Patent Publication Number: US-6222940-B1

Title: Pattern matching system and method which detects rotated and scaled template images

Description:
FIELD OF THE INVENTION 
     The present invention relates to improved methods for performing pattern matching to locate one or more instances of a template image in a target image, wherein the invention includes an efficient method for characterizing the template image, improved methods for performing the pattern matching, and improved methods for locating rotated and/or scaled images. 
     DESCRIPTION OF THE RELATED ART 
     In many applications it is necessary or desired to find a template image or image object in a larger target image. Such applications include machine vision applications including process monitoring, feedback control, and laboratory automation; image and video compression; and jitter compensation in video cameras, among others. 
     Prior art pattern recognition systems have typically used a template matching technique wherein the stored image or pattern to be located, referred to as the template, is iteratively compared with various corresponding portions of an image in which it is desired to locate the template, referred to as the target image. FIG. 1 illustrates the pattern matching problem as known in the prior art. As shown, the pattern matching problem involves a template image, wherein one or more instances of the template image are desired to be located in the target image. The template image and the target image are provided to a pattern matching algorithm which performs the pattern matching. The pattern matching algorithm generally operates to compare the pixels in the template image, or a selected subset of sample pixels, against each of the possible various locations in the target image. Typically, the pattern matching algorithm involves comparing the template image, or a subset of sample pixels representing the template image, against locations in the target image on a horizontal pixel column basis and horizontal scan line basis. In other words, the sample pixels representing the template image are compared against a portion of the pixels in the target image, such as by using a 2D correlation, the sample pixels representing the template are then moved down or across a one pixel scan line or one pixel column in the target image, and the pattern matching algorithm is repeated, etc. Thus, the pattern matching algorithm generally involves comparing the template image pixels against all possible locations in the target image in an iterative fashion. The pattern matching produces the location of the template in the image, the quality of match and possibly the orientation, size and/or scaling of the template. 
     The template is compared with portions of the target image typically utilizing a correlation based pattern matching, i.e., using normalized two dimensional correlation (normalized 2D correlation). This 2D correlation is performed by placing the template over the respective portion of the image and performing a complete normalized 2D correlation between the pixels in the template and the pixels in the corresponding portion of the image. This correlation generally produces a correlation value which indicates the degree of correlation or match. For example, the correlation value may range between −1 and +1, wherein +1 indicates a complete match, 0 indicates no match, i.e., that the two images are uncorrelated, and −1 indicates that the two images are anti-correlated, i.e., a complete reversal of a match. 
     The normalized 2D correlation operation is based on a point-wise multiplication wherein the template is first placed over a portion of the image, each point or pixel of the template is multiplied with the corresponding pixel in the respective portion of the image, and the result is summed over the entire template. Also, as noted above, the template image is generally compared with each possible portion of the target image in an iterative fashion. This correlation-based pattern matching technique is thus very computationally intensive. 
     Various optimizations or algorithms have been developed to provide a more efficient correlation-based pattern matching. One prior art technique is to use selected samples or pixels from the template image, referred to as sample pixels, to represent the template image and hence to reduce the number of computations in the correlation. 
     FIG. 2 illustrates the pattern matching process of the prior art which involves characterization of the template with a reduced number of sample pixels. In this process, a characterization of the template is performed to extract features from the template image. In other words, the template is characterized to represent the template image with a lesser number of points or pixels, referred to as sample pixels, which presumably accurately characterize the template image. The template image is characterized in this fashion because the time required for the pattern matching is generally directly proportional to the number of points or pixels representing the template image which are used in the pattern matching. Thus the template is characterized to reduce the number of samples or pixels which are used in the correlation operation, thereby reducing the amount of computation. Once a lesser number of sample pixels have been generated, these sample pixels are then used in the pattern matching algorithm to locate instances of the template image in the target image. 
     Prior art techniques for characterizing the template image have utilized a homogeneous sampling of the template, such as a grid-based sampling of the template, Another prior art technique is to utilize random points or pixels within the template image and to use these random sample pixels in the correlation-based pattern matching. However, each of the above prior art techniques operates to select a subset of the pixels in the template image which do not necessarily best represent or characterize the template image. In other words, homogeneous sampling or random sampling of the template image does not produce the optimum subset of samples or pixels which best represent the template image. 
     Therefore, an improved system and method is desired for correlation based pattern matching. More particularly, an improved system and method is desired for characterizing or selecting samples or pixels from a template image which best represent the template image with the fewest samples possible. 
     In addition, an improved system and method is also desired which reduces the number of correlation operations which are required in a pattern matching operation. Further, improved techniques are desired for performing pattern matching for rotated images, translated images and images which have changed in size. 
     SUMMARY OF THE INVENTION 
     The present invention comprises a system and method for performing pattern matching to locate zero or more instances of a template image in a target image. The pattern matching is preferably performed in a computer system. The template image is received and/or stored in the computer system and comprises a first plurality of pixels. The target image is preferably acquired by the system, such as by a camera and provided to the computer system for the pattern matching. 
