Patent Publication Number: US-7221779-B2

Title: Object measuring apparatus, object measuring method, and program product

Description:
This application is based on application No. 2003-360580 filed in Japan, the contents of which are hereby incorporated by reference. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an object measuring apparatus for performing a process of counting the number of moving objects, and techniques related thereto. 
   2. Description of the Background Art 
   There are techniques of using an optical flow in order to measure movement of a moving object (for example, see “Tracking a Person with 3-D Motion by Integrating Optical Flow and Depth”, by R. Okada, Y. Shirai, and J. Miura, Proc. 4th Int. Conf. on Automatic Face and Gesture Recognition, pp. 336-341, March, 2000 (Non-Patent Document 1) and Japanese Patent Application Laid-Open No. 2002-8018 (Patent Document 1)). The optical flow denotes a “vector field” constructed by “motion vectors” of corresponding pixels in two images. 
   In such techniques, a camera is located at a predetermined position and an optical flow is obtained from a motion image captured by the camera. For example, by obtaining motion vectors in a plurality of positions (detection points) in a two-dimensional region, an optical flow is obtained. By using the obtained optical flow, a moving object is detected and tracked. 
   With the techniques employed, in accordance with whether a tracked object passes a boundary line or not, the number of objects passing the boundary line can be counted. 
   However, in the case of employing the technique disclosed in Non-Patent Document 1 (also referred to as “first conventional art”) in the above-described techniques, it is necessary to obtain a large number of motion vectors in a plurality of positions (detection points) in a two-dimensional region. It causes problems of a heavy processing load and long calculation time. 
   To address such a problem, Patent Document 1 discloses a technique of measuring the number of passages of moving objects not by obtaining motion vectors in a plurality of detection points provided in a two-dimensional region but by using motion vectors in a relatively small number of detection points provided in a one-dimensional direction (also referred to as “second conventional art”). More specifically, about 40 to 80 detection points are disposed in a one-dimensional direction of an approach position of a moving object, and motion vectors are detected with respect to the detection points. A time point when the total number of detection points at each of which a motion vector that is not zero (zero vector) is detected among the detection points becomes a threshold value or more is regarded as a time point when the head of a moving object passes, and a time point when the total number of similar detection points becomes a threshold value or less is regarded as a time point when the end of the moving object passes, thereby measuring a physical amount of the moving object. According to such a technique, as compared with the case of obtaining motion vectors in a number of detection points in a two-dimensional region, by decreasing the number of detection points, processing speed can be improved. 
   However, the technique of Patent Document 1 (second conventional art) has a problem in that the number of passages of moving objects is erroneously counted in the case where a plurality of moving objects pass a boundary line simultaneously. A situation is assumed that while a moving object (the first moving object) passes a boundary line, another moving object (the second moving object) reaches the boundary line. In this situation, when the second conventional art is employed, the total number of detection points in each of which a motion vector which is not zero is detected regarding the second moving object increases to a threshold or more before the total number of similar detection points regarding the first moving object decreases to the threshold or less. Consequently, there is a case that two moving objects cannot be counted separately. 
   SUMMARY OF THE INVENTION 
   The present invention aims to provide an object measuring system capable of performing high speed process and accurately counting the number of a plurality of objects even in the case where the plurality of objects pass a boundary line simultaneously. 
   In order to achieve the aim, according to a first aspect of the present invention, an object measuring system comprises: an extractor for extracting motion vectors at a plurality of times in each of a plurality of positions on the boundary line on the basis of a plurality of images; an integrator for obtaining at least one integral value derived by integrating perpendicular components perpendicular to the boundary line of the motion vectors, the at least one integral value being derived by integrating the perpendicular components of one of positive and negative signs; and a calculator for calculating the number of moving objects passing the boundary line on the basis of the at least one integral value. 
   According to the object measuring system, it is sufficient to obtain motion vectors on a boundary line; therefore, it is unnecessary to calculate an optical flow with respect to a wide two-dimensional region. Accordingly, processing load can be lessened and higher processing speed can be achieved. At least one integral value is obtained by integrating components perpendicular to the boundary line of the motion vector with respect to one of positive and negative signs and the number of moving objects is calculated on the basis of the integral value. Consequently, even in the case where a plurality of moving objects pass the boundary line in opposite directions at the same time, erroneous counting can be prevented and the number of passing objects can be measured accurately. As described above, the number of moving objects passing the boundary line can be calculated accurately at high speed. 
