
                                 x 
                                 
                                   ❘ 
                                   &#34;\[LeftBracketingBar]&#34; 
                                 
                               
                             
                             ⁢ 
                             
                               Z 
                               ∈ 
                             
                           
                           ] 
                         
                         } 
                       
                       
                         
                                                   
                           
                             
                               elevation 
                                  
                             
                             _ 
                           
                         
                         
                                               
                           difference 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ? 
             
             indicates text missing or illegible when filed 
           
         
       
     
     In equation (1), Ze indicates a height. Δ xl Ze indicates an elevation difference between neighboring pixels. v indicates a displacement velocity. Δt k,l  indicates a temporal baseline. The baseline corresponds to a difference in shooting time between the image k and the image  1 . Hereafter, this difference is referred to as the shooting time difference. Δ xl vΔt k,l  indicates the velocity difference between neighboring pixels. Δ xl  a k,l  indicates a value corresponding to the phase difference. β k,l  is a value associated with the vertical baseline. The vertical baseline is a distance between the orbits when images k and l were taken, respectively. This distance is hereafter referred to as the baseline distance. S is a set of interferometric SAR images obtained from a pair of (k,l). 
     The respective obtained displacement velocities are then merged over the entire image using the merging equation of equation (2). When the displacement velocity after merging is not converged, optimization using equation (1) is performed again. “Convergence” means, for example, that a difference between the displacement velocity obtained by optimization using equation (1) and the displacement velocity obtained before the re-optimization is less than a predetermined value (as an example, less than a predetermined threshold). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     2 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   v 
                   = 
                   
                     
                       1 
                       
                         
                           ∑ 
                           p 
                         
                         
                           w 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         p 
                       
                       
                         
                           w 
                           ⁡ 
                           ( 
                           p 
                           ) 
                         
                         [ 
                         
                           
                             v 
                             ⁡ 
                             ( 
                             p 
                             ) 
                           
                           - 
                           
                             Δ 
                             ⁢ 
                             
                               v 
                               ⁡ 
                               ( 
                               p 
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In equation (2), p corresponds to the image number. W(p) is a weight in the pth interferometric SAR image. The weight is a parameter that contributes to noise reduction. Equation (2) is a merging equation for a displacement velocity, however it is also merged for an elevation difference in the same way. 
     CITATION LIST 
     Patent Literature 
     