     According to a first embodiment, the method and system first comprises sampling the template image using a Low Discrepancy sequence, also referred to as a quasi-random sequence, to determine a plurality of sample pixels in the template image which characterize the template image. The Low Discrepancy sequence is designed to produce sample points which maximizes the distance between sample points. Also, the Low Discrepancy sequence sampling results in fewer points and/or a better characterization of the template image than a random sequence sampling or a uniform sampling. Examples of the Low Discrepancy sequence include Halton, Sobol, Faure, and Niederreiter sequences. The sampling or characterization of the template image is preferably performed off-line prior to receipt of a target image. Thus the sampling or characterization of the template image is preferably not constrained by real time requirements. 
     After the template image is sampled or characterized, the method then performs pattern matching using the sample pixels and the target image to determine zero or more locations of the template image in the target image. 
     According to a second embodiment, the method and system comprises sampling the template image, wherein the template image comprises a first plurality of pixels, and wherein the sampling produces a second lesser number of sample pixels. This sampling may use any of various sampling techniques, including a Low Discrepancy sequence as described above. 
     The method then performs a local stability analysis around at least a subset of the sample pixels to determine a lesser third number of sample pixels which have a desired degree of stability. The local stability analysis operates to ensure stability of each of the subset of sample pixels to spatial perturbations around the sample pixel. For each pixel, the local stability analysis preferably comprises finding a neighborhood around the sample pixel where the value of the sample pixel correlates highly with the template image pixel values in the neighborhood. The local stability analysis is preferably performed for all of the sample pixels. The method then performs a pattern matching using the third plurality of sample pixels and the target image to determine zero or more locations of the template image in the target image. 
     In one embodiment, the local stability analysis determines a plurality of sets of sample pixels with differing stability neighborhood sizes, and the pattern matching comprises performing a plurality of iterations of pattern matching using different sets of sample pixels. The iterations are preferably performed in a coarse to fine manner, e.g., using sets of sample pixels with successively smaller stability neighborhood sizes. These plurality of iterations of pattern matching may also use different step sizes for each of the different sets of sample pixels, wherein the step size preferably corresponds with the stability neighborhood size. Thus the plurality of iterations of pattern matching in the coarse to fine manner preferably uses sets of sample pixels with successively smaller stability neighborhood sizes and/or successively smaller step sizes. For example, a first iteration of pattern matching may determine one or more candidate locations in the target image which possibly include the template image, and one or more second iterations of pattern matching are performed at the determined one or more candidate locations in the target image, and so on. 
     In a third embodiment, the present invention comprises a system and method for performing pattern matching to locate one or more instances of a rotated or scaled template image in a target image. The method comprises first sampling the template image along one or more rotationally invariant paths, preferably circular perimeters, to produce one or more sets of sample pixels. The method then comprises performing pattern matching using a cyclic correlation between each of the one or more sets of sample pixels and the target image to determine zero or more locations of the template image in the target image. This pattern matching detects rotated versions of the template image in the target image. 
     In one embodiment, the method includes performing a local stability analysis around at least a subset of the sample pixels. The method then performs pattern matching uses one or more sets of sample pixels along one or more circular perimeters based on the local stability analysis. The local stability analysis preferably determines a plurality of sets of sample pixels with differing stability neighborhood sizes. In this case, the pattern matching comprises performing a plurality of iterations of pattern matching using different sets of sample pixels, preferably in a coarse to fine manner, e.g., using sets of sample pixels from circular paths with successively smaller stability neighborhood sizes. The pattern matching may also use different step sizes for each of the different sets of sample pixels. As discussed above, a first iteration of pattern matching may determine one or more candidate locations and corresponding rotation values in the target image which possibly include the template image, and one or more second iterations of pattern matching are performed at the determined one or more candidate locations in the target image using the respective rotation values, and so on. A final pattern matching may utilize substantially all of the template image pixels at the respective candidate locations and using the determined rotation values. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A better understanding of the present invention can be obtained when the following detailed description of the preferred embodiment is considered in conjunction with the following drawings, in which: 
     FIG. 1 illustrates the pattern matching as performed in the prior art; 
     FIG. 2 illustrates pattern matching performed in the prior art which includes characterization of the template image with fewer pixels for reduced computation; 
     FIG. 3 illustrates a machine vision system according to one embodiment of the present invention; 
     FIG. 4 is a high-level block diagram of the machine vision system; 
     FIG. 5 is a flowchart diagram illustrating the pattern matching method of the present invention, including sampling of the template image with a Low Discrepancy sequence; 
     FIG. 6 is a flowchart diagram illustrating the generation of sample pixels using local stability analysis according to the preferred embodiment; 
     FIG. 7 is a flowchart diagram illustrating the pattern matching method using a coarse to fine search according to the preferred embodiment; 
     FIG. 8 is a flowchart diagram illustrating the pattern matching method of the preferred embodiment, incorporating the flowcharts of FIGS. 5-7; 
     FIGS. 9 a - 9   f  illustrate pattern matching without a step size according to the prior art; 
     FIGS. 10 a - 10   f  illustrate pattern matching using a 9×9 step size based on local stability analysis performed according to the present invention; 
     FIGS. 11 a - 11   f  illustrate pattern matching using a 5×5 step size based on local stability analysis performed according to the present invention; 
     FIG. 12 is a flowchart diagram illustrating the pattern matching method for rotation invariant matching according to the present invention; 
     FIG. 13 is a flowchart diagram illustrating the pattern matching method for rotation invariant matching according to the preferred embodiment of the present invention; 
     FIGS.  14 A, 14 B and  15  illustrate the rotation invariant pattern matching method; and 
     FIG. 16 illustrates an image characterization method using a Low Discrepancy sequence. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention comprises a system and method for performing pattern matching. The pattern matching system and method of the present invention may be used in a number of different applications including various types of machine vision systems, e.g., industrial automation, robotic vision, or traffic analysis, and image or video compression, such as MPEG compression, among others. 