   According to a second aspect of the present invention, an object measuring system comprises: an extractor for extracting motion vectors at a plurality of times in each of a plurality of positions on the boundary line on the basis of a plurality of images; an integrator for obtaining an integral value by integrating components perpendicular to the boundary line of the motion vector; and a calculator for calculating the number of moving objects passing the boundary line on the basis of the at least one integral value and a reference value regarding the integral value. 
   According to the object measuring system, it is sufficient to obtain motion vectors on a boundary line; therefore, it is unnecessary to calculate an optical flow with respect to a wide two-dimensional region. Accordingly, processing load can be lessened and higher processing speed can be achieved. Further, since the number of moving objects passing the boundary line is obtained on the basis of an integral value derived by integrating components perpendicular to the boundary line of the motion vector and a reference value regarding the integral value, even in the case where a plurality of moving objects pass the boundary line at the same time, erroneous counting can be prevented and the number of passing objects can be measured accurately. 
   The present invention is also directed to an object measuring method and a program product. 
   These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a diagram showing an object measuring apparatus; 
       FIG. 2  is a block diagram showing a hardware configuration of a controller; 
       FIG. 3  is a diagram showing an image captured by a camera unit; 
       FIG. 4  is a flowchart showing the operation in the object measuring apparatus; 
       FIG. 5  is a diagram showing motion vectors V in a captured image after lapse of predetermined time since the state of  FIG. 3 ; 
       FIG. 6  is a diagram showing an X-direction component u and a Y-direction component v of the motion vector V; 
       FIG. 7  is a diagram showing an image of a plurality of objects in proximity traveling in the same direction; 
       FIG. 8  is a flowchart showing the detailed operation of generating an optical flow; 
       FIG. 9  is a conceptual diagram showing a process of generating a Laplacian pyramid; 
       FIG. 10  is a diagram showing an example of a Laplacian filter; 
       FIG. 11  is a conceptual diagram showing Laplacian pyramids at time t and time (t−1); 
       FIG. 12  is a conceptual diagram showing an outline of the operation in a multi-resolution strategy; 
       FIG. 13  is a conceptual diagram showing a process of generating an enlarged optical flow FT 2 ; 
       FIG. 14  is a conceptual diagram showing the operation of obtaining a predictive image Q 02 ; 
       FIG. 15  is a conceptual diagram showing a modification of obtaining an optical flow; and 
       FIG. 16  is a flowchart according to a modification of  FIG. 15 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Hereinafter, embodiments of the present invention will be described with reference to the drawings. 
   Configuration 
     FIG. 1  is a diagram showing an object measuring apparatus  1  according to an embodiment of the present invention. As shown in  FIG. 1 , the object measuring apparatus  1  comprises a controller  10  and a camera unit (image capturing unit)  20 . A case is assumed herein that the camera unit  20  is disposed on the ceiling of a predetermined position (e.g., a path, an entrance, an exit or the like) in a shop to grasp a moving state of a human. 
   The camera unit  20  is disposed so that the optical axis of a lens of the camera unit  20  is parallel with a vertical direction (direction perpendicular to the floor face), and captures an image including a virtual boundary line BL (see  FIG. 3  and the like) which divides a region into a first region R 1  and a second region R 2  in the shop. The object measuring apparatus  1  obtains the number of moving objects (humans) passing the boundary line BL on the basis of an image captured by the camera unit  20 . 
   The controller  10  is disposed in a place (such as a monitoring room) apart from the camera unit  20 . 
     FIG. 2  is a block diagram showing a hardware configuration of the controller  10 . As shown in  FIG. 2 , hardware of the controller  10  is configured as a computer system (hereinafter, also simply referred to as “computer”) having: a CPU  2 ; a storing unit  3  including a main storage formed by a semiconductor memory such as a RAM (and/or ROM) and an auxiliary storage such as a hard disk drive (HDD); a media drive  4 ; a display unit  5  such as a liquid crystal display; an input unit  6  such as a keyboard and a mouse; and a communication unit  7  such as a network card. 
   The controller  10  is configured so as to be able to transmit/receive data to/from the camera unit  20  by wireless or wired data communication or the like via the communication unit  7 . 
   The media drive  4  reads out information recorded in a portable recording medium  9  such as a CD-ROM, a DVD (Digital Versatile Disk), a flexible disk, or a memory card. 
   The controller  10  realizes various functions in the object measuring apparatus  1  by loading a software program (hereinafter, also simply referred to as “program”) recorded in the recording medium  9  and executing the program using the CPU  2  and the like. The program having various functions is not limited to be supplied via the recording medium  9  but may be supplied to the computer via a network such as a LAN and the Internet. 
