Patent Publication Number: US-10311576-B2

Title: Image processing device and image processing method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2016-187515, filed on Sep. 26, 2016, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to an image processing device and an image processing method. 
     BACKGROUND 
     In recent years, a system that displays an image by using an augmented reality (AR) technology has become popular (see, for example, Patent Document 1). As an example of the AR technology, an object is photographed by using a camera mounted on a personal computer (PC), a portable terminal device, or the like, and the position and posture of the camera in a three-dimensional space are estimated from an image of the object. Content information is superimposed and displayed in an arbitrary position within the image by using the determined position and posture of the camera as a reference. 
       FIG. 1  illustrates an example of a method for obtaining the position and posture of a camera by using feature points included in a captured image. In this method, a three-dimensional map  201  indicating a set of three-dimensional coordinates of map points  211  on an object is generated in advance. 
     When an image  202  is captured, the map points  211  are projected onto the image  202  by using a transformation matrix M for transforming a three-dimensional coordinate system  203  into a camera coordinate system  204  such that projection points  212  are obtained. The position and posture of the camera in the three-dimensional coordinate system  203  are estimated by associating the projection points  212  with feature points  213  detected from the image  202 . As an example, the position of the camera is indicated by a relative position of the camera coordinate system  204  with respect to the three-dimensional coordinate system  203 , and the posture of the camera is indicated by a relative angle of the camera coordinate system  204  with respect to the three-dimensional coordinate system  203 . 
     Three-dimensional coordinate Sp of a map point p, two-dimensional coordinate xp′ of a projection point that corresponds to the map point p, and two-dimensional coordinate xp of a feature point that corresponds to the map point p are respectively expressed according to the expressions below.
 
 Sp =( x,y,z )  (1)
 
 xp ′=( u′,v ′)  (2)
 
 xp =( u,v )  (3)
 
     In this case, the sum of squares E of a distance between the projection point and the feature point on the image is expressed by the expression below. 
     
       
         
           
             
               
                 
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                             xp 
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                           - 
                           xp 
                         
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     The position and posture of the camera are determined by obtaining a transformation matrix M that minimizes the sum of squares E in expression (4). 
       FIG. 2  illustrates an example of a method for generating the three-dimensional map  201 . In this generation method, stereoscopic photographing and stereoscopic measurement are used. An image  301  and an image  302  that are respectively captured from a photographing position  311  and a photographing position  312  are used as key frames, and a feature point  313  in the image  301  and a feature point  314  in the image  302  are associated with each other such that a map point  315  in a three-dimensional space is restored. A plurality of map points are restored by associating a plurality of feature points in an image with a plurality of feature points in another image, and a three-dimensional map  201  indicating a set of the plurality of map points is generated. 
     Technologies, such as a polyhedron representation for computer vision, visual tracking of structures, and machine perception of three-dimensional solids, are also known (see, for example, Non-Patent Document 1 to Non-Patent Document 3).
     Patent Document 1: Japanese Laid-open Patent Publication No. 2015-118641   Non-Patent Document 1: Bruce G. Baumgart, “A polyhedron representation for computer vision”,  Proceedings of the May  19-22, 1975 , national computer conference and exposition , pp. 589-596, 1975   Non-Patent Document 2: Tom Drummond and Roberto Cipolla, “Real-Time Visual Tracking of Complex Structures”,  IEEE Trans. Pattern Analysis and Machine Intelligence , pp. 932-946, 2002   Non-Patent Document 3: L. G. Robert, “Machine perception of three-dimensional solids”,  MIT Lincoln Lab. Rep., TR 3315, pp. 1-82, May 1963   

