Abstract: System and method for determining the presence of an object of interest from a template image in an acquired target image, despite of or using various types of affine transformations of the object of interest in the target image. A template image discrete curve is determined from the template image corresponding to the object of interest, and a template curve canonical transform calculated based on the curve. The canonical transform is applied to the template curve to generate a mapped template curve. The target image is received, a target image discrete curve determined, and a target curve canonical transform computed based on the target curve canonical transform. The target canonical transform is applied to the target curve to generate a mapped target curve. Geometric pattern matching is performed using the mapped template and target image discrete curves to generate pattern matching results, and the pattern matching results are output.

Abstract: A system and method for improving the accuracy and convergence rate in determining the affine transformation of one image or array of values with respect to another image or array of values. A particular embodiment of the present invention comprises a reference and an input image. A gradient matrix, &lgr;, may be constructed to contain gradient information of the position values of the reference image. Also, an estimate matrix, &rgr;, may be constructed to contain initial estimates of at least one of position, angle and scale of the input image. The input image is then subtracted from the reference image pixel by pixel producing an error matrix, e. The error matrix, e, is then multiplied with the matrices, &lgr; and &rgr;. The result is the new change in the position, angle and scale of the input image. New values for the position, angle and scale are calculated from the changes in the position, angle and scale values of the input image.

Abstract: A system and method for estimating the shift between two signals. The shift estimation system method comprises: (a) receiving a first signal, where the first signal may be represented as a vector g having N components; (b) projecting the vector g to a space with dimension K less than N to obtain a projection vector X having K components; (c) computing measures of distance between the projection vector X and each vector in a set of stored vectors; (d) determining a stored vector p in the set of stored vectors with a minimum distance to the projection vector X. The stored vectors are generated from a template signal f, also represented as a vector with N components, by projecting shifted versions of the template signal f to the space of dimension K. The shifted versions of the template signal f may be referred to as shifted template vectors, or simply, shift vectors.

Abstract: System and method for determining the presence of an object of interest in a target data set. Portions of a target data set may be located that match an object of interest, e.g., in a template data set, with respect to various information, e.g., edge or boundary information. The invention includes improved methods for mapping point sets or curves to new point sets or curves for curve matching. The method determines the presence of an object of interest in a target data set despite of or using various types of topological transformations of the object of interest in the target data set. One or more mapping operators are determined based on template curves and/or example target curves. Pattern matching is performed on one or more target data sets using the mapping operator(s) to generate pattern matching results, and the pattern matching results output.

Abstract: System and method for determining the presence of an object of interest in a target image. Regions of a target image may be located that match an object of interest, e.g., in a template image, with respect to various information, e.g., luminance, color and/or other types of boundary information. The invention includes improved methods for mapping point sequences (e.g., pixel sequences) or curves to new point sets or curves for curve matching. The method determines the presence of an object of interest in a target image despite of or using various types of topological transformations of the object of interest in the target image. One or more mapping operators are determined based on template curves and/or example target curves. Pattern matching is performed on one or more target images using the mapping operator(s) to generate pattern matching results, and the pattern matching results output.

Abstract: System and method for estimating a rotational shift between a first discrete curve and a second discrete curve, where the second discrete curve is a rotationally shifted version of the first discrete curve. First and second discrete curves are received. A rotational shift between the first discrete curve and the second discrete curve is estimated based on the first discrete curve and the second discrete curve. A cumulative rotational shift is updated based on the estimated rotational shift. A rotationally shifted version of the second discrete curve is generated based on the cumulative rotational shift. The estimating, updating, and generating are performed in an iterative manner using the respective rotationally shifted discrete curve for each iteration until a stopping condition occurs, thereby determining a final estimate of the rotational shift between the first discrete curve and the second discrete curve. The final estimate may be used to perform curve matching.

Abstract: System and method for determining a mapping operator for use in a pattern matching application, where the mapping operator enhances differences between respective objects of interest and background objects, e.g., objects not of interest. First and second information is received regarding an object of interest and objects that may appear with the object of interest in an acquired target data set, respectively. The mapping operator is determined using the first information and the second information by determining a template discrete curve characterizing the object of interest, determining one or more target discrete curves characterizing the background objects, and generating a mapping operator that enhances differences between the mapped template discrete curve and the mapped target discrete curves. The operator is stored in a memory and is operable to be used in a pattern matching application to locate instances of the object of interest in acquired target data sets or images.

Abstract: System and method for re-sampling discrete curves, thereby efficiently characterizing point sets or curves in a space. The method may also provide improved means for mapping point sets or curves to new point sets or curves for curve matching. A weight vector or function is determined based on a plurality of discrete curves, e.g., from one or more template data sets or images. The weight function enhances differences between weighted discrete curves. A set of orthonormal polynomials is determined based on the computed weight function, where the set of orthonormal polynomials comprises a set of orthogonal eigenfunctions of a Sturm-Liouville differential equation. Values for a plurality of zeros for one of the set of orthonormal polynomials is determined that comprise resampling points for the plurality of discrete curves. Each of the plurality of discrete curves is resampled based on the determined values of the plurality of zeros.