   Referring again to  FIG. 1 , the controller  10  has a moving image input unit  11 , an optical flow calculating unit  12 , an optical flow integrating unit  13 , a passing-objects-number calculating unit  14  and a result output unit  15 . The processing units  11  to  15  are schematically shown as functional portions which realize various functions of the controller  10 . 
   The moving image input unit  11  is a processing unit for receiving, as moving images, a plurality of images sequentially captured by the camera unit  20 . The optical flow calculating unit  12  is a processing unit for extracting motion vectors at a plurality of time points in each of a plurality of positions (also referred to as detection points) on the boundary line BL on the basis of a plurality of received images. The optical flow integrating unit  13  is a processing unit for obtaining an integral value by integrating components perpendicular to the boundary line of motion vectors with respect to each of positive and negative signs. The passing-objects-number calculating unit  14  is a processing unit for calculating the number of moving objects passing the boundary line on the basis of the integral value. The object measuring apparatus  1  measures the number of moving objects passing the boundary line by using the processing units. The operation in the processing units will be described in detail later. 
   Operation 
     FIG. 3  is a diagram showing an image captured by the camera unit  20  and corresponds to an overhead view of a place (path or the like) where the camera unit  20  is disposed. Herein, X-, Y- and Z-axes are relatively fixed to the path. The Y-axis direction is a travel direction of a human as a moving object in the path. The X-axis direction is a width direction of the path (the direction orthogonal to the travel direction of a human). The Z-axis direction is a vertical direction. 
     FIG. 3  schematically shows a state where two humans HM 1  and HM 2  travel in opposite directions, respectively. Concretely, the human HM 1  travels from the bottom to top of the diagram (i.e., in the +Y direction), and the human HM 2  travels from the top to bottom of the diagram (i.e., in the −Y direction). 
   An image capturing region R 0  of the camera unit  20  includes a virtually set boundary line BL. The boundary line BL is a virtual line for partitioning a region into the first and second regions R 1  and R 2  in a shop. In this case, the boundary line BL is a straight line extending in the lateral direction of a captured image and is positioned in an almost center in the vertical direction of the captured image. The object measuring apparatus  1  calculates the number of moving objects passing the boundary line BL by the principle described as follows. 
     FIG. 4  is a flowchart showing the operation in the object measuring apparatus  1 . In the following, description will be continued with reference to  FIG. 4 . 
   First, in step S 1 , the moving image input unit  11  receives a plurality of images (time-series images) sequentially captured by the camera unit  20 . By the plurality of images, a moving image is constructed. 
   Next, in step S 2 , the optical flow calculating unit  12  extracts a motion vector V(x, t) at a plurality of times t in each of a plurality of positions x (also referred to as detection points) on the boundary line BL on the basis of the plurality of inputted images. That is, the optical flow calculating unit  12  calculates an optical flow. In step S 2 , a process of obtaining motion vectors on the one-dimensional boundary line BL (more specifically, motion vectors in a relatively small number of representative detection points) is performed. 
   The motion vector (also referred to as a flow vector) V(x, t) is extracted on the basis of a plurality of images captured over a period of time. The motion vector V(x, t) is a function of the X-coordinate value x and time t on the boundary line BL. In the following, for simplification, the motion vector will be also simply expressed as V. 
     FIG. 5  is a diagram showing the motion vector V in an image captured after a lapse of predetermined time since the state of  FIG. 3 . As shown in  FIG. 5 , the human HM 1  travels upward in the diagram (i.e., in the +Y direction), so that the motion vector V(x, t) has a component in the +Y direction. On the other hand, the human HM 2  travels downward in the diagram (i.e., in the −Y direction), so that the motion vector V(x, t) has a component in the −Y direction. In such a manner, the motion vectors V in the plurality of detection points on the boundary line BL are obtained. 
   Further, in step S 3 , the optical flow integrating unit  13  calculates an integral value by integrating components perpendicular to the boundary line BL of the motion vector V (in this case, components v in the Y direction) with respect to each of the positive and negative signs. Concretely, on the basis of Equations 1 and 2, integral values E 1  and E 2  are calculated, respectively. Each of the integral values E 1  and E 2  is an integral value derived by integrating components perpendicular to the boundary line BL of the motion vector V (with respect to time and space). The integral value can be also expressed as an integral value obtained by integrating components of one of the sign components of the positive and negative sign components v 1  and v 2  of the perpendicular component. For simplicity,  FIG. 5  shows the case where the motion vector V has only components in the Y direction. In reality, however, the motion vector (velocity vector) V of the human HM also includes a component u in the X direction. In this case, it is sufficient to extract only a component v in the Y direction of the motion vector V.
 