     SUMMARY 
     According to an aspect of the embodiments, a non-transitory computer-readable recording medium stores an image processing program causing a computer to execute the following process. 
     (1) The computer extracts a plurality of candidate lines that are observed from a position of an imaging device that captures an image of an object from among a plurality of candidate lines included in shape information of the object. 
     (2) The computer generates plural pieces of association information indicating a prescribed number of combinations obtained by respectively associating the prescribed number of candidate lines of the observed plurality of candidate lines with the prescribed number of feature lines of a plurality of feature lines detected from the image. 
     (3) The computer determines an association result according to respective errors of the plural pieces of association information. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  illustrates a method for obtaining the position and posture of a camera; 
         FIG. 2  illustrates a method for generating a three-dimensional map; 
         FIG. 3  illustrates an image of an object; 
         FIG. 4  illustrates CAD data; 
         FIG. 5A  illustrates edge lines; 
         FIG. 5B  illustrates association of edge lines and contour lines; 
         FIG. 5C  illustrates superimposition display; 
         FIG. 6  is a functional block diagram of an image processing device; 
         FIG. 7  is a flowchart of image processing; 
         FIG. 8  is a functional block diagram illustrating a specific example of an image processing device; 
         FIG. 9  is a flowchart illustrating a specific example of image processing; 
         FIG. 10  illustrates a specified rectangular region; 
         FIG. 11  illustrates a specified circular region; 
         FIG. 12  illustrates a reference line; 
         FIG. 13  illustrates candidate lines; 
         FIG. 14  illustrates remaining candidate lines; 
         FIG. 15  illustrates candidate lines indicating an outline edge of an object; 
         FIG. 16  illustrates candidate lines indicating an outer periphery of an object; 
         FIG. 17  illustrates corresponding pairs; 
         FIG. 18  illustrates a calculation method based on the area of a region; 
         FIG. 19  illustrates a calculation method based on a distance; 
         FIG. 20  illustrates line segments rotated by 180 degrees; 
         FIG. 21A  illustrates four candidate lines parallel to each other; 
         FIG. 21B  illustrates two candidate lines that exist on the same straight line; and 
         FIG. 22  is a block diagram of an information processing device. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments are described below in detail with reference to the drawings. 
     In a case in which computer-aided design (CAD) data of an object is used as the three-dimensional map  201  of  FIG. 1  when obtaining the position and posture of a camera, a feature of “appearance” such as a pattern or a tint is often different between the CAD data and the object. When it is assumed that this feature of “appearance” is coincident, it is difficult to automatically associate a feature point in an image with a map point indicated by the CAD data by performing image processing. Therefore, the feature point and the map point may be manually associated by operating a mouse on a screen of a PC. In this case, it is conceivable that the problems below are generated. 
     (A) It is difficult to accurately detect a feature point from an image. 
     (B) It is difficult to perform an operation to select a projection point obtained by projecting a map point onto an image and the feature point, by using a mouse or the like. 
     (C) It is difficult to perform an operation to select the projection point and the feature point, and the number of combinations (corresponding pairs) of the projection point and the feature point that are selected is limited due to time and effort of a manual operation. 
     (D) The number of corresponding pairs is small, and therefore the accuracy of the calculation of the position and posture of a camera is reduced. 
     Accordingly, a method for associating edge lines detected from an image with contour lines indicated by CAD data, as described in Patent Document 1 or the prior Japanese Patent Application No. 2015-218318, is also conceivable. 
       FIG. 3  illustrates an example of an image of an object, and  FIG. 4  illustrates an example of CAD data that indicates the shape of the object of  FIG. 3 .  FIG. 5A  to  FIG. 5C  illustrate an example of the association of edge lines detected from the image of  FIG. 3  with contour lines indicated by the CAD data of  FIG. 4 . 
     First, an image processing device such as a portable terminal device performs edge detection processing so as to detect edge lines from an image, as illustrated in  FIG. 5A . Then, as illustrated in  FIG. 5B , the image processing device displays contour lines indicated by CAD data and the detected edge lines in the image, and a user selects an edge line and a contour line by using a mouse or the like so as to associate these lines with each other. In order to obtain the position and posture of a camera, it is preferable that at least four corresponding pairs be used. 
     The image processing device calculates the position and posture of the camera by using combinations of the edge line and the contour line that have been associated. As illustrated in  FIG. 5C , the image processing device superimposes and displays the contour lines indicated by the CAD data onto the image of the object according to the calculated position and posture of the camera. 
     By employing the association method above, edge lines can be detected accurately, and an edge line and a contour line can be easily selected, and therefore problems (A) and (B) described above can be solved, but it is conceivable that the problems below are generated. 