     The present invention also comprises a system and method for representing an image with a reduced number of sample pixels. This system and method for representing an image using a reduced number of sample pixels may also be used in a large number of different applications, such as pattern matching, image compression, video compression, archival of image data, etc. 
     FIG.  3 —Machine Vision System 
     FIG. 3 illustrates an example of a machine vision application wherein the pattern matching system and method of the present invention may be used. The machine vision system comprises a host computer  102  and a video source  112 . The video source  112  preferably produces a digital video signal which comprises an image or a sequence of images or video frames, or other data desired to be acquired. The digital video signal is provided through a wire or cabling  122  to the host computer  102  for storage and/or processing. The host computer  102  includes various standard components, such as at least one CPU, memory, etc. 
     The host computer  102  stores a template image or pattern. According to the present invention, the host computer  102  also stores software which performs pattern matching to locate zero or more instances of the template image in the target image. According to the present invention, the software is executable to sample the template image to generate sample pixels which best represent or characterize the template image, and to use these sample pixels in the pattern matching operation. 
     In the embodiment of FIG. 3, the host computer  102  receives the target image from the video source  112  and performs pattern matching using sample pixels generated from the stored template image. However, in other embodiments, the computer  102  may receive the target image and/or the template image from another source, or one or both of the target image and the template image may be pre-stored on the computer. 
     FIG. 3 illustrates a machine vision application, wherein the computer system  102  is coupled to a camera  112  and operates to receive a target image and perform pattern matching to locate one or more instances of a template image in the target image. The computer system of FIG. 3 is programmed according to the present invention to represent the template image with a reduced number of sample pixels and/or to perform the improved pattern matching methods of the present invention. The pattern matching and/or image characterization techniques of the present invention may be used in various types of machine vision applications. For example, the computer  102  may be embodied in various form factors and/or architectures, e.g., a robot, among others. It is also noted that the pattern matching and/or image characterization techniques of the present invention may be performed in any of various manners, either in software, programmable logic, or hardware, or a combination thereof 
     FIG.  4 —Video Capture System Block Diagram 
     FIG. 4 is a high-level block diagram of the video capture system of FIG.  3 . It is noted that the block diagram of FIG. 4 is exemplary only, and other computer system architectures may be used as desired. For example, the present invention may be implemented in a “smart camera”, for example, which integrates a sensor, analog to digital (A/D) converter, CPU and communications devices together in a single unit. The present invention may be embodied in other architectures or embodiments, as desired. 
     As shown in FIG. 4, the host computer  102  preferably comprises a CPU  202 , a Bus Bridge  204 , system memory  206 , and a peripheral bus  212 . The CPU  202  is coupled to the Bus Bridge  204 . The Bus Bridge  204  is coupled to the system memory  206  and the CPU  202 , and couples to the peripheral bus  212 . In the preferred embodiment, the peripheral bus  212  is the PCI expansion bus, although that other types of buses may be used. 
     In this embodiment, the host computer system  102  also includes a video capture board  214  which is adapted for coupling to the video source  112 . The video capture board  214  is preferably coupled to the peripheral bus  212 . In addition to the video capture board  214 , other peripheral devices ( 216  and  218 ) may be coupled to the peripheral bus  212 , such as audio cards, modems, graphics cards, network cards, etc. 
     The video source  112  supplies the digital video signals to the video capture board  214 . The video capture board  214  transfers the digitized video frames to the system memory  206  through peripheral bus  212  and Bus Bridge  204 . In this embodiment, the video capture board  214  acquires the target image and transfers the target image to system memory  206 . 
     The system memory  206  preferably stores a template image or pattern. The system memory  206  also preferably stores software according to the present invention which operates to characterize the template image with a reduced number of samples. The software samples the template image using a Low Discrepancy sequence, such as a Halton sequence or Sobol sequence. The sampling of the template image using a Low Discrepancy sequence according to the present invention is discussed further below. The system memory  206  also preferably stores software according to the present invention which performs pattern matching using the sample pixels with improved efficiency. 
     The present invention is preferably implemented in one or more software programs which are executable by a processor or CPU. The software program(s) of the present invention are preferably stored in a memory medium. As used herein, the term “memory medium” is intended to include an installation media, e.g., a CD-ROM, DVD, or floppy disks, a computer system memory such as DRAM, SRAM, EDO RAM, etc., or a non-volatile memory such as a magnetic medium, e.g., a hard drive, or optical storage, among other types of memory. 
     FIG.  5 —Pattern Matching Flowchart 
     FIG. 5 is a flowchart diagram illustrating a method for performing pattern matching according to the present invention. 
     As shown, in step  402  the template image is received by or stored m the computer system. The template image may be received from any of various sources, as desired. The template image preferably comprises a first plurality of pixels. 