 E 1=∫ t0   t1 ∫ x0   x1   v 1( x, t ) d×dt   Equation 1
 
 E 2=∫ t0   t1 ∫ x0   x1   v 2( x, t ) d×dt   Equation 2
 
   An integration range with respect to a position x is a range from a position x 0  to a position x 1 . An integration range with respect to time t is a range from time t 0  to time t 1 . For example, it is sufficient to set time t 0  as a time point when the motion vector V which is not zero comes to be detected at any of detection points, and to set time t 1  as a time point when the motion vector V which comes not to be zero is not detected at any detection points after that. The value v 1 (x, t) and the value v 2 (x, t) are expressed by Equations 3 and 4, respectively. The value v 1  indicates a positive-sign component (more specifically, the absolute value of the positive-sign component) in the Y-direction component v of the motion vector V. The value v 2  indicates a negative-sign component (more specifically, the absolute value of the negative-sign component) in the Y-direction component v of the motion vector V. 
   
     
       
         
           
             
               
                 
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   In step S 4 , the passing-objects-number calculating unit  14  calculates the number of moving objects passing the boundary line on the basis of an integral value. Concretely, on the basis of Equations 5 and 6, the passing-objects-number calculating unit  14  calculates the number of people Cin who travel in the +Y direction and enter the upper region R 1  from the lower region R 2 , and the number of people Cout who travel in the −Y direction and go out from the upper region R 1 . 
   
     
       
         
           
             
               
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   The principle of calculation is based on the fact that each of the integral values E 1  and E 2  can be approximated to a square measure on an image of a passing object. By preliminarily setting a reference value S to a proper value and dividing each of the integral values E 1  and E 2  by the reference value S, the numbers of people Cin and Cout can be obtained. 
   As the reference value S, an average value of the square measure (or integral value) on an image of one moving object (the region of one human body) is preliminarily set. The average value can be preliminarily calculated from an image captured by the camera unit  20 . Alternately, it is also possible to preliminarily calculate the square measure (or integral value) on an image of a human of an average size and use the calculated value as the reference value S. 
   In step S 5 , the result output unit  15  outputs the result of measurement. Concretely, the numbers of people Cin and Cout in the respective directions are displayed on the display unit  5  or the like and a file including information of the numbers of passing people Cin and Cout is outputted and stored into the storing unit  3 . 
   In such a manner, the object measuring apparatus  1  measures the number of moving objects passing the boundary line in each of the directions of passage. 
   In the operation, it is sufficient to obtain the motion vectors V with respect to a relatively small number of detection points on the one-dimensional boundary line BL. As compared with the case of obtaining the motion vectors V with respect to a relatively large number of detection points in a two-dimensional region (e.g., the first conventional art), the number of detection points can be decreased. Therefore, higher processing speed can be achieved. 
   And the number of moving objects (people) is calculated with respect to each of the directions of travel on the basis of at least one of the integral values E 1  and E 2  (in this case, both of the integral values) obtained by integrating the components v in the Y direction perpendicular to the boundary line BL of the motion vector V with respect to the positive and negative signs, respectively. Consequently, even in the case where two moving objects traveling in the opposite directions simultaneously pass the boundary line BL, while preventing erroneous counting, the number of passing objects can be accurately measured. In other words, erroneous counting (concretely, erroneous counting which occurs in the case such that while a human HM 1  passes the boundary line, another human HM 2  who travels in the opposite direction also arrives at the boundary line) can be prevented. As described above, the object measuring apparatus  1  can count the number of moving objects passing the boundary line accurately at high speed. 
   Further, the passing-objects-number calculating unit  14  counts the number of moving objects on the basis of the integral values E 1  and E 2  and the reference value S of the integral values, so that the number of passing moving objects can be measured more accurately. 
     FIG. 7  is a diagram showing an image of a plurality of objects close to each other and traveling in the same direction. For example, as shown in  FIG. 7 , the second conventional art has a problem in that erroneous counting occurs in the case where a plurality of objects (humans HM 1  and HM 2  in  FIG. 7 ) traveling in the same direction exist in positions close to each other. It is considered that the erroneous counting occurs while the human HM 1  as one of them is passing the boundary line, another human HM 2  traveling in the same direction also arrives at the boundary line. 
   In contrast, in the operation of the foregoing embodiment, the number of moving objects is counted on the basis of the reference value S. Consequently, even in the case where a plurality of objects (humans HM 1  and HM 2  in  FIG. 7 ) exist in positions close to each other, such erroneous counting is prevented and more accurate counting process can be performed. 
   Although the case of obtaining the number of moving objects on the basis of the value derived by dividing each of the integral values E 1  and E 2  by the reference value S has been described in the foregoing embodiment, the present invention is not limited thereto. For example, it is also possible to obtain the number of moving objects by determining that one moving object exists each time the integral value from predetermined time exceeds the reference value S. 
   More specifically, at the time point when the integral value E 1  from time t 0  reaches the reference value S, the number of passing people is counted up, and the integral value E 1  is reset (cleared). After that, each time the integral value E 1  reaches the reference value S, similar operation is repeated. Alternately, at the time point when the integral value E 1  from the time t 0  reaches n×S (a value which is n times as large as the reference value S), the number of passing people may be sequentially updated from (n−1) to n. 
   Optical Flow 
   An example of the detailed operation of step S 2 , that is, the operation of calculating an optical flow will now be described. In diagrams to be described below ( FIG. 9  and subsequent diagrams), for convenience of the diagrams, a whole region of each image is shown. In an actual process, it is sufficient to perform imaging process (to be described later) only on a region around the boundary line BL in the whole region of each image. By the process, motion vectors V of a relatively small number of detection points on the one-dimensional boundary line BL, in other words, an optical flow in a region in the vicinity of the boundary line BL can be obtained. 
   As methods of calculating an optical flow, various methods such as a correlation method and a gradient method can be used. A case of calculating an optical flow by using a gradient method capable of realizing higher processing speed will be described herein. The gradient method uses that the following equation 7 regarding a pixel value I(x, y, t) at time t of a pixel in a position (x, y) and a flow vector V=(u, v) T  (T which is the capital letter of the numerical subscript at the upper right denotes ‘transpose’ of a vector or matrix, this definition will be the same also in the following) is satisfied. In the following, the pixel value I(x, y, t) or the like will be also simply described as a pixel value I or the like.
 