         
         PTL 1: International Publication No. 2010/000870 
       
    
     Non Patent Literature 
     
         
         NPL 1: G. Fornaro, et. al., “Deformation monitoring over large areas with multipass differential SAR interferometry: a new approach based on the use of spatial differences”, International Journal of Remote Sensing, Vol. 30, No. 6, 20 Mar. 2009, 1455-1478 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     The interferometric SAR analysis described in non-patent literature 1 can obtain an average linear displacement velocity and an average elevation difference that are somewhat robust to spatially smooth but temporally nonlinear phase motions. However, according to the interferometric SAR analysis described in non-patent literature 1, the displacement velocity and the elevation difference may not converge or may converge to incorrect values when extremely nonlinear phase motion in time is included. 
       FIGS.  22 A to  22 C  are explanatory diagrams showing an example of convergence to an incorrect value. As shown in  FIG.  22 (A) , there are N SAR images (specifically, interferometric SAR images), as an example. In addition, take as an example the respective phase differences between the pixel indicated by the black dot and its neighboring pixels a to d.  FIG.  22 (B)  shows an example of changes in the respective phase differences. The phase differences between pixels a-c and the pixel indicated by the black dot varies almost linearly, however the phase difference between pixel d and the pixel indicated by the black dot varies rapidly in space and has an extremely large degree of non-linearity. 
     As illustrated in  FIG.  22 (C) , the displacement velocities v based on the phase differences between the pixels a to c and the pixel indicated by the black dot converges to a similar value X, however the displacement velocity v based on the phase difference between the pixel d and the pixel indicated by the black dot converges to the value Y which is far from the value X. Under such circumstances, when the displacement velocities are merged over the entire image, including the phase difference between the pixel d and the pixel indicated by the black dot, the merging result will be erroneous. The same argument can be made for an elevation. 
     It is an object of the present invention to provide an image analyzing device and an analysis method that can obtain a highly reliable merging result when obtaining a displacement velocity and an elevation of an entire image by merging pixel-by-pixel displacement velocity differences and elevation differences based on phase differences. 
     Solution to Problem 
     The image analyzing device according to the present invention includes inter-image phase difference calculation means for calculating a phase difference image of a pair of images, inter-pixel phase difference calculation means for calculating a phase difference between close pixels in the phase difference image, evaluation function generation means for generating an evaluation function that includes at least the phase difference between pixels, optimization means for optimizing the evaluation function for each pair of pixels or each pair of close pixels, random number generation means for generating a random number, threshold setting means for setting a threshold based on a result of evaluation of the random number using the evaluation function, and merging means for obtaining merged data of an entire image by merging values of variables when the optimization means performs optimization except for variables for which evaluation value using the evaluation function is less than the threshold. 
     The image analyzing method according to the present invention includes calculating a phase difference image of a pair of images, calculating a phase difference between close pixels in the phase difference image, generating an evaluation function that includes at least the phase difference between pixels, optimizing the evaluation function for each pair of pixels or each pair of close pixels, generating a random number, setting a threshold based on a result of evaluation of the random number using the evaluation function, and obtaining merged data of an entire image by merging values of variables when the evaluation function is optimized except for variables for which evaluation value using the evaluation function is less than the threshold. 
     The image analyzing program according to the present invention causes a computer a process of calculating a phase difference image of a pair of images, a process of calculating a phase difference between close pixels in the phase difference image, a process of generating an evaluation function that includes at least the phase difference between pixels, a process of optimizing the evaluation function for each pair of pixels or each pair of close pixels, a process of generating a random number, a process of setting a threshold based on a result of evaluation of the random number using the evaluation function, and a process of obtaining merged data of an entire image by merging values of variables when the evaluation function is optimized except for variables for which evaluation value using the evaluation function is less than the threshold. 
     Advantageous Effects of Invention 
     According to the present invention, a highly reliable merging result can be obtained. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1 A  It depicts an explanatory diagram for explaining schematic concept of each example embodiment. 
         FIG.  1 B  It depicts an explanatory diagram for explaining schematic concept of each example embodiment. 
         FIG.  1 C  It depicts an explanatory diagram for explaining schematic concept of each example embodiment. 
         FIG.  1 D  It depicts an explanatory diagram for explaining schematic concept of each example embodiment. 
         FIG.  2    It depicts a block diagram showing a configuration example of the image analyzing device of the first example embodiment. 
         FIG.  3    It depicts a flowchart showing an example of an operation of the image analyzing device of the first example embodiment. 
         FIG.  4    It depicts a block diagram showing a configuration example of the image analyzing device of the second example embodiment. 
         FIG.  5    It depicts a flowchart showing an example of an operation of the image analyzing device of the second example embodiment. 
         FIG.  6    It depicts a block diagram showing a configuration example of the image analyzing device of the third example embodiment. 
         FIG.  7    It depicts a flowchart showing an example of an operation of the image analyzing device of the third example embodiment. 
         FIG.  8    It depicts a block diagram showing a configuration example of the image analyzing device of the fourth example embodiment. 
         FIG.  9    It depicts a flowchart showing an example of an operation of the image analyzing device of the fourth example embodiment. 
         FIG.  10    It depicts an explanatory diagram for explaining improvement, etc. of falling into a local solution. 
         FIG.  11    It depicts a block diagram showing a configuration example of the image analyzing device of the fifth example embodiment. 
         FIG.  12    It depicts a flowchart showing an example of an operation of the image analyzing device. 
         FIG.  13    It depicts a block diagram showing a configuration example of the image analyzing device of the sixth example embodiment. 
         FIG.  14    It depicts a flowchart showing an example of an operation of the image analyzing device of the sixth example embodiment. 
         FIG.  15    It depicts an explanatory diagram for explaining the mechanism for reducing a calculation amount. 
         FIG.  16    It depicts a block diagram showing a configuration example of the image analyzing device of the seventh example embodiment. 
         FIG.  17    It depicts a flowchart showing an example of an operation of the image analyzing device of the seventh example embodiment. 
         FIG.  18    It depicts a block diagram showing a configuration example of the image analyzing device of the eighth example embodiment. 
         FIG.  19    It depicts a flowchart showing an example of an operation of the image analyzing device of the eighth example embodiment. 
         FIG.  20    It depicts a block diagram showing an example of a computer with a CPU. 
         FIG.  21    It depicts a block diagram showing an overview of the image analyzing device. 
         FIG.  22 A  It depicts an explanatory diagram showing an example of convergence to an incorrect value. 
         FIG.  22 B  It depicts an explanatory diagram showing an example of convergence to an incorrect value. 
         FIG.  22 C  It depicts an explanatory diagram showing an example of convergence to an incorrect value. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, example embodiments of the present invention will be described with reference to the drawings. 
     First, schematic concept of each example embodiment will be described with reference to explanatory diagrams of  FIGS.  1 A- 1 D . 
     As shown in  FIG.  1 (A) , there are N SAR images (specifically, interferometric SAR images), as an example. In addition, take as an example the respective phase differences between the pixel indicated by the black dot and its neighboring pixels a to d.  FIG.  1 (B)  shows an example of changes in the respective phase differences in the upper side. The phase differences between the pixels a-c and the pixel indicated by the black dot varies almost linearly, however the phase difference between the pixel d and the pixel indicated by the black dot varies rapidly in space and has an extremely large degree of non-linearity. 
     In each example embodiment, a predetermined random number is generated and the evaluation function is optimized (for example, maximized) using the random number as the phase difference.  FIG.  1 (B)  shows in the lower side an example of the change in phase difference with the pixel indicated by the black dot when a random number is used. 
       FIG.  1 (C)  shows an example of an evaluation value (calculated value of the evaluation function) regarding displacement velocities of the pixels a-d and an evaluation value regarding displacement velocities when using random numbers. As illustrated in the upper side of  FIG.  1 (C) , the evaluation value related to pixel d is small. In addition, as illustrated in the lower side of  FIG.  1 (C) , the evaluation values when using random numbers are generally smaller. 
     Therefore, in case each evaluation value using each random number is used as an evaluation index, when an evaluation value using an actual displacement velocity difference (displacement velocity difference based on an observed phase difference) is smaller than the evaluation index, the pair (the set) of pixels that present that the displacement velocity difference is excluded from the displacement velocity evaluation target. 
     In each example embodiment, the maximum value (or the average value), to which a margin is added, of each of the evaluation values when random numbers are used is set to the threshold, for example. Then, when the evaluation value of the displacement velocity difference is less than the threshold, the pair of pixels presenting that displacement velocity difference is excluded. 
     Although  FIGS.  1 A- 1 D  show the concept regarding a threshold using a displacement velocity as an example, the same concept can be applied to an elevation as an example. 
     Example Embodiment 1 
       FIG.  2    is a block diagram showing a configuration example of the image analyzing device of the first example embodiment. The image analyzing device  10  shown in  FIG.  2    includes a SAR image storage  100 , a shooting time and orbit storage  110 , an inter-image phase difference calculation unit  120 , an inter-pixel phase difference calculation unit  130 , an evaluation function generator  140 , an evaluation function optimization unit  150 , a merging unit  170 , a random number generator  200 , a threshold evaluation value calculation unit  210 , and a threshold generator  220 . In the first to eighth example embodiments, interferometric SAR images are illustrated as images, however the images that can be handled in each example embodiment are not limited to interferometric SAR images, and other types of images such as SAR images can also be handled. 
     The SAR image storage  100  stores N (N≥3) SAR images (specifically, interferometric SAR images). The shooting time and orbit storage  110  stores information (data) indicating a shooting time of the SAR image and information (data) capable of identifying the orbit of a flying object at the time the image was taken. 
     The inter-image phase difference calculation unit  120  calculates a phase difference (φm,n (m, n≤N) between a pair of SAR images. The phase difference (phase difference between two SAR images) between a pair of SAR images means a phase difference between corresponding pixels in respective images. The inter-image phase difference calculation unit  120  may calculate the phase difference of all pairs in the N SAR images, however, the inter-image phase difference calculation unit  120  may also calculate the phase difference for some of the pairs. 
     The inter-pixel phase difference calculation unit  130  calculates a phase difference between pixels in a single phase difference image. For example, for the SAR image m and the SAR image n, Δ k,l φ M,N  is calculated as the phase difference between close pixels k and l. Similarly, the inter-pixel phase difference calculation unit  130  calculates, for all phase difference images calculated by the inter-image phase difference calculation unit  120 , phase differences between various pairs of close pixels. 
     The evaluation function generator  140  generates an evaluation function. In the first example embodiment, the evaluation function of equation (3) is generated, for example. 
     