     (E) The number of combinations (corresponding pairs) of a contour line and an edge line that are selected is limited due to time and effort of a manual operation. 
     (F) The number of corresponding pairs is small, and therefore the accuracy of the calculation of the position and posture of a camera is reduced. 
     Accordingly, a method for automatically adding a corresponding pair and recalculating the position and posture of a camera, as described in Japanese Patent Application No. 2016-66086, which is another prior application, is also conceivable. The calculation accuracy is improved by increasing the number of corresponding pairs. However, also in this method, a prescribed number of initial corresponding pairs are selected by a user, and a specific method for automatically selecting initial corresponding pairs is not described. 
     When a user who is not an expert manually selects corresponding pairs by visual observation, it takes time to perform an operation and an erroneous selection may be performed. 
     A method for performing brute-force calculation by using all of the combinations of an edge line detected from an image and a contour line indicated by CAD data is also conceivable. As an example, when four edge lines are selected from m edge lines and four contour lines are selected from n contour lines such that four corresponding pairs are generated, the total number of combinations is  m C 4 × n C 4 . Therefore, when the number of edge lines and the number of contour lines increase, the total number of combinations becomes enormous, and a calculation amount for generating corresponding pairs increases. 
     The problems above are not generated only in a case in which an image of an object is associated with CAD data, but are also generated in a case in which the image of the object is associated with other shape information. 
       FIG. 6  is an example of a functional configuration of an image processing device according to the embodiments. An image processing device  601  illustrated in  FIG. 6  includes a storage  611 , a generator  612 , and a determination unit  613 . The storage  611  stores shape information  621  of an object. 
       FIG. 7  is a flowchart illustrating an example of image processing performed by the image processing device  601  of  FIG. 6 . First, the generator  612  extracts a plurality of candidate lines that are observed from the position of an imaging device that captures an image of an object from among a plurality of candidate lines included in the shape information  621  of the object (step  701 ). The generator  612  generates plural pieces of association information indicating a prescribed number of combinations obtained by respectively associating the prescribed number of candidate lines of the observed plurality of candidate lines with the prescribed number of feature lines of a plurality of feature lines detected from the image (step  702 ). The determination unit  613  determines an association result on the basis of respective errors of the plural pieces of association information (step  703 ). 
     By employing the image processing device  601  described above, a calculation amount for associating an image of an object with shape information indicating the shape of the object can be reduced. 
       FIG. 8  illustrates a specific example of the image processing device  601  of  FIG. 6 . The image processing device  601  of  FIG. 8  includes a storage  611 , a generator  612 , a determination unit  613 , an image obtaining unit  811 , a feature detector  812 , a candidate detector  813 , a position calculator  814 , an error calculator  815 , and an output unit  816 . 
     The image processing device  601  may be a portable terminal device such as a tablet, a laptop PC, or a smart device, or may be an information processing device such as a desktop PC. 
     An imaging device  801  is, for example, a camera, and the imaging device  801  captures an image  821  of an object. The image obtaining unit  811  obtains the image  821  from the imaging device  801 , and stores the image  821  in the storage  611 . The storage  611  stores the image  821 , CAD data  822 , and a parameter  823 . 
     The CAD data  822  corresponds to the shape information  621  of  FIG. 6 , and the CAD data  822  includes vertex information of a plurality of vertices indicating a three-dimensional shape of an object, and line segment information of a plurality of line segments. The vertex information includes three-dimensional coordinates of each of the vertices of the object, and the line information includes identification information indicating vertices at both ends of each of the line segments. 
     The parameter  823  indicates the position and posture of the imaging device  801  that are specified in advance in a three-dimensional space. The position and posture indicated by the parameter  823  are a provisional position and posture, and do not always match a position and a posture of the imaging device  801  at the time when the image  821  was captured. 
     The feature detector  812  performs edge detection processing so as to detect a plurality of edge lines from the image  821 , and stores the detected edge lines as feature lines  824  in the storage  611 . The candidate detector  813  detects a plurality of line segments included in the CAD data  822 , and stores the detected line segments as a plurality of candidate lines  825  in the storage  611 . 
     The generator  612  extracts a plurality of feature lines that satisfy a prescribed condition from among the feature lines  824  detected from the image  821 . Examples of the prescribed condition include that at least a portion of a feature line is included in a specified region within the image  821 , and that a feature line exists within a range of a prescribed distance from a reference position within the image  821 . In addition, the generator  612  extracts a plurality of candidate lines observed from the position and posture indicated by the parameter  823  from among the candidate lines  825  detected from the CAD data  822 . 