 I   x   ·u+I   y   ·v+I   t =0  Equation 7
 
   where I x  denotes a partial differential of the pixel value I with respect to a position x, I y  denotes a partial differential of the pixel value I with respect to a position y, and It indicates a partial differential of the pixel value I with respect to time t. Each of the values I x , I y  and I t  is obtained on the basis of two images with a subtle time interval, for example, an image I (t−1)  at time (t−1) and an image I (t)  at time t. 
   In Equation 7, two unknown values (u, v) exist, so that a solution is not unconditionally obtained only by Equation 7. Consequently, it is assumed that the relational expression of Equation 7 regarding the same unknown values (u, v) is satisfied with respect to each of a plurality of pixels (e.g., 5 pixels×5 pixels=25 pixels) in a local region, and a plurality of equations are led. An approximate solution satisfying the plurality of equations is calculated by the least square method and is used as a solution to the unknown values (u, v). 
   In the case where a subject travels at high speed, a displacement distance of corresponding pixels in two images is large. Consequently, in the case of using only an original image having relatively high resolution, a motion vector may not be accurately obtained. A case of employing a multi-resolution strategy using a plurality of images of different resolutions (also referred to as pyramid images or simply a pyramid) will now be described herein. With the strategy, also in the case where not only a subtle change between images but also a relatively large change (i.e., high-speed change) exist, a motion vector can be obtained more accurately. 
   In order to enhance robustness against a change in space of brightness of a background, herein, it is assumed that the gradient method is applied to a Laplacian image. Concretely, images of different resolutions (i.e., pyramid images) in the multi-resolution strategy are obtained as Laplacian images. 
     FIG. 8  is a detailed flowchart showing the optical flow generating process in step S 2 . 
   As shown in  FIG. 8 , first, with respect to each of the image I (t−1)  at time (t−1) and the image I (t)  at time t, a Gaussian pyramid is generated (step S 21 ) and a Laplacian pyramid is generated (step S 22 ). 
     FIG. 9  is a diagram conceptually showing a Laplacian pyramid generating process. Referring to  FIG. 9 , the process of generating a Laplacian pyramid (H 01 , H 02  and H 03 ) regarding the image I (t−1)  at time (t−1) will be described. Each of images G 12  to G 14 , G 21  to G 23 , and H 01  to H 03  in  FIG. 9  is an image generated by being derived from an original image G 11  having original resolution at time (t−1) and is the image I (t−1)  at time (t−1). Although an image pyramid of three (or four) levels is illustrated as an example herein, the present invention is not limited thereto, but an image pyramid having an another number of levels may be generated. 
   Concretely, a size reducing process accompanying a Gaussian process smoothing process) is performed on the image G 11  having the original resolution at time (t−1), thereby generating images G 12 , G 13  and G 14  having resolutions of ½, ¼ and ⅛ of the original resolution, respectively. In such a manner, a Gaussian pyramid constructed by a plurality of images G 11 , G 12 , G 13  and G 14  in a plurality layers is generated. 
   Next, by performing a Gaussian enlarging process (enlarging process accompanying the smoothing process) on the reduced images G 14 , G 13  and G 12  at the hierarchical levels of the Gaussian pyramid, each of the reduced images is doubled, thereby generating images G 23 , G 22  and G 21 , respectively, having resolutions matching to those of images at levels higher by one level. For example, by performing the Gaussian enlarging process on the reduced image G 14 , the image G 23  having the same resolution as that of the reduced image G 13  is generated. Similarly, the image G 22  having the same resolution as that of the reduced image G 12  is generated, and the image G 21  having the same resolution as that of the reduced image G 11  is also generated. 
   By subtracting the pixel values of the images G 13 , G 12  and G 11  from the pixel values of the images G 23 , G 22  and G 21  subjected to the Gaussian enlarging process, at the respective corresponding level, the Laplacian images H 03 , H 02  and H 01  at respective levels are obtained. The Laplacian images H 03 , H 02  and H 01  are images equivalent to, for example, processed images obtained by a Laplacian filter (edge emphasizing filter) as shown in  FIG. 10 . 
   By the process as described above, a plurality of Laplacian images of a plurality of resolutions, that is, the Laplacian pyramid (H 01 , H 02  and H 03 ) are/is obtained. 
   Similar processes are performed on the image I (t)  at time t and, as shown in  FIG. 11 , a plurality of Laplacian images of different resolutions are generated as a Laplacian pyramid (H 111 , H 112  and H 113 ). 
   By the above, as shown in  FIG. 11 , the Laplacian pyramids (H 01 , H 02 , H 03 ) and (H 11 , H 112 , H 113 ) with respect to the images I (t)  and I (t−1)  at two time points t and (t−1) are obtained. 