       
         
           
             
               
                 
                                   
                   
                     [ 
                     
                       Math 
                       . 
                           
                       3 
                     
                     ] 
                   
                 
               
               
                  
               
             
             
               
                 
                   
                     J 
                     ⁡ 
                     ( 
                     
                       
                         Δ 
                         ⁢ 
                         
                           v 
                           
                             k 
                             , 
                             l 
                           
                         
                       
                       , 
                       
                         Δ 
                         ⁢ 
                         
                           h 
                           
                             k 
                             , 
                             l 
                           
                         
                       
                       , 
                       
                         
                           Δ 
                           
                             k 
                             , 
                             l 
                           
                         
                         ⁢ 
                         
                           ϕ 
                           ∵ 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ∑ 
                       
                         m 
                         , 
                         n 
                       
                     
                     
                       
                         w 
                         
                           m 
                           , 
                           n 
                         
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           
                             
                               Δ 
                               
                                 k 
                                 , 
                                 l 
                               
                             
                             ⁢ 
                             
                               ϕ 
                               
                                 m 
                                 , 
                                 n 
                               
                             
                           
                           - 
                           
                             
                               t 
                               
                                 m 
                                 , 
                                 n 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                               v 
                               
                                 k 
                                 , 
                                 l 
                               
                             
                           
                           - 
                           
                             
                               b 
                               
                                 m 
                                 , 
                                 n 
                               
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                               h 
                               
                                 k 
                                 , 
                                 l 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In equation (3), “·” indicates all elements. For example, “·,·” in φ, means phase differences of all pairs. w m,n  is a weight for a phase difference between a SAR image m and a SAR image n. t m,n  is a shooting time difference. b m,n  is a baseline distance. Thus, equation (3) is an evaluation function of pixels k and l regarding a displacement velocity difference Δv k,l  and an elevation difference Δh k,l  using the shooting time difference t m,n , the baseline distance b m,n , and the phase difference Δ k,l φ m,n . 
     The evaluation function optimization unit  150  calculates the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  that maximizes the evaluation function for each pair of pixels. 
     The merging unit  170  merges the displacement velocity differences Δv k,l  to obtain the displacement velocity v k  in the entire image. The merging unit  170  also merges the elevation differences Δh k,l  to obtain the elevation h k  in the entire image. The merging unit  170  may repeat the calculation of the evaluation function in the merging process until the predetermined merging equation converges to the optimal value. 
     The random number generator  200  generates a predetermined random number. The threshold evaluation value calculation unit  210  applies the generated random number to the displacement velocity difference and the elevation difference and calculates an evaluation value using the evaluation function of equation (3). The threshold generator  220  determines a threshold based on the evaluation value. 
     Next, the operation of the image analyzing device  10  will be described with reference to the flowchart of  FIG.  3   . 
     The inter-image phase difference calculation unit  120  calculates phase differences φ m,n  between pairs of SAR images in the N SAR images stored in the SAR image storage  10  to obtain a phase difference image (step S 100 ). The inter-pixel phase difference calculation unit  130  calculates phase difference Δ k,l φ m,n  between close pixels k and l in one phase difference image (step S 101 ). The close pixels k, l may be a pair of pixels that are adjacent to each other vertically, horizontally, left or right, two pixels that sandwich one pixel, or a pair of pixels that are within a certain radius of one pixel. The inter-pixel phase difference calculation unit  130  may generate such a pair as described above only for some pixels in the image. When the pairs are generated only for some pixels in the image, information such as displacement, etc. is finally obtained only for some pixels. 
     The evaluation function generator  140  generates an evaluation function (equation (3)) that includes the shooting time difference t m,n , the baseline distance b m,n , and the phase difference Δ k,l φ m,n  (step S 102 ). 
     The random number generator  200  generates a predetermined random number (step S 110 ). The predetermined random number is a uniform random number between −π and π, as an example. 
     The threshold evaluation value calculation unit  210  sets Δv k,l =0 and Δh k,l =0 in the evaluation function of equation (3) and regards the generated random number as a phase difference to calculate an evaluation value (step S 111 ). It should be noted that, in detail, the random numbers are applied as phases before φ m,n  is calculated, instead of assigning a random numbers to φ m,n . The threshold evaluation value calculation unit  210  uses a value (for example, average value×3) based on an average of the values of the evaluation functions calculated using a large number of random numbers as the evaluation value, for example. The threshold evaluation value calculation unit  210  may also use a value based on an average value to which a variance is added as the evaluation value. 
     The threshold generator  220  determines the threshold based on the evaluation value (step S 112 ). The threshold generator  220  uses the evaluation value itself calculated by the threshold evaluation value calculation unit  210 , or the evaluation value to which a margin is added, to the threshold. 
     The evaluation function optimization unit  150  calculates for each pair of pixels the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  that maximizes the evaluation function (equation (3)) (step S 120 ). 
     The merging unit  170  checks whether any of the evaluation function values (evaluation values) calculated by the evaluation function optimization unit  150  have an evaluation value less than the threshold. When there are evaluation values below the threshold, the merging unit  170  determines not to use in the merging process the pair of pixels that was used when the evaluation value was calculated (step S 122 ). 
     The merging unit  170  then executes the merging process (step S 123 ). The merging process is a process which merges the displacement velocity differences Δv k,l  to obtain the displacement velocity v k  in the entire image, and merges the elevation differences Δh k,l  to obtain the elevation h k  for the entire image by the merging unit  170 . As mentioned above, the merging unit  170  does not use the pairs of pixels that were used when the evaluation value below the threshold was calculated in the merging process. 
     As explained above, in the first example embodiment, the threshold generator  220  calculates the evaluation value using random numbers and an evaluation function, and determines a threshold based on the calculated evaluation value, and the merging unit  170  executes a merging process by excluding pairs of pixels used when an evaluation value is calculated to be less than the threshold. The threshold is a similar value to the evaluation value corresponding to the displacement velocity difference which varies rapidly in space and has an extremely large degree of non-linearity. Therefore, by performing the merging process excluding the pairs of pixels used when the evaluation value below the threshold is calculated, a highly reliable merging result can be obtained. 
     Example Embodiment 2 
       FIG.  4    is a block diagram showing a configuration example of the image analyzing device of the second example embodiment. The image analyzing device  20  shown in  FIG.  4    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , a weight determination unit  160 , the merging unit  170 , the random number generator  200 , the threshold evaluation value calculation unit  210 , and the threshold generator  220 . 
     The components other than the weight determination unit  160  are the same as the components in the first example embodiment. However, the merging unit  170  performs a process different from the process in the first example embodiment. The weight determination unit  160  calculates the weights WV k,l , Wh k,l . 
     Next, the operation of the image analyzing device  20  will be described with reference to the flowchart of  FIG.  5   . The processes of steps S 100 -S 120  are the same as the processes in the first example embodiment (refer to  FIG.  3   ). 
     In the second example embodiment, the weight determination unit  160  calculates the weights Wv k,l , Wh k,l  (step S 121 ). The weight determination unit  160  uses the second-order differential or the like when calculating a weight. The weight determination unit  160  gives a weight proportional to the second-order differential to the evaluation value (calculated value of the evaluation function), for example. 
     When there is an evaluation value below the threshold, the weight determination unit  160  sets the weights Wv k,l , Wh k,l  corresponding to the pair of pixels used when the evaluation value was calculated to 0 (step S 124 ). 
     The merging unit  170  merges the displacement velocity differences Δv k,l  in the merging process to obtain the displacement velocity v k  in the entire image. The merging unit  170  also merges the elevation differences Δh k,l  in the merging process to obtain the elevation h k  in the entire image. 
     That is, in the merging process, the merging unit  170  calculates the displacement velocity v k  and the elevation h k  in the entire image using equation (4), the displacement velocity differences Δv k,l  and the elevation differences Δh k,l  obtained in the process of step S 120 , for example. When the calculated displacement velocity and the elevation are not converged, equation (4) is applied repeatedly to the other pixels until convergence is achieved (step S 125 ). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     4 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       v 
                       k 
                     