     In step  404  the template image is characterized or sampled to represent the template image with a lesser number of pixels or samples which accurately characterize the template image. According to the preferred embodiment of the invention, the pixels comprising the template image are sampled using a Low Discrepancy sequence. Low Discrepancy sequences comprise mathematical sequences that are efficient samples of high dimensional spaces. A Low Discrepancy sequence is also referred to as a quasi-random sequence or a sub-random sequence. The Low Discrepancy sequence is designed to produce sample points which maximally avoid each other, i.e., is designed to produce sample pixels which best represent the image. Examples of Low Discrepancy sequences include the Halton sequence, the Sobol sequence, the Faure sequence and the Niederreiter sequence, wherein differences between these are minor from a real world applications point of view. Sampling the template image using a Low Discrepancy sequences results in much fewer sample pixels to characterize the template image and/or a better characterization of the template image than would a random sampling technique or a uniform sampling technique. 
     The following is an example of the operation of a Low Discrepancy sequence (Halton set). 
     First, at step  1  the method selects the type of Low Discrepancy sequence, e.g., Halton, 2d (2-dimensional). In general, mathematicians are interested in nd applications of low-discrepancy sets where n&gt;10, sometimes n&gt;100. However, for a 2-dimensional image, a 2d sequence is used. 
     At step  2  the method then selects a criteria for construction of the Halton set, for example, construction in the unit square [0,1]×[0,1], it being noted that the general case can be derived by a scaling operation. 
     At step  3  the method then selects two prime numbers p and q. It is very common to use p=2 and q=3, although this is not necessary. Every pair of (p,q) results in a slightly different Halton set, wherein all of these sets are equivalent. 
     The variables (x n ,y n ) denote the nth element of the Halton set. Given n, at step  4  the method notates n in the p-ary system (in the case where p=2 it is the well-known binary system). The result is n=a k , . . . a 1 , a 0  where the a&#39;s are 0 or 1 in case of the binary system, but 0, 1, . . . , p-1 in the general case. 
     At step  5 , the method then reverses the order of a k , . . . a 1 , a 0 . This results in a 0 , a 1 , . . . a k . 
     At step  6  the method then adds the (n-ary) point, i.e. a k , . . . a 1 , a 0 . This number is in between 0 and 1 and represents the x-component of the nth Halton point (xn,yn). 
     At step  7  the method repeats steps ( 4 )-( 6 ) based on the other number system q. This produces the y-component. 
     After steps  1 - 7 , the nth point of the Halton sequence has been constructed. 
     The following is an example of the construction of a Low Discrepancy sequence in 2d. Here it is assumed that p=2 and q=3. This example determines the 10th element, i.e., (x 10 , y 10 ). 
     The method starts with the x-component as follows: 
     (4′) 10=1010 (decimal=binary) because 10=1*8+0*4+1*2+0*1 
     (5′) reverse the order-&gt;0101 
     (6′) add the point -&gt;×10=0.0101 (0.0101 can be translated into 0*(½)+1*(¼)+0*(⅛)+1 *({fraction (1/16)})=¼+{fraction (1/16)}={fraction (5/16)} 
     Now the y-component is computed as follows: 
     (4″) 10=101 (decimal-ternary) because 10=1*9+0*3+1*1 
     (5″) reverse the order -&gt;101 
     (6″) add the point -&gt;y10=0.101 (0.101 can be translated into 1*(⅓)+0*({fraction (1/9)})+1*({fraction (1/27)})={fraction (10/27)} 
     For more information on Low Discrepancy sequences, please see “Numerical Recipes in Fortran  77 : The Art of Scientific Computing” (ISBN -521-43064-X) Cambridge University Press, pgs. 299-306, which is hereby incorporated by reference as though fully and completely set forth herein. 
     In step  406  the target image is received and/or stored in the computer system. In the embodiment of FIG. 3, the target image is received from the camera  112 . However, as noted above, the target image may be received from any of various sources, as desired. The target image is usually significantly larger than the template image. 
     In step  408  pattern matching is performed using the sample pixels generated in step  404  to find zero or more instances of the template image in the target image. In the preferred embodiment, the sample pixels determined in step  404  are iteratively compared with selected portions of the target image, preferably using a 2D correlation technique, to find matches and hence to determine instances or locations of the template image in the target image. The pattern matching may use a computed step size to step across the image and/or use a coarse to fine search method for improved efficiency. 
     In many applications, it is necessary or desired to perform the pattern matching in real time when the target image is acquired. In machine vision applications, “real time” often refers to “video real time”, i.e., to performing the function for every single image acquired by the camera, e.g., for a NTSC camera that acquires 30 flames/second. For example, in the machine vision embodiment shown in FIG. 3, the pattern matching is preferably performed in real time when the target image is acquired by the camera  112 . However, in these real time embodiments, the template image is typically pre-stored in the computer  102 , and there is generally a large amount of time in which to characterize or process the template image to produce the sample pixels. Once the sample pixels have been generated, the system can perform the pattern matching method a plurality of times for a plurality of acquired target images, preferably in real time. 
     In step  410  the pattern matching results are generated, preferably providing an indication of the locations of the template image in the target image. The pattern matching method may also provide information on the orientation(s) of the template image, the size of the template, and other information. 
     The Low Discrepancy sequence used for sampling the template image according to the present invention optimally samples the template image to determine a plurality of sample pixels which best represent the template image with the fewest number of pixels. 