   The multi-resolution strategy using a Laplacian pyramid will now be described. The distance between corresponding pixels in images (reduced images) having relatively low resolution at two time points with a subtle time interval is smaller than that of corresponding pixels of images at the same time points of the original resolution (relatively high resolution), so that a “motion vector (flow vector)” is obtained more easily. In the multi-resolution strategy, by using such a characteristic, a motion vector is obtained first in the images of relatively low resolution. By gradually setting the motion vector to that of the image of relatively high resolution (the image at a higher level), the motion vector at the highest resolution (original resolution) is obtained. By employing the method, as described above, even in the case where a sufficiently accurate motion vector cannot be obtained only from the image of the original resolution since the motion vector is large, the motion vector can be obtained relatively accurately. 
     FIG. 12  is a conceptual diagram showing an outline of the operation in the multi-resolution strategy. In the following, description will be continued also with reference to  FIG. 12 . 
   First, in step S 23 , a flow vector at the lowest level is calculated. Concretely, as shown in  FIG. 9 , an optical flow FL 03  is calculated on the basis of the image H 03  having the lowest resolution at time (t−1) and the image H 13  having the lowest resolution at time t. Specifically, as described above, on assumption that a plurality of pixels in a local area have the same motion vector, a motion vector (u, v) T  of each of pixels in a plurality of positions is calculated by the least square method, thereby generating the optical flow FL 03  with respect to an image at the lowest level. 
   On the basis of the optical flow FL 03  at the lowest level, an optical flow FL 02  of an image at the next higher level is obtained (steps S 24  to S 27 ). 
   First, in step S 24 , an enlarging process accompanying a predetermined interpolating process (bilinear interpolation or the like) is performed on the optical flow FL 03 , thereby generating an enlarged optical flow FT 2  in which a motion vector at each of pixels of an image having a resolution twice as high as that of the image at the lower level is specified (see  FIG. 13 ). 
     FIG. 13  is a conceptual diagram showing a state of generation of the enlarged optical flow FT 2 . As shown in  FIG. 13 , as a rule, the motion vector in each of the pixels of the enlarged optical flow FT 2  is obtained by doubling the motion vector of the corresponding pixel in the optical flow FL 03 . For example, in  FIG. 13 , the motion vector in the position shown by a blank circle in the enlarged optical flow FT 2  is obtained by doubling the motion vector in the corresponding position (position indicated by the painted circle) in the optical flow FL 03 . With respect to a pixel in a position where a corresponding pixel does not exist, a motion vector in the position is obtained by an interpolating process using motion vectors of peripheral pixels. For example, the motion vector in the position indicated by x in the enlarged optical flow FT 2  is obtained by the interpolating process based on the motion vectors in the peripheral positions (the position indicated by the blank circle and the position indicated by the painted circle in  FIG. 13 ). 
   In step S 25 , by using the enlarged optical flow FT 2  and a Laplacian image H 12  at the same level at the following time t, a predictive image Q 02  at time (t−1) is obtained. 
   The image at time (t−1) is the image H 12  at the following time t after a travel by the motion vector. Therefore, on assumption that the predictive image Q 02  is correct, the pixel value of each of pixels in the predictive image Q 02  is equal to that of the pixel after movement by the motion vector of the enlarge optical flow FT 2  in the image H 12 . 
   On the basis of such a characteristic, the pixel value of each of pixels in the predictive image Q 02  is obtained as a pixel value in the corresponding position in the image H 12 . The corresponding position in the image H 12  is a position at the end point of the motion vector of which start point is the original position (x, y). 
   In order to obtain a more accurate value, as shown in  FIG. 14 , a weighted mean value of pixel values of four pixels (pixels in positions of blank circles in  FIG. 14 ) around the end point position of the motion vector is calculated. The weighted mean value is determined as a pixel value of the pixel in the predictive image Q 02 . 
   By repeating such an operation with respect to each of pixels, the predictive image Q 02  can be obtained. 
   When the enlarged optical flow FT 02  is correct, the predictive image Q 02  and the Laplacian image H 02  at time (t−1) coincide with each other. However, in many cases, a difference amount exists. 