     The generator  612  generates N combinations obtained by respectively associating N candidate lines (N is an integer that is greater than or equal to 2) of the extracted candidate lines with N feature lines of the extracted feature lines. The generator  612  stores the generated N combinations as N corresponding pairs  826  in the storage  611 . The corresponding pair  826  corresponds to the association information. 
     The position calculator  814  calculates a position and a posture of the imaging device  801  at the time when the image  821  was captured, by using the N corresponding pairs  826 , and stores the calculated position and posture as a parameter  827  in the storage  611 . 
     At this time, the position calculator  814  generates a projection line by projecting a candidate line included in each of the corresponding pairs onto the image  821  while sequentially changing variables indicating the position and posture of the imaging device  801  by a prescribed value. The error calculator  815  calculates an error indicating a deviation between the position of the projection line generated by the position calculator  814  and the position of the feature line included in each of the corresponding pairs. The position calculator  814  obtains values of variables that minimize the total of errors calculated by the error calculator  815  as the parameter  827 . 
     The position calculator  814  repeats a process for calculating the parameter  827  plural times while changing the selection of N corresponding pairs. The determination unit  613  generates N projection lines by projecting candidate lines included in the N corresponding pairs selected by the position calculator  814  onto the image  821  by using the position and posture of the imaging device  801  indicated by the parameter  827 , every time the parameter  827  is calculated. The determination unit  613  calculates the total of errors between the positions of the N projection lines and the positions of the N feature lines, similarly to the error calculator  815 , and stores the calculated total of errors as an index  828  in the storage  611 . 
     The determination unit  613  determines N corresponding pairs that minimize the total of errors on the basis of the index  828  calculated by using the respective parameters  827 . These N corresponding pairs correspond to an association result. The determination unit  613  calculates the position and posture of the imaging device  801  in a three-dimensional space by using the determined N corresponding pairs, and stores the calculated position and posture as a parameter  829  in the storage  611 . The output unit  816  outputs the parameter  829  as a processing result. 
     By employing the image processing device  601  described above, corresponding pairs of a candidate line detected from the CAD data  822  and a feature line detected from the image  821  can be automatically generated without a user performing a selection operation. At this time, candidate lines and feature lines used to generate the corresponding pairs are narrowed by the generator  612 , and therefore a calculation amount to determine N corresponding pairs is greatly reduced in comparison with a case in which brute-force calculation is performed. 
       FIG. 9  is a flowchart illustrating a specific example of image processing performed by the image processing device  601  of  FIG. 8 . First, the image obtaining unit  811  obtains the image  821  from the imaging device  801  (step  901 ), and the feature detector  812  detects a plurality of feature lines  824  from the image  821  (step  902 ). In addition, the candidate detector  813  detects a plurality of candidate lines  825  from the CAD data  822  (step  903 ). 
     The generator  612  extracts a plurality of feature lines that satisfy a prescribed condition from among the plurality of feature lines  824  (step  904 ). As the prescribed condition, the conditions below are used, for example. 
     (C1) At least a portion of a feature line is included in a specified region within the image  821 . 
     (C2) A feature line exists within a range of a prescribed distance from a reference position within the image  821 . 
     When condition (C1) is used, a user can narrow feature lines used to generate corresponding pairs by a user only performing a simple operation to specify a region in which an object is photographed. 
     When condition (C2) is used, feature lines used to generate corresponding pairs can be narrowed on the basis of a reference position of a reference point, a reference line, or the like that is set in advance without a user specifying a region. When a user photographs an object, the object often appears near the center position of the image  821 , and therefore it is effective to use the center position of the image  821  as a reference position. 
       FIG. 10  illustrates an example of a specified rectangular region in the image  821 . When a rectangular region  1001  is specified within the image  821  by a user, the generator  612  extracts a feature line for which a portion or the entirety is included in the rectangular region  1001 . In this case, nine feature lines are extracted from eighteen feature lines detected from the image  821 . 
       FIG. 11  illustrates an example of a specified circular region within the image  821 . When a circular region  1101  is specified in the image  821  by a user, the generator  612  extracts a feature line for which a portion or the entirety is included in the circular region  1101 . Also in this case, nine feature lines are extracted from eighteen feature lines detected from the image  821 . 
       FIG. 12  illustrates an example of a reference line within the image  821 . The generator  612  extracts a feature line that exists within a range of a prescribed distance from a straight line  1201  that passes through the center position of the image  821 . As a distance from the straight line  1201  to the feature line, the length of a perpendicular line that is drawn from one endpoint of the feature line onto the straight line  1201  may be used, or the length of a perpendicular line that is drawn from a middle point of the feature line onto the straight line  1201  may be used. 