     FIG.  6 —Sampling of the Template Image 
     FIG. 6 is a flowchart diagram illustrating an alternate embodiment of the template characterization or representation performed in step  404  of FIG.  5 . The flowchart of FIG. 6 thus illustrates an alternative method for representing an image, such as a template image, with a reduced number of sample pixels which accurately characterize the image. 
     As shown, in step  442  the image is sampled to produce a plurality of sample pixels which represent the image. In this embodiment, the template image may be sampled using any of various sampling techniques, such as a uniform sampling technique, i.e., a uniform grid based sampling, a random sampling sequence, or using Low Discrepancy sequences such as the Halton or Sobol sequence as described with respect to step  404  of FIG.  5 . In the preferred embodiment, a Low Discrepancy sequence is used to sample the image because the Low Discrepancy sequence produces the fewest sample pixels or points which accurately characterize the image. 
     After the sampling of the image has been performed to produce a plurality of sample pixels, in step  444  a local stability analysis is performed for at least a subset of and preferably for all of the generated sample pixels to determine stability of the respective sample pixels to spatial perturbations. For each candidate sample pixel value for which this local analysis is performed, the method operates to determine a neighborhood around the respective candidate sample pixel where the template image pixel values comprised in the neighborhood correlate highly with the candidate sample pixel value. In other words, for each candidate sample pixel value for which the local stability analysis is performed, a correlation is performed with neighboring pixel values within the template image to determine if the candidate sample pixel value is stable within its neighborhood, i.e., the neighboring pixel values have similar or correlated values with the respective candidate sample pixel value. 
     In step  446  the method optionally operates to save only those candidate sample pixel values which have a requisite stability within a predetermined or predefined neighborhood size. Sample pixel values generated in step  442  which are not stable within the pre-defined neighborhood are preferably thrown out or not used. Thus, this method operates to further reduce the number of sample pixel values used in the pattern matching operation. Stated another way, the method shown in FIG. 6 operates to represent an image, such as a template image used in pattern matching, with an even further reduced number of sample pixel points. 
     In one embodiment of the invention, described below with respect to FIG. 7, after either of steps  444  or  446 , in step  448  the method further operates to find or detect different respective stability regions or neighborhood sizes for which each of the respective subset or all of the sample pixel values are stable, according to a stability criteria or varing stability levels. Stated another way, the method operates to detect and categorize subsets of sample pixel values with varying stability regions, i.e., operates to categorize subsets of sample pixel values according to stability region size. 
     The different stability region sizes are also preferably used to determine a step size for stepping the respective sample pixels across the target image in the pattern matching process. This step size is used during the pattern matching operation to reduce the number of correlations required to be performed in the pattern matching. Thus, for a set of sample pixel values which have a larger stability neighborhood size, the set of sample pixel values can be stepped across the target image during the iterative correlation process with a larger step size. A set of sample pixel values with a smaller stability neighborhood size are stepped across the target image during the iterative correlation process with a correspondingly smaller step size. 
     As described below with respect to FIG. 7, in the subsequent pattern matching process, the sample pixel values having different stability neighborhood sizes are then used in a coarse to fine search, preferably using the respective computed step sizes. Thus the method operates to determine different stability neighborhood sizes and corresponding step sizes for use in a coarse to fine pattern matching search. 
     As described above, in machine vision applications, generally a large or infinite amount of time is available for characterizing the template image. In contrast, when the target image is obtained, it is generally desirable for the pattern matching to occur as quickly as possible. Therefore, a relatively large amount of processing may be performed to characterize or represent the template image, including sampling the template image using Low Discrepancy sequences, local stability analysis for each of the sample pixel values and computation of desired step sizes. This preprocessing is not required to be performed in real time. Rather this preprocessing of the template image is performed to enable a faster pattern matching computation when the target image is acquired. 
     FIG.  7 —Pattern Matching Using Computed Step Sizes and Coarse to Fine Searching 
     FIG. 7 is a flowchart diagram illustrating the pattern matching process performed in step  408  of FIG. 5 according to the preferred embodiment of the present invention The flowchart of FIG. 7 illustrates pattern matching using different stability neighborhood sizes and corresponding step sizes in a coarse to fine search. Steps which are similar or identical with those in FIGS. 5 and 6 have the same reference numerals for convenience. 
     As shown, in step  462  the method operates to perform a coarse pattern matching using a first set of sample pixel values which have a first stability neighborhood size and a corresponding first step size. Thus the method performs a first iteration of pattern matching using the first set of sample pixel values and the first step size. The first set of sample pixels used for the initial coarse pattern matching preferably have the largest stability neighborhood size and hence the largest step size. This coarse pattern searching produces zero or more possible locations for the template image in the target image. In other words, this coarse pattern searching produces zero or more candidate locations in the target image which possibly include the template image. 
     After step  462 , in step  464  the method operates to perform a finer pattern matching at these possible locations or candidate locations using a second set of sample pixel values which have a second stability neighborhood size and a corresponding second step size, wherein the second stability neighborhood size and the second step size are smaller than the first stability neighborhood size and first step size. This finer pattern searching produces zero or more possible locations for the template image in the target image, and typically involves discarding one or more false matches produced in the coarse search performed in step  462 . 