   In step S 26 , a correction optical flow FC 2  for correcting the difference amount is calculated. The correction optical flow FC 2  is calculated on the basis of two images Q 02  and H 02 . Concretely, as described above, on assumption that a plurality of pixels in a local area have the same motion vector, a motion vector in each of pixels in a plurality of positions is calculated by using the least square method. 
   In step S 27 , an optical flow obtained by correcting the original enlarged optical flow FT 2  on the basis of the correction optical flow FC 2  by using a vector adding process is calculated as an optical flow FL 02 . 
   In such a manner, on the basis of the optical flow FL 03  at the lowest level, the optical flow FL 02  of an image at the next higher level is generated. 
   Further, in step S 28 , whether the optical flow FL 01  at the highest level is generated or not is determined. Since the optical flow FL 01  of the highest level is not generated yet at this time point, the program returns to step S 24 . 
   By repeating the processes in steps S 24  to S 27  on the basis of the optical flow FL 02 , the optical flow FL 01  at the next higher level is obtained. The processes in steps S 24  to S 27  are repeated until generation of the optical flow at the highest level is recognized in step S 28 . 
   After completion of the process up to the highest level is recognized in step S 28 , the process is finished. As a result, the optical flow FL 01  is generated as an optical flow at the time (t−1) regarding the image of the maximum resolution (original resolution). 
   The optical flow at the following time t is generated by applying the processes in steps S 21  to S 28  on the basis of the image I (t)  at time t and the image I (t+1)  at time (t+1). The optical flows at the time points are sequentially generated by repeating processes similar to the above. 
   Although the case of obtaining a predictive image at time (t−1) on the basis of the optical flow at time (t−1) in step S 25  has been described as an example, the present invention is not limited thereto. For example, it is also possible to obtain a predictive image regarding the following time t on the basis of the optical flow at time (t−1) and compare the predictive image with the image I (t) , thereby generating a correction optical flow. In this case, however, peripheral pixels as shown in  FIG. 14  cannot be assumed, so that it is difficult to improve precision of generation of the predictive image regarding the time t. 
   Another Method Of Obtaining Optical Flow (Modification) 
   In the above, the case of generating the optical flow at each time by repeating the processes in steps S 21  to S 28  has been described. The present invention, however, is not limited thereto. For example, an optical flow at each time may be generated by using a process as described below. 
   Concretely, once an optical flow F (t−1)  at time (t−1) is obtained by the processes of steps S 21  to S 28  or the like, an optical flow F (t)  at the following time t can be generated by using the optical flow F (t−1)  at the preceding time (t−1). By this method, without using the multi-resolution strategy, in other words, without using an image pyramid, the optical flow F (t)  can be obtained. Thus, higher processing speed can be achieved. In the following, the operation of the modification will be described with reference to  FIGS. 15 and 16 .  FIG. 15  is a conceptual diagram showing the operation, and  FIG. 16  is a flowchart showing the operation. 
   It is assumed here that the optical flow F (t−1)  and Laplacian images I (t+1)  and I (t)  are obtained in advance. The Laplacian image I (t+1)  can be obtained by performing an imaging process using, for example, the Laplacian filter shown in  FIG. 10  on an original image captured at time (t+1). The Laplacian image I (t)  can be obtained by performing an imaging process using a similar Laplacian filter on the original image captured at time t. 
   As shown in  FIGS. 15 and 16 , first, in step S 121 , on the basis of the optical flow F (t−1)  at time (t−1) and the Laplacian image I (t+1)  at time (t+1), a predictive image W (t)  at time t is obtained. 
   The image at time t becomes the Laplacian image I (t+1)  at the following time (t+1) after movement by the motion vector of the optical flow F (t) . Therefore, on assumption that the predictive image W (t)  is correct, the pixel value of each of pixels of the predictive image W (t)  is equal to that of a pixel in a position after the movement according to the motion vector of the optical flow F (t)  in the Laplacian image I (t+1) . 
   On the basis of such a characteristic, the pixel value of each of the pixels of the predictive image W (t)  is obtained as a pixel value in a corresponding position in the Laplacian image I (t+1) . The corresponding position in the Laplacian image I (t+1)  is an end point position (x+u (t−1) , y+v (t−1) ) of a motion vector (u (t−1) , v (t−1) ) T  using the original position (x, y) as a start point. In this case, however, is it assumed that the optical flow F (t)  is equal to the optical flow F (t−1) . 
   The pixel value of each of pixels of the predictive image W (t)  is obtained by, concretely, the following Equation 8.
 