                     = 
                     
                       
                         
                           ∑ 
                           l 
                         
                         
                           
                             W 
                             
                               v 
                               
                                 k 
                                 , 
                                 l 
                               
                             
                           
                           ( 
                           
                             
                               v 
                               l 
                             
                             - 
                             
                               Δ 
                               ⁢ 
                               
                                 v 
                                 
                                   k 
                                   , 
                                   l 
                                 
                               
                             
                           
                           ) 
                         
                       
                       
                         
                           ∑ 
                           l 
                         
                         
                           W 
                           
                             v 
                             
                               k 
                               , 
                               l 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
                       h 
                       k 
                     
                     = 
                     
                       
                         
                           ∑ 
                           l 
                         
                         
                           
                             W 
                             
                               h 
                               
                                 k 
                                 , 
                                 l 
                               
                             
                           
                           ( 
                           
                             
                               h 
                               l 
                             
                             - 
                             
                               Δ 
                               ⁢ 
                               
                                 h 
                                 
                                   k 
                                   , 
                                   l 
                                 
                               
                             
                           
                           ) 
                         
                       
                       
                         
                           ∑ 
                           l 
                         
                         
                           W 
                           
                             h 
                             
                               k 
                               , 
                               l 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Once it is determined that equation (4) for v k  and h k  is converged, the process shown in  FIG.  5    is terminated. 
     As explained above, even in the second example embodiment, the threshold generator  220  calculates the evaluation value using random numbers and an evaluation function, and determines a threshold based on the calculated evaluation value, and the merging unit  170  executes a merging process by excluding pairs of pixels used when an evaluation value is calculated to be less than the threshold. The threshold is a similar value to the evaluation value corresponding to the displacement velocity difference which varies rapidly in space and has an extremely large degree of non-linearity. Therefore, by performing the merging process excluding the pairs of pixels used when the evaluation value below the threshold is calculated, a highly reliable merging result can be obtained. 
     In addition, in the second example embodiment, since the weights Wv k,l , Wh k,l  are reflected in the merging process, convergence is easier to achieve in the merging process. 
     Example Embodiment 3 
       FIG.  6    is a block diagram showing a configuration example of the image analyzing device of the third example embodiment. The image analyzing device  30  shown in  FIG.  6    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the merging unit  170 , a displacement and elevation evaluation function generator  180 , the random number generator  200 , the threshold evaluation value calculation unit  210 , and the threshold generator  220 . 
     The components other than the displacement and elevation evaluation function generator  180  are the same as the components in the first example embodiment shown in  FIG.  2   . However, the merging unit  170  performs the process in the first example embodiment and an added process. 
     In the third example embodiment, the merging process is executed by considering prior information indicating a degree to which a displacement velocity difference and an elevation of close pixels should be similar. The displacement and elevation evaluation function generator  180  generates a conditional formula (evaluation function) for evaluating a degree to which a displacement velocity difference and an elevation of close pixels are similar. For example, the displacement and elevation evaluation function generator  180  generates the conditional formula of equation (5). 
       [Math. 5] 
       α h |h k −h l | 2 +β h h k   2 +α v |v k −v l | 2 +β v v k   2   (5)
 
     In equation (5), α v  is a value representing how similar the displacement velocities v k  at neighboring pixels are. α n  is a value representing how similar the heights (elevations) at neighboring pixels are. β v  is a value representing how close to 0 the displacement velocity v k  should be. β h  is a value representing how close to 0 the elevation h k  should be. 
     Next, the operation of the image analyzing device  30  will be described with reference to the flowchart of  FIG.  7   . The processes of steps S 100 -S 122  are the same as the processes in the first example embodiment (refer to  FIG.  3   ). In the third example embodiment, in the process of step S 120 , the evaluation function optimization unit  150  may optimize the evaluation function (equation (3)) generated by the evaluation function generator  140 , however the evaluation function optimization unit  150  may optimize a function made by subtracting the formula (equation (5)) generated by the displacement and elevation evaluation function generator  180  from the evaluation function generated by the evaluation function generator  140 . 
     In the third example embodiment, the merging unit  170  performs the same merging process as in the first example embodiment while decreasing the value of the conditional formula (equation (5)) generated by the displacement and elevation evaluation function generator  180  (step S 123 A). 
     In the third example embodiment, since the displacement and elevation evaluation function generator  180  generates a conditional formula for evaluating a degree to which a displacement velocity difference and an elevation difference of neighboring pixels are similar, and the merging unit  170  uses the conditional formula in the merging process, a displacement velocity and an elevation with respect to an imaginary pixel between the pixel k and the pixel l will now be used and a converged displacement velocity v k  and a converged elevation h k  are easier to obtain, even if it is difficult to obtain the optimal displacement velocity v k  or the optimal elevation h k  in the merging process (for example, the calculated value becomes 0 or does not converge). 
     Example Embodiment 4 
       FIG.  8    is a block diagram showing a configuration example of the image analyzing device of the fourth example embodiment. The image analyzing device  40  shown in  FIG.  8    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the weight determination unit  160 , the merging unit  170 , the displacement and elevation evaluation function generator  180 , the random number generator  200 , the threshold evaluation value calculation unit  210 , and the threshold generator  220 . 
     The components other than the displacement and elevation evaluation function generator  180  are the same as the components in the second example embodiment shown in  FIG.  4   . However, the merging unit  170  performs the process in the second example embodiment and an added process. In addition, the displacement and elevation evaluation function generator  180  performs the same process as it of the displacement and elevation evaluation function generator  180  in the third example embodiment. That is, the displacement and elevation evaluation function generator  180  generates the conditional formula of equation (5). 
     Next, the operation of the image analyzing device  20  will be described with reference to the flowchart of  FIG.  9   . The processes of steps S 100 -S 124  are the same as the processes in the second example embodiment (refer to  FIG.  5   ). 
     The merging unit  170  merges the displacement velocity differences Δv k,l  in the merging process to obtain a displacement velocity v k  in the entire image. The merging unit  170  also merges the elevation differences Δh k,l  in the merging process to obtain an elevation h k  in the entire image. 
     In the fourth example embodiment, the merging unit  170  calculate a displacement velocity v k  and an elevation h k  using equation (6), the displacement velocity differences Δv k,l  and the elevation differences Δh k,l  obtained in the process of step S 120 . When the calculated displacement velocity v k  and the elevation h k  are not converged, equation (6) is applied repeatedly to the other pixels until convergence is achieved (step S 125 A). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     6 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     
                       