     The generator  612  extracts a plurality of candidate lines observed from a position and a posture that are indicated by the parameter  823  from among a plurality of candidate lines  825  (step  905 ). As an example, the generator  612  removes hidden lines from the plurality of candidate lines  825  by using the position and posture indicated by the parameter  823  as the position and posture of the imaging device  801 , according to the method described in Non-Patent Document 3 such that the remaining candidate lines can be extracted. 
     The hidden lines are not observed from the imaging device  801 , and therefore many feature lines that correspond to the hidden lines are not detected from the image  821 . Accordingly, by removing the hidden lines from the candidate lines  825 , candidate lines used to generate corresponding pairs can be effectively narrowed. 
       FIG. 13  illustrates an example of the candidate lines  825  detected from the CAD data  822  of an object photographed in the image  821  illustrated in  FIG. 10  to  FIG. 12 . In this example, 25 candidate lines  825  are detected. 
       FIG. 14  illustrates an example of the remaining candidate lines after hidden lines are removed from the candidate lines  825  illustrated in  FIG. 13 . By removing  11  hidden lines from the 25 candidate lines  825 , 14 candidate lines are extracted. 
     The generator  612  may extract candidate lines indicating an outline edge of an object from the remaining candidate lines, and the generator  612  may further extract candidate lines indicating an outer periphery of the object from the candidate lines indicating the outline edge. The candidate lines indicating the outer periphery of the object indicate contour lines of the object, and can be detected by using a boundary representations technology in computer graphics (CG). 
     As disclosed in Non-Patent Document 1, for example, data having a winged-edge structure, which is an example of boundary representations, includes information indicating a contour line, and vertices and faces that form the contour line, and information indicating a connection relationship with another contour line. Whether respective candidate lines detected from CAD data correspond to an outer periphery can be determined on the basis of these pieces of information. 
     When the feature line  824  detected from the image  821  is a contour line, a boundary line between the object and a background is detected as the feature line  824 . The object and the background are physically separated from each other, and therefore a manner in which light such as the sun or illumination strikes is often different, or a material or color is often different. Therefore, a clearer feature line is likely to be detected, and the accuracy of the position of the feature line increases. In addition, by generating a large number of corresponding pairs indicating contour lines, a distribution range of the corresponding pairs in the image  821  increases, and it can be considered that this results in improvements in the accuracy of the calculation of the parameter  829 . 
       FIG. 15  illustrates an example of candidate lines indicating an outline edge of an object. From among the 14 candidate lines illustrated in  FIG. 14 , 11 candidate lines illustrated with a bold line are extracted as candidate lines indicating an outline edge. 
       FIG. 16  illustrates an example of candidate lines indicating an outer periphery of an object. From among the 11 candidate lines illustrated in  FIG. 15 , 8 candidate lines illustrated with a bold line are extracted as candidate lines indicating an outer periphery. 
     The generator  612  may select and use a candidate line that is longer than a prescribed length when the candidate line is projected onto the image  821 , from among the candidate lines illustrated in  FIG. 14  to  FIG. 16 . When a projection line is long, a contour line itself that indicates the shape of an object is long, and therefore the projection line is highly likely to be associated with a longer feature line. In addition, a longer feature line is considered to have a high reliability. Further, in calculating the position and posture of the imaging device  801 , as both a projection line and a feature line become longer, the accuracy of the calculation of an error between the projection line and the feature line is improved, and therefore the accuracy of the calculation of the parameter  829  is also improved. 
     The generator  612  generates N corresponding pairs  826  obtained by associating N candidate lines and N feature lines with each other (step  906 ), and the position calculator  814  calculates a parameter  827  by using these corresponding pairs  826  (step  907 ). 
       FIG. 17  illustrates an example of corresponding pairs. In this example, a candidate line  1711  to a candidate line  1714  are respectively associated with a feature line  1701  to a feature line  1704  such that four corresponding pairs are generated. 
     In step  907 , the position calculator  814  can calculate the parameter  827  by using a least-squares method, for example. In this case, the position calculator  814  generates a projection line by projecting a candidate line included in each of the corresponding pairs onto the image  821  while sequentially changing variables indicating the position and posture of the imaging device  801  by a prescribed value. The error calculator  815  estimates an error Ei (i=1 to N) between the position of the projection line and the position of a feature line included in each of the corresponding pairs, and obtains values of variables that minimize the total E of square errors with respect to the N corresponding pairs as the parameter  827 . The total E of square errors is calculated according to the expression below.
 