     Step  464  may be repeated one or more times to perform even finer pattern matching using other sets of sample pixel values which have even smaller stability neighborhood sizes and corresponding second step sizes. Step  464  is preferably repeated at the remaining candidate locations. After one or more iterations of step  464 , the method may involve performing a final pattern matching in step  464  using all of the sample pixel values to determine if any remaining possible matches are actual matches. Alternatively, after one or more iterations of step  464  and/or after a pattern matching step using all of the sample pixel values, in step  466  the method further optionally performs a pattern matching using all of the template pixels for the remaining candidate locations in the target image. The number of iterations that are performed in step  464  depends on the degree of desired preciseness in the pattern matching. In a similar manner, the decision whether step  466  is performed also depends on the degree of desired preciseness in the pattern matching. 
     Thus the pattern matching comprises performing a plurality of iterations of pattern matching using different ones of the sets of sample pixels, preferably with different step sizes. Where the local stability analysis determines a plurality of sets of sample pixels with differing stability neighborhood sizes, the pattern matching comprises performing a plurality of iterations of pattern matching using different ones of said sets of sample pixels in a coarse to fine manner, e.g., with successively smaller stability neighborhood sizes and/or successively smaller step sizes. If a first iteration of pattern matching determines one or more candidate locations in the target image which possibly include the template image, then one or more second iterations of pattern matching are performed at the determined one or more candidate locations in the target image. The first iteration of pattern matching utilizes a first stability neighborhood size and a first step size, and each of the one or more second iterations of pattern matching preferably utilize a smaller stability neighborhood size and a smaller step size. 
     As an example of the operation of the pattern matching performed in FIG. 7, presume the method in step  448  detects a first set of sample pixel values which have a 9×9 stability neighborhood size and a second set of sample pixel values with a 5×5 stability neighborhood size, etc. When performing the pattern matching search in step  462 , the method preferably starts using the sample pixel values which have the larger stability neighborhood size, e.g., the 9×9 stability neighborhood size. This search also uses a step size corresponding to this stability neighborhood size, e.g., a step size of 9 pixels. Thus, because these points or sample pixel values are stable over a 9×9 region, the search process is performed whereby, instead of visiting each pixel in the target image to compute the match values, the pattern matching is preferably performed at a step size of every 9 pixels. 
     Once this initial core search determines an initial set of possible matches, the second set of sample pixel values with a smaller neighborhood size, e.g., with the 5×5 stability regions, are used to perform a pattern matching at these initial match locations to perform a more refined search of these locations. This coarse to fine search based on stability neighborhood size and step size may be performed for a plurality of coarse to fine iterations until a desired degree of pattern matching has been accomplished. 
     FIG.  8 —Pattern Matching Method of the Preferred Embodiment 
     FIG. 8 illustrates the pattern matching method of the preferred embodiment. FIG. 8 comprises the combination of FIGS. 5,  6  and  7  displayed in a single flowchart. 
     FIGS. 9 a - 9   f:  Comparing the Template Image with Every Possible Portion of the Target Image 
     FIGS. 9 a - 9   f  illustrate a prior art pattern matching technique wherein the template image or sample pixels representing the template image are compared against every possible portion of the target image. In FIGS. 9 a - 9   f , the shaded block represents the template image or the sample pixels representing the template image. 
     As shown in FIGS. 9 a - 9   f , in a prior art pattern matching techniques the template image is compared with each possible portion of the target image. Thus, for example, in FIG. 9 a  the template image is compared with a corresponding portion of the target image at the upper left portion of the target image. After this comparison has been performed, the template image is moved down one scan line of pixels as shown in FIG. 9 b  and compared with the next perspective portion of the target image. After this comparison, the template image is moved down again one pixel scan line as shown in FIG. 9 c  and is compared with another portion of the target image. This is repeated a plurality of times until the template image reaches the very bottom left portion of the target image as shown in FIG. 9 d.  After the template image is compared with the bottom left portion of the target image as shown in FIG. 9 d,  the template image, for example, is moved back to the very top of the target image and moved across one vertical column of pixels to begin a new set of comparisons as shown in FIG. 9 e . After this comparison is performed in FIG. 9 e , the template image is moved down one horizontal scan line of pixels and compared with the next respective portion of the target image as shown in FIG. 9 f . This operation again repeats a plurality of times until the template image again reaches the bottom of the target image. At this point, the template image is moved back to the top of the target image and across one more vertical column of pixels (not shown) to perform another set of comparisons. The comparisons repeat until the template image has been compared with every possible corresponding portion of the target image. As can be readily seen, this results in a large amount of computations. It is also noted that the template image may be moved in various manners across the target image, such as horizontally, vertically, or combinations thereof. 