                         
                           v 
                           k 
                         
                         = 
                         
                           
                             
                               
                                 ∑ 
                                 l 
                               
                               
                                 
                                   W 
                                   
                                     h 
                                     
                                       k 
                                       , 
                                       l 
                                     
                                   
                                 
                                 ( 
                                 
                                   
                                     v 
                                     l 
                                   
                                   - 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                       v 
                                       
                                         k 
                                         , 
                                         l 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 α 
                                 v 
                               
                               ⁢ 
                               
                                 v 
                                 l 
                               
                             
                           
                           
                             
                               β 
                               v 
                             
                             + 
                             
                               
                                 ∑ 
                                 l 
                               
                               
                                 ( 
                                 
                                   
                                     
                                       W 
                                       v 
                                     
                                     
                                       k 
                                       , 
                                       l 
                                     
                                   
                                   + 
                                   
                                     α 
                                     v 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           h 
                           k 
                         
                         = 
                         
                           
                             
                               
                                 ∑ 
                                 l 
                               
                               
                                 
                                   ( 
                                   
                                     
                                       h 
                                       l 
                                     
                                     - 
                                     
                                       Δ 
                                       ⁢ 
                                       
                                         h 
                                         
                                           k 
                                           , 
                                           l 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 α 
                                 h 
                               
                               ⁢ 
                               
                                 v 
                                 l 
                               
                             
                           
                           
                             
                               β 
                               h 
                             
                             + 
                             
                               
                                 ∑ 
                                 l 
                               
                               
                                 ( 
                                 
                                   
                                     W 
                                     
                                       h 
                                       
                                         k 
                                         , 
                                         l 
                                       
                                     
                                   