 E=Σ   i=1   N ( Ei ) 2   (11)
 
     The error calculator  815  can calculate the error Ei by using, for example, the method illustrated in  FIG. 18  or  FIG. 19 .  FIG. 18  illustrates an example of a calculation method based on the area of a region between a projection line and a feature line. When a projection line included in the i-th corresponding pair is a line segment  1801 , and a feature line is a line segment  1802 , a line segment  1803  and a line segment  1804  that respectively connect both ends of the line segment  1801  and both ends of the line segment  1802  can be defined. In this case, the area Ai of a region surrounded by the line segment  1801  to the line segment  1804  can be used as the error Ei.
 
 Ei=Ai   (12)
 
     As the area Ai becomes smaller, the error Ei also becomes smaller, and when the line segment  1801  overlaps the line segment  1802 , the error Ei is 0. 
       FIG. 19  illustrates an example of a calculation method based on a distance between a projection line and a feature line. The lengths of a perpendicular line  1901  and a perpendicular line  1902  that are drawn from both ends of a line segment  1802  onto a line segment  1801  are assumed to be Li 1  and Li 2 , respectively. In this case, the sum of Li 1  and Li 2  can be used as the error Ei.
 
 Ei=Li 1+ Li 2  (13)
 
     As Li 1  and Li 2  become shorter, the error Ei becomes smaller, and when the line segment  1801  overlaps the line segment  1802 , the error Ei is 0. 
     The determination unit  613  generates N projection lines by projecting candidate lines included in the N corresponding pairs onto the image  821  by using the position and posture of the imaging device  801  indicated by the parameter  827  (step  908 ). 
     The determination unit  613  calculates the index  828  indicating the total of errors between the positions of the N projection lines and the positions of the N feature lines (step  909 ), and checks whether the index  828  has been calculated a prescribed number of times (step  910 ). When the index  828  has not been calculated a prescribed number of times (step  910 , No), the position calculator  814  changes the selection of N corresponding pairs (step  906 ), and the image processing device  601  repeats the processes of step  907  and the subsequent steps. 
     When the index  828  has been calculated a prescribed number of times (step  910 , Yes), the determination unit  613  selects N corresponding pairs that minimize the total of errors (step  911 ), and calculates the parameter  829  on the basis of the corresponding pairs (step  912 ). The output unit  816  outputs the selected N corresponding pairs and the parameter  829  (step  913 ). 
     In the image processing of  FIG. 9 , N corresponding pairs that minimize the total of errors can be obtained by repeating the calculation of the index  828  while automatically changing the selection of N corresponding pairs. By doing this, an operation time of a selection operation performed by a user is reduced, and a processing time is also reduced. In addition, the accuracy of the estimation of the position and posture of the imaging device  801  is improved. 
     In addition, an erroneous selection due to a human error is not performed, and therefore a processing time does not increase due to re-selection. Even a user who is not an expert can obtain N optimum corresponding pairs, and therefore the type of an operation to which an association result is applied and a target for the operation can be increased. 
     In step  910  of  FIG. 9 , the image processing device  601  may abort a repeating process when the error indicated by the index  828  becomes smaller than a prescribed value, instead of aborting the repeating process when the index  828  has been calculated a prescribed number of times. 
     In step  907  and step  909 , the image processing device  601  may estimate a degree of similarity between a projection line and a feature line instead of an error between the position of the projection line and the position of the feature line. As the degree of similarity between the projection line and the feature line, a degree of similarity between two line segments described in Patent Document 1 can be used, for example. In this case, a parameter  827  that maximizes the total of degrees of similarity is obtained in step  907 , and N corresponding pairs that maximize the total of degrees of similarity is selected in step  911 . 
     Even when the total of errors of the N corresponding pairs selected in step  911  is the smallest, respective projection lines may indicate line segments obtained by rotating respective feature lines by 180 degrees. 