     FIGS. 10 a - 10   f:  Comparing the Template Image with the Target Image Using a 9 Pixel Step Size 
     FIGS. 10 a - 10   f  illustrate the pattern matching performed using a step size of 9 pixels from the example above. As shown, for the coarse search using a step size of 9 pixels, the template image is stepped across respective portions of the target image with a 9 pixel step size instead of a 1 pixel step size. In other words, as shown in FIG. 10 a,  the template image, or the sample pixels representing the template image, are initially compared with a corresponding portion of the target image, such as the upper left corner of the target image. After this comparison has been performed in FIG. 10 a , the template image, for example, is moved downward 9 pixel scan lines as shown in FIG. 10 b  and is compared with the next respective portion of the target image. After this comparison has been performed in FIG. 10 b , the template image is moved another 9 scan lines downward as shown in FIG. 10 c,  and the sample pixels are again compared with the respective portion of the target image. The comparisons are repeated until the template image reaches the bottom left portion of the target image, as shown in FIG. 10 d . After this comparison, the template image, for example, is moved back to the top of the target image and is moved over 9 vertical pixel columns to perform another comparison, as shown in FIG. 10 e.  After this comparison is performed in FIG. 10 e , the template image is moved down 9 horizontal scan lines of pixels and compared with the next respective portion of the target image as shown in FIG. 10 f . This operation again repeats a plurality of times until the template image again reaches the bottom of the target image. At this point, the template image is moved back to the top of the target image and across 9 more vertical column of pixels (not shown) to perform another set of comparisons. This operation is performed until the template image has been stepped across the entire target image, using a 9 pixel step size. It is noted that FIGS. 10 a - 10   f  are merely an example of stepping the template image across the target image, it being noted that the template image may be stepped across the target image in any of various manners, i.e., left to right, right to left, top to bottom, bottom to top, or other methodologies. 
     FIGS. 11 a - 11   f:  Comparing the Template Image with the Target Image Using a 5 Pixel Step Size 
     FIGS. 11 a - 11   f  illustrate the pattern matching performed using a step size of 5 pixels from the example above. As shown, for the finer search using a step size of 5 pixels, the template image is stepped across respective portions of the target image with a 5 pixel step size. In the preferred embodiment, the finer search is only performed at locations which are indicated to be possible matches in the initial coarse search. 
     Thus, FIG. 10 a - 10   f  illustrate performance of a pattern matching using a first set of sample pixel values with a larger stability neighborhood. FIGS. 11 a - 11   f  illustrate the pattern matching algorithm using a second set of sample pixel values with a smaller stability neighborhood size and smaller step size, preferably performed at possible match locations indicated by the first pattern matching step. As discussed above with respect to step  464 , this finer search may be repeated zero or more times, each iteration preferably with a smaller step size and a greater number of samples, until a desired degree of precision has been obtained. A final pattern matching iteration may involve using all pixels in the template image at the one or more locations in the target image which are possible matches. 
     It is noted that performing pattern matching using a step size is a prior art technique. However, prior art methods generally use the same sample pixels or template image regardless of step size. 
     Therefore, in the preferred embodiment of the present invention, the method operates to select a subset of sample pixels for a respective pattern matching comparison based on a local stability analysis. The method of the present invention also operates to compute a step size based on a determined stability region or neighborhood of the respective sample pixels. The method further operates to use different subsets of sample pixels and different corresponding step sizes in a coarse to fine analysis. 
     FIG.  12 —Rotation Invariant Pattern Matching 
     FIG. 12 is a flowchart diagram illustrating a method for performing rotation invariant pattern matching. The method of FIG. 12 includes characterizing or representing the template image for rotation invariant matching. Thus, in FIG. 12 the objective is to efficiently sample the image to find a reduced set of sample pixel values or points that characterize the template accurately, and which are also conducive for finding the template image in the target image irrespective of the orientation of the template image in the target image. Steps in FIG. 12 which are similar or identical to previously discussed steps have the same reference numerals for convenience. 
     As shown in FIG. 12, in step  402  the method receives/stores the template image. 
     In step  502  the method operates to sample or locate pixel values in the template image along one or more rotationally invariant paths, e.g., the circular perimeter of one or more circles. This essentially operates to sample the image in a manner which is rotationally invariant, i.e., locate pixels in the template image along one or more circular perimeters or circular paths. 
     After step  502 , in step  406  the target image is received and/or stored in the computer system. 
     After the target image is received and/or stored in step  406 , in step  504  the method performs pattern matching using the circular perimeter sample pixels and the target image. The pattern matching may be performed for each of the one or more circles located in the template image. This rotation invariant pattern matching preferably uses a cyclic correlation. The cyclic correlation method first correlates the two signals, i.e., the samples pixels taken from the circular path and the respective pixels in the target image, to determine a correlation value. After this first correlation, the method shifts one signal, e.g., the sample pixels, with respect to the other signal by one sample pixel and again performs a correlation. This process is repeated, preferably until all possible correlations have been performed, i.e., until the sample pixels have been shifted back to their original location. After each of these correlations has been performed, the method determines the location and/or rotation of maximum correlation. This provides information (good estimations) on the location and rotation of the template image in the target image. 
     The pattern matching performed in step  504  may also be used to search for changes in size of the template image in the target image. In other words, the pattern matching performed in step  504  may also be used to search for scaled versions (larger or smaller) of the template image. This is accomplished by scaling (increasing or decreasing) the size of the search circles. More particularly, for scale invariant matching, the method uses sample pixels from a respective circular perimeter from the template (e.g., of radius “R”). During the pattern matching, the method changes the radius of the search circle. The method increases the radius R when searching for patterns that are bigger than the template image and decreases the radius R when searching for patterns in the image that are smaller than the template image. 
     FIG.  13 —Rotation Invariant Pattern Matching Including a Coarse to Fine Search 
     FIG. 13 is a flowchart diagram illustrating a method for performing rotation invariant pattern matching using a coarse to fine search procedure. 
     In step  402  the method receives / stores the template image. 