                                   + 
                                   
                                     α 
                                     h 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Once it is determined that equation (6) for v k  and h k  have converged, the process shown in  FIG.  9    is terminated. 
     Since equation (6) includes α(α v , α h ) and β(β v , β h ), the fourth example embodiment has the same effect as it of the third example embodiment. 
     Example Embodiment 5 
     When performing optimization using an evaluation function, it is possible to fall into a local solution.  FIG.  10    is an explanatory diagram for explaining improvement, etc. of falling into a local solution. As shown in  FIG.  10   , given an initial value of a certain condition, a non-optimal evaluation value may be obtained as a result of optimization. In the fifth example embodiment and the sixth example embodiment, the merged displacement velocity difference Δv k,l  of the pixels k, l is recalculated. As a result, for example, it is assumed that the point e in  FIG.  10    is obtained as the displacement velocity difference Δv k,l . As shown in  FIG.  10   , the possibility of obtaining the evaluation value that is the optimal solution increases by performing the optimization again using the evaluation function with the displacement velocity difference Δv k,l  of the point e as the initial value. 
     Although the displacement velocity difference Δv k,l  is illustrated in  FIG.  10   , the same concept applies to the elevation difference Δh k,l . 
       FIG.  11    is a block diagram showing a configuration example of the image analyzing device of the fifth example embodiment. The image analyzing device  50  shown in  FIG.  11    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the merging unit  170 , a recalculation unit  190 , the random number generator  200 , the threshold evaluation value calculation unit  210 , and the threshold generator  220 . 
     The components other than the recalculation unit  190  are the same as the components in the first example embodiment shown in  FIG.  2   . However, the merging unit  170  performs the process in the first example embodiment and an added process. 
     The recalculation unit  190  recalculates the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  of pixels k and l from the displacement velocity v k  and the elevation h k  calculated by the merging unit  170 . 
     Next, the operation of the image analyzing device  50  will be described with reference to the flowchart of  FIG.  12   . The processes of steps S 100 -S 123  are the same as the processes in the first example embodiment (refer to  FIG.  3   ). 
     After executing the process of step S 123 , the merging unit  170  checks whether the termination condition has been satisfied (step S 130 ). 
     The termination condition is, for example, a condition using the result (displacement velocity difference Δv k,l  and elevation difference Δh k,l ) of the process of optimization input to the merging unit  170 . As an example, the merging unit  170  determines that the termination condition is satisfied, when the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  from the evaluation function optimizer  150  is not changed from the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  previously input from the evaluation function optimizer  150 . 
     The merging unit  170  may determine that the termination condition is satisfied, when the situation, that the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  from the evaluation function optimizer  150  is not changed from the displacement velocity difference Δv k,l  and the elevation difference Δh k,l  previously input from the evaluation function optimizer  150 , continues for a predetermined number of times. 
     When the termination condition is not satisfied, the recalculation unit  190  recalculates the displacement difference Δv k,l  and the elevation difference Δh k,l  of pixels k and l from the displacement velocity v k  and the elevation h k  calculated by the merging unit  170  (step S 131 ). That is, for example, the recalculation unit  190  finds a difference between the displacement velocities v k  and a difference between the elevations h k  of two neighboring pixels to obtain the displacement velocity difference Δv k,l  and the elevation difference Δh k,l . The recalculation unit  190  gives the calculated displacement velocity difference Δv k,l  and the elevation difference Δh k,l  to the evaluation function optimization unit  150  as initial values (step S 132 ). The evaluation function optimization unit  150  again executes the process of step S 120 . 
     In the fifth example embodiment, the possibility of obtaining the evaluation value that is the optimal solution increases and a higher reliable merging result can be obtained. 
     Example Embodiment 6 
       FIG.  13    is a block diagram showing a configuration example of the image analyzing device of the sixth example embodiment. The image analyzing device  60  shown in  FIG.  13    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the weight determination unit  160 , the merging unit  170 , a recalculation unit  190 , the random number generator  200 , the threshold evaluation value calculation unit  210 , and the threshold generator  220 . 
     The components other than the recalculation unit  190  are the same as the components in the second example embodiment shown in  FIG.  4   . However, the merging unit  170  performs the process in the second example embodiment and an added process. The recalculation unit  190  performs the same processing as it in the fifth example embodiment. 
     Next, the operation of the image analyzing device  60  will be described with reference to the flowchart of  FIG.  14   . The processes of steps S 100 -S 125  are the same as the processes in the second example embodiment (refer to  FIG.  5   ). The processes of steps S 130 -S 132  are the same as the processes in the fifth example embodiment (refer to  FIG.  12   ). 
     In the sixth example embodiment, as in the case of the fifth example embodiment, the possibility of obtaining the evaluation value that is the optimal solution increases and a higher reliable merging result can be obtained. 
     Example Embodiment 7 
     The process of optimization using an evaluation function is a process requiring a large calculation amount. In the seventh example embodiment and the eighth example embodiment, a mechanism to reduce a calculation amount is added.  FIG.  15    is an explanatory diagram for explaining the mechanism for reducing a calculation amount. As shown in  FIG.  15   , a loose threshold is used. The loose threshold is smaller than the strict threshold. The loose threshold is determined based on an evaluation value calculated using random numbers and the evaluation function of equation (3), for example. As an example, when the average value×3 of the value of the evaluation function calculated by the threshold generator  220  using random numbers is set as the threshold, the loose threshold is determined to be the average value×2. 
     As shown in  FIG.  15   , when the evaluation value actually calculated using an evaluation function (for example, the evaluation function of equation (3)) using a certain initial value is less than the loose threshold, the process of optimization using the initial value is considered to have the possibility of not outputting the optimal value. When the calculated evaluation value is greater than or equal to the strict threshold, the process of optimization using the initial value is likely to output an optimal value. 
     Referring to  FIG.  10   , it is preferable that the process of optimization (recalculation of the evaluation function) is performed again with the displacement velocity difference Δv k,l , as the initial value, recalculated from the merged displacement velocity v k . However, even if the process of optimization is performed again with the displacement velocity difference Δv k,l , as the initial value, corresponding to the evaluation value below the loose threshold, a value closer to the optimal value cannot be obtained. Therefore, it can be said that the process of optimization had not better be performed based on the displacement velocity difference Δv k,l  corresponding to the evaluation value below the loose threshold. When the process of optimization is not performed, the displacement velocity difference Δv k,l  corresponding to the evaluation value below the loose threshold will not be reflected to the merging result. 
       FIG.  16    is a block diagram showing a configuration example of the image analyzing device of the seventh example embodiment. The image analyzing device  70  shown in  FIG.  16    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the merging unit  170 , the recalculation unit  190 , the random number generator  200 , the threshold evaluation value calculation unit  210 , the threshold generator  220 , and a second threshold generator  221 . 
     The components other than the second threshold generator  221  are the same as the components in the fifth example embodiment shown in  FIG.  11   . However, the evaluation function optimization unit  150  performs the process in the fifth example embodiment and an added process. 
     Next, the operation of the image analyzing device  70  will be described with reference to the flowchart of  FIG.  17   . The processes of steps S 100 -S 132  are the same as the processes in the fifth example embodiment (refer to  FIG.  12   ). 
     In the seventh example embodiment, the second threshold generator  221  generates the loose threshold described above. The threshold generated by the threshold generator  220  corresponds to the strict threshold described above. 
     After generating the evaluation function, the evaluation function optimization unit  150  checks whether the obtained evaluation value is greater than or equal to the loose threshold (step S 133 ). When the evaluation value is greater than or equal to the loose threshold, the processes from step S 120  onward are executed. That is, the process of optimization (step S 120 ) and subsequent processes are executed. 
     When the obtained evaluation value is less than the loose threshold, the process of step S 120  is not performed. In other words, the process of optimization is skipped. 
     In the seventh example embodiment, since the process of optimization is not performed in case there is a high possibility that the calculation to optimize (in this example embodiment, maximize) the evaluation function will not yield the optimal value (in this example embodiment, the maximum value), a calculation amount is reduced. 