       FIG. 20  illustrates an example of line segments rotated by 180 degrees. Among the projection lines and the feature lines of  FIG. 20 , a projection line  2012  overlaps a feature line  2002 . A projection line  2011 , a projection line  2013 , and a projection line  2014  respectively correspond to line segments obtained by rotating the feature line  2002 , a feature line  2003 , and a feature line  2004  by 180 degrees with the projection line  2012  as an axis. In this case, the area Ai in expression (12) is almost 0, and therefore the total of errors may be the smallest. 
     In order to prohibit the association above, the determination unit  613  may select N corresponding pairs that minimize the total of errors from among N corresponding pairs that satisfy the conditions below. 
     (C11) Among N projection lines, a prescribed ratio of projection lines are included in the image  821 . 
     (C12) Among N projection lines, a prescribed ratio of projection lines exist near a prescribed position within the image  821 . 
     (C13) A ratio of a distribution range of N projection lines with respect to the area of the image  821  is greater than or equal to a prescribed value. 
       FIG. 21A  and  FIG. 21B  illustrate examples of candidate lines that are not suitable for the calculation of the parameter  827 .  FIG. 21A  illustrates four candidate lines parallel to each other. In a case in which four candidate lines are parallel to each other, even when the candidate lines are moved in parallel in the direction of an arrow  2101 , errors do not change, and it may be difficult to fix the positions of the candidate lines. 
       FIG. 21B  illustrates two candidate lines that exist on the same straight line. In a case in which two candidate lines exist on the same straight line, even when the candidate lines are enlarged or reduced in the direction of an arrow  2102 , errors do not change, and it may be difficult to fix a scale. 
     Accordingly, in step  906  of  FIG. 9 , the generator  612  may select N candidate lines that satisfy the conditions below, and may generate N corresponding pairs. 
     (C21) Among N candidate lines, at least two candidate lines are not parallel to each other. 
     (C22) Among N candidate lines, no two candidate lines exist on the same straight line. 
     For a similar reason, the generator  612  may select N feature lines that satisfy the conditions below, and may generate N corresponding pairs. 
     (C31) Among N feature lines, at least two feature lines are not parallel to each other. 
     (C32) Among N feature lines, no two feature lines exist on the same straight line. 
     The configurations of the image processing devices  601  illustrated in  FIG. 6  and  FIG. 8  are examples, and some components may be omitted or changed according to the purpose or condition of the image processing device  601 . As an example, when a process for detecting the feature line  824  from the image  821  is performed by a device external to the image processing device  601 , the feature detector  812  of  FIG. 8  can be omitted. 
     When a process for extracting the candidate line  825  from the CAD data  822  is performed by an external device, the candidate detector  813  can be omitted. Another shape information indicating the shape of an object may be used instead of the CAD data  822 . 
     The flowcharts of  FIG. 7  and  FIG. 9  are examples, and some processes may be omitted or changed according to the configuration or condition of the image processing device  601 . As an example, when a process for detecting the feature line  824  from the image  821  is performed by a device external to the image processing device  601 , the processes of step  901  and step  902  in  FIG. 9  can be omitted. When a process for detecting the candidate line  825  from the CAD data  822  is performed by an external device, the process of step  903  in  FIG. 9  can be omitted. 
     When the posture of the imaging device  801  is determined in advance, only the position of the imaging device  801  may be obtained as a parameter in step  907  and step  912  of  FIG. 9 . 
     The three-dimensional map and the image illustrated in  FIG. 1  are examples, and a three-dimensional map and an image change according to an object to be photographed. The method of  FIG. 2  for generating a three-dimensional map is an example, and a three-dimensional map may be generated by using another method according to the configuration or condition of the image processing device  601 . 
     The image of  FIG. 3 , the CAD data of  FIG. 4 , and the edge lines and the contour lines of  FIG. 5A  to  FIG. 5C  are examples, and an image, CAD data, and edge lines and contour lines change according to an object to be photographed, or the configuration or condition of the image processing device  601 . 
     The specified regions of  FIG. 10  and  FIG. 11 , and the reference line of  FIG. 12  are examples, and a specified region having another shape and another reference line may be used according to the configuration or condition of the image processing device  601 . 