 W   (t) ( x,y )= I   (t+1) ( x+u   (t−1) ( x,y ),  y+v   (t−1) ( x,y ))  Equation 8
 
   In Equation 8, the pixel value in each pixel position (x, y) in the predictive image W (t) is expressed as W (t) (x, y). 
   In order to obtain a value which is more accurate, in a manner similar to step S 25 , a weighted mean value of pixel values of four pixels around the end point position (x+u (t−1) , y+v (t−1) ) in the image I (t+1) of the motion vector (u (t−1) , v (t−1) ) T  using the original position (x, y) as a start point is calculated. The weighted mean value is determined as the pixel value of the pixel in the predictive image W (t) . 
   By repeating such an operation with respect to each of the pixels, the predictive image W (t)  is obtained. 
   When the optical flows F (t)  and F (t−1)  are the same, the predictive image W (t)  and the Laplacian image I (t)  coincide with each other. However, in many cases, a difference exists. 
   In the following step S 122 , a correction optical flow FE (t)  for correcting the difference amount is calculated. The correction optical flow FE (t)  is calculated on the basis of the predictive image W (t) and the Laplacian image I (t) . 
   Concretely, assuming that a plurality of pixels in a local area have the same motion vector, a motion vector of each of pixels in a plurality of positions is calculated by using the least square method. 
   In step S 123 , an optical flow obtained by correcting the optical flow F (t−1)  on the basis of the correction optical flow FE (t)  by using a vector adding process is derived as the optical flow F (t) . 
   Concretely, elements of each motion vector (u (t) , v (t) ) T  in the optical flow F (t)  is expressed by the following Equations 9 and 10 by using a correction motion vector (u e   (t) , v e   (t) ) T  of the correction optical flow FE (t) . In Equations 9 and 10, each of the elements u (t) , v (t) , u (t−1) , v (t−1) , u e   (t)  and v e   (t)  is a function in a position x, y.
 
 u   (t) ( x, y )= u   e   (t) ( x, y )+ u   (t−1) ( x+u   e   (t) ( x, y ),  y+v   e   (t) ( x, y ))  Equation 9
 
 v   (t) ( x, y )= v   e   (t) ( x, y )+ v   (t−1) ( x+u   e   (t) ( x, y ),  y+v   e   (t) ( x, y ))  Equation 10
 
   In such a manner, the optical flow F (t)  at the following time t can be generated by using the optical flow F (t−1)  at the preceding time (t−1). 
   Similarly, the optical flow F (t+1)  at the following time (t+1) can be also generated by using the optical flow F (t)  at time t. Concretely, it is sufficient to apply operations similar to those in steps S 121  to S 123  to the optical flow F (t)  at time t and the Laplacian image I (t+2)  at time (t+2). 
   Subsequently, an optical flow at the following time can be similarly generated by using an optical flow at the immediately preceding time. 
   As described above, by such an operation, without using the multi-resolution strategy, that is, without using an image pyramid, the optical flow can be obtained. Thus, higher processing speed can be achieved. 
   Other Modifications 
   In the foregoing embodiments, the case of realizing the process by software process in a computer has been described. The present invention is not limited thereto, and a similar process may be executed by using a dedicated hardware circuit. 
   Although a general computer system has been mentioned as a computer in the foregoing embodiments, the present invention is not limited to the general computer system. A similar process may be executed by using, as the “computer”, an embedded microcomputer or the like (computing processor). A program may be loaded into such an embedded microcomputer. 
   Further, the case of obtaining both of the number of passing people in the +Y direction and the number of passing people in the −Y direction has been described in the foregoing embodiments. However, the present invention is not limited to the case, and only the number of passing people in one direction (e.g., the number of passing people in the +Y direction) may be calculated. In other words, although the case of obtaining both of the first integral value E 1  regarding component values of the positive sign and the second integral value E 2  regarding component values of the negative sign has been described above, the present invention is not limited thereto. Only the integral value of the component values of one of the positive and negative signs may be obtained. 
   Concretely, only the number of passing people in the +Y direction may be obtained on the basis of only the integral value E 1  obtained by integrating v 1  as positive-sign components in components v perpendicular to the boundary line of a motion vector. 
   As described above, it is sufficient to obtain the number of moving objects (humans) passing the boundary line BL on the basis of the integral value E 1  and/or the integral value E 2  (in other words, at least one of the integral values E 1  and E 2 ) obtained by integrating components perpendicular to the boundary line of the motion vector with respect to the positive and negative signs. 
   In the foregoing embodiments, the case of obtaining, as an integral value obtained by integrating components perpendicular to the boundary line BL of the motion vector, at least one integral value obtained by integrating perpendicular components of one of the positive and negative signs, the perpendicular components being distinguished from another perpendicular components of the other one of both signs, has been described. Consequently, even there is the possibility that a plurality of moving objects travel not only in the same direction but also in the opposite direction, erroneous counting is prevented, and the number of passing objects can be measured accurately. 
   The present invention, however, is not limited to such a mode. For example, in the case where it is preliminarily known that the directions of movement of a plurality of moving objects are the same, the components perpendicular to the boundary line BL of the motion vector are always non-negative components (or always non-positive component). It is therefore sufficient to obtain the number of moving objects passing the boundary line on the basis of an integral value obtained by (without intentionally integrating components for each of the signs independently but simply) integrating components perpendicular to the boundary line BL of the motion vector. Particularly, when the number of moving objects passing the boundary line BL is calculated on the basis of an obtained integral value and a reference value regarding the integral value, the number of moving objects can be obtained more accurately. 
   While the invention has been shown and described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is therefore understood that numerous modifications and variations can be devised without departing from the scope of the invention.