     Example Embodiment 8 
       FIG.  18    is a block diagram showing a configuration example of the image analyzing device of the eighth example embodiment of an image analyzing device. The image analyzing device  80  shown in  FIG.  18    includes the SAR image storage  100 , the shooting time and orbit storage  110 , the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the weight determination unit  160 , the merging unit  170 , the recalculation unit  190 , the random number generator  200 , the threshold evaluation value calculation unit  210 , the threshold generator  220 , and the second threshold generator  221 . 
     The components other than the second threshold generator  221  are the same as the components in the sixth example embodiment shown in  FIG.  13   . However, the evaluation function optimization unit  150  performs the process in the sixth example embodiment and an added process. 
     Next, the operation of the image analyzing device  80  will be described with reference to the flowchart of  FIG.  19   . The processes of steps S 100 -S 132  are the same as the processes in the sixth example embodiment (refer to  FIG.  14   ). 
     In the eighth example embodiment, the second threshold generator  221  generates the loose threshold. After generating the evaluation function, the evaluation function optimization unit  150  checks whether the obtained evaluation value is greater than or equal to the loose threshold (step S 133 ). When the evaluation value is greater than or equal to the loose threshold, the processes from step S 120  onward are executed. That is, the process of optimization (step S 120 ) and subsequent processes are executed. 
     When the obtained evaluation value is less than the loose threshold, the process of step S 120  is not performed. In other words, the process of optimization is skipped. 
     In the eighth example embodiment, as in the case of the seventh example embodiment, a calculation amount related to the process of optimization is reduced. 
     In each of the above example embodiments, the image analyzing devices are shown that handle both the displacement velocity v k  and the elevation h k . However, the image analyzing device may handle only the displacement velocity v k  or only the elevation h k . 
     When the image analyzing device handles only the displacement velocity v k , an evaluation function is used in which the term regarding the elevation difference is deleted in the evaluation function illustrated as equation (1), for example. In addition, an evaluation function in which b m,n Δh k,l  is deleted in the evaluation function illustrated as equation (3) is used. 
     When the image analyzing device handles only the elevation h k , an evaluation function is used in which the term regarding displacement is deleted in the evaluation function illustrated as equation (1), for example. In addition, an evaluation function in which t m,n Δv k,l  is deleted in the evaluation function illustrated as equation (3) is used. 
     In each of the above example embodiments, the analysis targets are a displacement difference (displacement velocity difference) and an elevation difference, however other elements can also be used as analysis targets. As an example, a thermal expansion coefficient of the observation target of synthetic aperture radar can be analyzed. 
     When using the above evaluation functions of equations (1) and (3) when analyzing a thermal expansion coefficient, the temperature difference at different observation points in time (temperature difference when each image comprising a pair is taken) is used instead of the shooting time difference t m,n . In addition, instead of the displacement velocity difference Δv k,l , the difference in thermal expansion coefficient between close pixels is used. For example, the thermal expansion coefficient can be obtained by using the evaluation functions of equations (1) and (3). 
     It is also possible to generate a device that combines the function of analyzing thermal expansion coefficient with the function of each of the above example embodiments of analyzing devices. 
     The image analyzing device and the image analyzing method of each of the above example embodiments can be suitably applied not only to an analysis of general displacement of structures on the ground surface or above ground, but also to an analysis of displacement based on underground construction and a ground subsidence analysis of a filled ground. 
     The functions (processes) in the above example embodiments may be realized by a computer having a processor such as a central processing unit (CPU), a memory, etc. For example, a program for performing the method (processing) in the above example embodiments may be stored in a storage device (storage medium), and the functions may be realized with the CPU executing the program stored in the storage device. 
       FIG.  20    is a block diagram showing an example of a computer having a CPU. The computer is implemented in the data processing device. The CPU  1000  executes processing in accordance with an image analysis program (software component: codes) stored in a storage device  1001  to realize the functions in the above example embodiments. That is, the functions of the the inter-image phase difference calculation unit  120 , the inter-pixel phase difference calculation unit  130 , the evaluation function generator  140 , the evaluation function optimization unit  150 , the merging unit  170 , the displacement and elevation evaluation function generator  180 , the recalculation unit  190 , the random number generator  200 , the threshold evaluation value calculation unit  210 , the threshold generator  220 , and the second threshold generator  221  in the image analyzing devices shown in  FIG.  2   ,  FIG.  4   ,  FIG.  6   ,  FIG.  8   ,  FIG.  11   ,  FIG.  13   ,  FIG.  16   ,  FIG.  18   . 
     The storage device  1001  is, for example, a non-transitory computer readable media. The non-transitory computer readable medium is one of various types of tangible storage media. Specific examples of the non-transitory computer readable media include a magnetic storage medium (for example, hard disk), a magneto-optical storage medium (for example, magneto-optical disk), a compact disc-read only memory (CD-ROM), a compact disc-recordable (CD-R), a compact disc-rewritable (CD-R/W), and a semiconductor memory (for example, a mask ROM, a PROM (programmable ROM), an EPROM (erasable PROM), a flash ROM). The memory device  1001  can also be used as the SAR image storage  100  and the shooting time and orbit storage  110 . 
     The image analysis program may be stored in various types of transitory computer readable media. The transitory computer readable medium is supplied with the program through, for example, a wired or wireless communication channel, i.e., through electric signals, optical signals, or electromagnetic waves. 
     A memory  1002  is a storage means implemented by a RAM (Random Access Memory), for example, and temporarily stores data when the CPU  1000  executes processing. It can be assumed that a program held in the storage device  1001  or a temporary computer readable medium is transferred to the memory  1002  and the CPU  1000  executes processing based on the program in the memory  1002 . 
       FIG.  21    is a block diagram showing the main part of the image analyzing device. The image analyzing device  1  shown in  FIG.  21    comprises an inter-image phase difference calculation unit (inter-image phase difference calculation means)  12  (in the example embodiments, realized by the inter-image phase difference calculation unit  120 ) which calculates a phase difference image of a pair of images, an inter-pixel phase difference calculation unit (inter-pixel phase difference calculation means)  13  (in the example embodiments, realized by the inter-pixel phase difference calculation unit  130 ) which calculates a phase difference between close pixels in the phase difference image, an evaluation function generation unit (evaluation function generation means)  14  (in the example embodiments, realized by the evaluation function generator  140 ) which generates an evaluation function that includes at least the phase difference between pixels, an optimization unit (optimization means)  15  (in the example embodiments, realized by the evaluation function optimization unit  150 ) which optimizes the evaluation function for each pair of pixels or each pair of close pixels, a random number generation unit (random number generation means)  21  (in the example embodiments, realized by the random number generator  200 ) which generates a random number, a threshold setting unit (threshold setting means)  22  (in the example embodiments, realized by the threshold evaluation value calculation unit  210  and the threshold generator  220 ) which sets a threshold based on a result of evaluation of the random number using the evaluation function, and a merging unit  17  which obtains merged data (in the example embodiments, the displacement velocity v k , the elevation h k ) of an entire image by merging values of variables (in the example embodiments, the displacement velocity difference Δv k,l , the elevation difference Δh k,l ) when the optimization unit  15  performs optimization except for variables for which evaluation value using the evaluation function is less than the threshold. 
     A part of or all of the above example embodiments may also be described as, but not limited to, the following supplementary note. 
     (Supplementary note 1) An image analyzing device comprising:
         inter-image phase difference calculation means for calculating a phase difference image of a pair of images;   inter-pixel phase difference calculation means for calculating a phase difference between close pixels in the phase difference image;   evaluation function generation means for generating an evaluation function that includes at least the phase difference between pixels;   optimization means for optimizing the evaluation function for each pair of pixels or each pair of close pixels;   random number generation means for generating a random number;   threshold setting means for setting a threshold based on a result of evaluation of the random number using the evaluation function; and   merging means for obtaining merged data of an entire image by merging values of variables when the optimization means performs optimization except for variables for which evaluation value using the evaluation function is less than the threshold.       