     The candidate lines of  FIG. 13  to  FIG. 16 ,  FIG. 21A , and  FIG. 21B , the feature lines and the candidate lines of  FIG. 17 , and the feature lines and the projection lines of  FIG. 20  are examples. Candidate lines, feature lines, and projection lines change according to an object to be photographed, or the configuration or condition of the image processing device  601 . 
     The methods of  FIG. 18  and  FIG. 19  for calculating an error are examples, and another calculation method may be used according to the configuration or condition of the image processing device  601 . Calculation expression (1) to calculation expression (13) are examples, and other calculation expressions may be used according to the configuration or condition of the image processing device  601 . 
       FIG. 22  is an example of the configuration of an information processing device (a computer) used as the image processing device  601  of  FIG. 6  or  FIG. 8 . The information processing device of  FIG. 22  includes a central processing unit (CPU)  2201 , a memory  2202 , an input device  2203 , an output device  2204 , an auxiliary storage  2205 , a medium driving device  2206 , and a network connecting device  2207 . These components are connected to each other via a bus  2208 . The imaging device  801  of  FIG. 8  may be connected to the bus  2208 . 
     The memory  2202  is a semiconductor memory such as a read-only memory (ROM), a random access memory (RAM), or a flash memory, and the memory  2202  stores a program and data used in image processing. The memory  2202  can be used as the storage  611  of  FIG. 6  or  FIG. 8 . 
     The CPU  2201  (a processor) operates as the generator  612  and the determination unit  613  of  FIG. 6  or  FIG. 8 , for example, by executing a program by using the memory  2202 . The CPU  2201  also operates as the feature detector  812 , the candidate detector  813 , the position calculator  814 , and the error calculator  815  of  FIG. 8 . 
     The input device  2203  is, for example, a keyboard, a pointing device, or the like, and the input device  2203  is used for an instruction from an operator or a user, or an input of information. The output device  2204  is, for example, a display device, a printer, a speaker, or the like, and the output device  2204  is used for an inquiry or an instruction to an operator or a user, and an output of a processing result. The processing result may be N corresponding pairs determined by the determination unit  613 . The output device  2204  can be used as the output unit  816  of  FIG. 8 . 
     The auxiliary storage  2205  is, for example, a magnetic disk drive, an optical disk drive, a magneto-optical disk drive, a tape device, or the like. The auxiliary storage  2205  may be a hard disk drive. The information processing device can store a program and data in the auxiliary storage  2205 , can load them into the memory  2202 , and can use them. The auxiliary storage  2205  can be used as the storage  611  of  FIG. 6  or  FIG. 8 . 
     The medium driving device  2206  drives a portable recording medium  2209 , and accesses its recording content. The portable recording medium  2209  is a memory device, a flexible disk, an optical disk, a magneto-optical disk, or the like. The portable recording medium  2209  may be a compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a universal serial bus (USB) memory, or the like. An operator or a user can store a program and data in the portable recording medium  2209 , can load them into the memory  2202 , and can use them. 
     As described above, a computer-readable recording medium that stores a program and data used in image processing is a physical (non-transitory) recording medium such as the memory  2202 , the auxiliary storage  2205 , or the portable recording medium  2209 . 
     The network connecting device  2207  is a communication interface that is connected to a communication network such as a local area network or a wide area network, and that performs data conversion associated with communication. The information processing device can receive a program and data from an external device via the network connecting device  2207 , can load them into the memory  2202 , and can use them. The network connecting device  2207  can be used as the output unit  816  of  FIG. 8 . 
     The information processing device does not need to include all of the components of  FIG. 22 , and some components can be omitted according to purposes or conditions. As an example, when the portable recording medium  2209  or a communication network is not used, the medium driving device  2206  or the network connecting device  2207  may be omitted. 
     All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.