     In step  502  the method operates to locate pixel values in the template image along one or more rotationally invariant paths, e.g., along a circular perimeter of one or more circles. This essentially operates to sample the image in a manner which is rotationally invariant, i.e., locate sample pixels in the template image along one or more circular perimeters or circular paths. 
     In step  512  the method optionally performs a local stability analysis on the sample pixel values from each circular path to determine respective stability with respect to spatial perturbations. For each sample pixel, the local stability analysis comprises finding a neighborhood around the sample pixel where the value of the sample pixel correlates highly with the template image pixel values in the neighborhood In step  512  the method determines the stability region or neighborhood size for the sample pixels of each of the respective circles. The method also preferably computes a step size for each of the circles. The local stability analysis thus determines a plurality of sets of sample pixels with differing stability neighborhood sizes. 
     In step  514  the method selects the sample pixels of the most stable circle for the initial search process. Alternatively, the method selects an ordering of sample pixels from at least a subset of the circles, preferably from most stable to least stable, for use in the coarse to fine search. 
     After step  514 , in step  406  the target image is received and/or stored in the computer system. 
     After the target image is received and/or stored in step  406 , in step  522  the method performs pattern matching using the sample pixels from one or more of the most stable circles. The method preferably compares the sample pixels with a plurality of portions of the target images, optionally using the computed step size to step the sample pixels across the target image. The pattern matching performed in step  522  preferably determines zero or more candidate locations where a rotated version of the template image may be located. This pattern matching also preferably determines a rotation value indicating the possible rotation of the template image in the target image based on the maximum correlation value obtained in the cyclic correlation. 
     After step  522 , in step  524  the method performs pattern matching using sample pixels from one or more other circles to improve results. In the preferred embodiment, the method performs a coarse to fine search, wherein in step  522  the method determines one or more candidate locations and corresponding rotation values where the template image may be located. In step  524  the method performs pattern matching using sample pixels from one or more other less stable circles at these candidate locations and preferably using these rotation values. Thus, the method performs a coarse to fine search process as described above, wherein sample pixel values for the most stable circular path are first used in an initial search process, and then sample pixel values from additional circles are used at possible match locations to improve the initial search results and accurately determine the template&#39;s position and rotation in the image. 
     In the preferred embodiment, the rotation invariant pattern matching method utilizes non-overlapping circular paths in the image. Also, in the preferred embodiment the method uses multiple circles to reject false matches. The method also may use concentric circles, as desired. FIGS. 14A and 14B illustrate the characterization of the template image (a printed circuit board) for rotation invariant matching using sample pixels taken from one or more circular paths. FIG. 14A shows the use of sample pixels from concentric circles, and FIG. 14B shows the use of non-concentric, non-overlapping circles. FIGS. 14A and 14B also show an example template image which is desired to be found in the target image. FIG. 15 is an actual screen shot illustrating the use of concentric and non-concentric circles. 
     After step  524 , in step  526  the method optionally performs a pattern matching using all of the template image pixels, preferably using a rotation value determined in either of steps  522  or  524  to rotate the template image pixels prior to the pattern matching. In other words, the template image is rotated to approximately match the orientation of the candidate template image in the target image, and then the pattern matching is performed using all of the template image pixels. This rotation of the template image prior to the pattern matching is necessary since the entire template image is not rotationally invariant. 
     After the pattern matching performed in steps  522 ,  524  and/or  526 , then method then generates the results in step  410 . In this case, the results include the location of zero or more template image instances in the target image, as well as the rotation or orientation of each instance. 
     The pattern matching performed in step  504  and/or the methods described in FIGS. 12 and 13 may also be used to search for changes in size of the template image in the target image. In other words, the pattern matching performed in step  504  may also be used to search for scaled versions (larger or smaller) of the template image. This is accomplished by scaling (increasing or decreasing) the size of the search circles. More particularly, for scale invariant matching, the method uses sample pixels from a respective circular perimeter from the template (e.g., a circle of radius “R”). During the pattern matching, the method changes the radius of the search circle. The method increases the radius R when searching for patterns that are bigger than the template image and decreases the radius R when searching for patterns in the image that are smaller than the template image. 
     FIG.  16 —Characterization of an Image for General Applications 
     FIG. 16 is a flowchart diagram illustrating a system and method for representing an image with a reduced number of pixel values according to the present invention. Thus, FIG. 16 illustrates a generalized method for representing an image with a reduced set of points or pixels. This method may be used to represent a template image in a pattern matching application. However, the general method shown in FIG. 16 may be used to represent an image for any of various different types of applications including those other than pattern matching, such as image compression, video compression, image archival, other applications. 
     As shown, in step  402 A the image is received by or stored in the computer system. The image may be received from any of various sources, as desired. The image preferably comprises a first plurality of pixels. 
     In step  404 A the image is characterized or sampled to represent the image with the lesser number of pixels or samples which accurately characterize the image. According to the preferred embodiment of the invention, the pixels comprising the image are sampled using a Low Discrepancy sequence as described above with respect to step  404  of FIG.  5 . 
     Although the system and method of the present invention has been described in connection with several embodiments, it is not intended to be limited to the specific forms set forth herein, but on the contrary, it is intended to cover such alternatives, modifications, and equivalents, as can be reasonably included within the spirit and scope of the invention as defined by the appended claims.