     (Supplementary note 2) The image analyzing device according to Supplementary note 1, wherein
         the evaluation function generation means generates the evaluation function that includes a shooting time difference of the pair of images, and in which a difference in displacement velocity between close pixels is the variable, and   the merging means merges differences in displacement velocity to obtain the displacement velocity of the pixel of the entire image.       

     (Supplementary note 3) The image analyzing device according to Supplementary note 1 or 2, wherein
         the evaluation function generation means generates the evaluation function that includes a baseline distance, and in which a difference in elevation between close pixels is the variable, and   the merging means merges differences in elevation to obtain the elevation of the pixel of the entire image.       

     (Supplementary note 4) The image analyzing device according to any one of Supplementary notes 1 to 3, further comprising
         recalculation means for deriving a value of the variable from merged data obtained by the merging means, and sets derived value of the variable as an initial value when optimizing the evaluation function.       

     (Supplementary note 5) The image analyzing device according to Supplementary note 4, further comprising
         second threshold generation means for generating a second threshold that is smaller than the threshold, and   determination means for determining whether or not there is a variable that makes the evaluation value using the evaluation function less than the second threshold,   wherein the optimization means does not execute a process of optimization when the determination means determines there is the variable.       

     (Supplementary note 6) The image analyzing device according to any one of Supplementary notes 1 to 5, wherein
         the evaluation function generation means generates the evaluation function that includes a temperature difference, and in which a difference in thermal expansion coefficient between close pixels is the variable, and   the merging means merges differences in thermal expansion coefficient to obtain the thermal expansion coefficient of the pixel of the entire image.       

     [Supplementary note 7) An image analyzing method comprising:
         calculating a phase difference image of a pair of images;   calculating a phase difference between close pixels in the phase difference image;   generating an evaluation function that includes at least the phase difference between pixels;   optimizing the evaluation function for each pair of pixels or each pair of close pixels;   generating a random number;   setting a threshold based on a result of evaluation of the random number using the evaluation function; and   obtaining merged data of an entire image by merging values of variables when the evaluation function is optimized except for variables for which evaluation value using the evaluation function is less than the threshold.       

     (Supplementary note 8) The image analyzing method according to Supplementary note 7, further comprising
         generating the evaluation function that includes a shooting time difference of the pair of images, and in which a difference in displacement velocity between close pixels is the variable, and   merging differences in displacement velocity to obtain the displacement velocity of the pixel of the entire image.       

     (Supplementary note 9) The image analyzing method according to Supplementary note 7 or 8, further comprising
         generating the evaluation function that includes a baseline distance, and in which a difference in elevation between close pixels is the variable, and   merging differences in elevation to obtain the elevation of the pixel of the entire image.       

     (Supplementary note 10) An image analyzing program causing a computer to execute
         the image analyzing program causes a computer to execute:   a process of calculating a phase difference image of a pair of images;   a process of calculating a phase difference between close pixels in the phase difference image;   a process of generating an evaluation function that includes at least the phase difference between pixels;   a process of optimizing the evaluation function for each pair of pixels or each pair of close pixels;   a process of generating a random number;   a process of setting a threshold based on a result of evaluation of the random number using the evaluation function; and   a process of obtaining merged data of an entire image by merging values of variables when the evaluation function is optimized except for variables for which evaluation value using the evaluation function is less than the threshold.       

     (Supplementary note 11) The image analyzing program according to Supplementary note 10, causing the computer to further execute
         the image analyzing program causes the computer to further execute   a process of generating the evaluation function that includes a shooting time difference of the pair of images, and in which a difference in displacement velocity between close pixels is the variable, and   a process of merging differences in displacement velocity to obtain the displacement velocity of the pixel of the entire image.       

     (Supplementary note 12) The image analyzing program according to Supplementary note 10 or 11, causing the computer to further execute
         a process of generating the evaluation function that includes a baseline distance, and in which a difference in elevation between close pixels is the variable, and   a process of merging differences in elevation to obtain the elevation of the pixel of the entire image.       

     (Supplementary note 13) A computer readable recording medium storing an image analyzing program, wherein
         the image analyzing program causes a computer to execute:   a process of calculating a phase difference image of a pair of images;   a process of calculating a phase difference between close pixels in the phase difference image;   a process of generating an evaluation function that includes at least the phase difference between pixels;   a process of optimizing the evaluation function for each pair of pixels or each pair of close pixels;   a process of generating a random number;   a process of setting a threshold based on a result of evaluation of the random number using the evaluation function; and   a process of obtaining merged data of an entire image by merging values of variables when the evaluation function is optimized except for variables for which evaluation value using the evaluation function is less than the threshold.       

     (Supplementary note 14) The recording medium according to Supplementary note 13, wherein
         the image analyzing program causes the computer to further execute   a process of generating the evaluation function that includes a shooting time difference of the pair of images, and in which a difference in displacement velocity between close pixels is the variable, and   a process of merging differences in displacement velocity to obtain the displacement velocity of the pixel of the entire image.       

     (Supplementary note 15) The recording medium according to Supplementary note 13 or 14, wherein
         the image analyzing program causes the computer to further execute   a process of generating the evaluation function that includes a baseline distance, and in which a difference in elevation between close pixels is the variable, and   a process of merging differences in elevation to obtain the elevation of the pixel of the entire image.       

     Although the invention of the present application has been described above with reference to example embodiments, the present invention is not limited to the above example embodiments. Various changes can be made to the configuration and details of the present invention that can be understood by those skilled in the art within the scope of the present invention. 
     REFERENCE SIGNS LIST 
     
         
           1  Image analyzing device 
           12  Inter-image phase difference calculation unit 
           13  Inter-pixel phase difference calculation unit 
           14  Evaluation function generator 
           15  Optimization unit 
           17  Merging unit 
           21  Random number generator 
           22  Threshold setting unit 
           10 ,  20 ,  30 ,  40 ,  50 ,  60 ,  70 ,  80  Image analyzing device 
           100  SAR image storage 
           110  Shooting time and orbit storage 
           120  Inter-image phase difference calculation unit 
           130  Inter-pixel phase difference calculation unit 
           140  Evaluation function generator 
           150  Evaluation function optimization unit 
           160  Weight determination unit 
           170  Merging unit 
           180  Displacement and elevation evaluation function generator 
           190  Recalculation unit 
           200  Random number generator 
           210  Threshold evaluation value calculation unit 
           220  Threshold generator 
           221  Second threshold generator 
           1000  CPU 
           1001  Storage device 
           1002  Memory