Abstract: System and method for determining the presence of an object of interest in a target image. Regions of a target image may be located that match an object of interest, e.g., in a template image, with respect to various information, e.g., luminance, color and/or other types of boundary information. The invention includes improved methods for mapping point sets or curves to new point sets or curves for curve matching. The method determines the presence of an object of interest in a target image despite of or using various types of topological transformations of the object of interest in the target image. A plurality of mapping operators are determined based on template curves and/or example target curves, e.g., background object curves. Pattern matching is performed on one or more target images using the mapping operators to generate pattern matching results, and the pattern matching results output.

Abstract: A system and method for performing pattern matching to locate zero or more instances of a template image in a target image. An image is received by a computer from an image source, e.g., a camera. First pattern matching is performed on the image using a first pattern matching technique to determine a plurality of candidate areas. Second pattern matching is performed on each of the candidate areas using a second different pattern matching technique to generate final pattern match results. An output is generated indicating the final pattern match results. The second pattern matching may determine a second plurality of candidate areas which may be analyzed to determine the final pattern match results. The first pattern matching may use a plurality of pattern matching techniques, the results of which may be used to select a best technique from the plurality of techniques to use for the second pattern match.

Abstract: A system and method for analyzing a surface. The system includes a computer including a CPU and a memory medium operable to store programs executable by the CPU to perform the method. The method may include: 1) receiving data describing an n-dimensional surface defined in a bounded n-dimensional space, where the surface is embedded in an m-dimensional real space via embedding function x( ), and where m>n; 2) determining a diffeomorphism f of the n-dimensional space; 3) computing the inverse transform f−1 of the diffeomorphism f; 4) selecting points, e.g., a Low Discrepancy Sequence, in the n-dimensional space; 5) mapping the points onto the surface using x(f−1), thereby generating mapped points on the surface; 6) sampling the surface using at least a subset of the mapped points to generate samples of the surface; and 7) analyzing the samples of the surface to determine characteristics of the surface.

Abstract: A system and method for performing a curve fit on a plurality of data points. In an initial phase, a subset Pmax of the plurality of points which represents an optimal curve is determined. This phase is based on a statistical model which dictates that after trying at most Nmin random curves, each connecting a randomly selected two or more points from the input set, one of the curves will pass within a specified radius of the subset Pmax of the input points. The subset Pmax may then be used in the second phase of the method, where a refined curve fit is made by iteratively culling outliers from the subset Pmax with respect to a succession of optimal curves fit to the modified subset Pmax at each iteration. The refined curve fit generates a refined curve, which may be output along with a final culled subset Kfinal of Pmax.

Abstract: A system and method for performing a curve fit on a plurality of data points. In an initial phase, a subset Pmax of the plurality of points which represents an optimal curve is determined. This phase is based on a statistical model which dictates that after trying at most Nmin random curves, each connecting a randomly selected two or more points from the input set, one of the curves will pass within a specified radius of the subset Pmax of the input points. The subset Pmax may then be used in the second phase of the method, where a refined curve fit is made by iteratively culling outliers from the subset Pmax with respect to a succession of optimal curves fit to the modified subset Pmax at each iteration. The refined curve fit generates a refined curve, which may be output along with a final culled subset Kfinal of Pmax.

Abstract: A signal analysis system/method, for identifying the closest vector in a vector collection to a given input signal vector, comprising an input, a memory, and a processing unit. The memory stores a collection of vectors, and a table of mutual distances between pairs of the vectors in the collection. The processing unit may receive an input vector corresponding to the input signal.

Abstract: A system and method for analyzing an image. The system may comprise a computer which includes a CPU and a memory medium which is operable to store one or more programs executable by the CPU to perform the method. The method may include: 1) receiving data describing an n-dimensional image, wherein the image is defined in a bounded n-dimensional space, wherein the image is embedded in an m-dimensional real space via an embedding function x( ), and wherein m>n; 2) determining a diffeomorphism (f,g) of the n-dimensional space; 3) computing the inverse transform (f−1,g−1) of the determined diffeomorphism (f,g); 4) selecting a plurality of points in the n-dimensional space; 5) mapping the plurality of points onto the image using x(f−1,g−1) thereby generating a mapped plurality of points on the image; and 6) analyzing the mapped plurality of points to determine characteristics of the image.

Abstract: A system and method for analyzing a surface. The system includes a computer including a CPU and a memory medium operable to store programs executable by the CPU to perform the method. The method may include: 1) receiving data describing an n-dimensional surface defined in a bounded n-dimensional space, where the surface is embedded in an m-dimensional real space via embedding function x( ), and where m>n; 2) determining a diffeomorphism f of the n-dimensional space; 3) computing the inverse transform f−1 of the diffeomorphism f; 4) selecting points, e.g., a Low Discrepancy Sequence, in the n-dimensional space; 5) mapping the points onto the surface using x(f−1), thereby generating mapped points on the surface; 6) sampling the surface using at least a subset of the mapped points to generate samples of the surface; and 7) analyzing the samples of the surface to determine characteristics of the surface.

Abstract: A system and method for performing pattern matching to locate an instance of one or more of a plurality of template images in a target image. In a preprocessing phase a unified signal transform (UST) is determined from the template images. The UST converts each template image to a generalized frequency domain. The UST is applied at a generalized frequency to each template image to calculate corresponding generalized frequency component values (GFCVs) for each template image. At runtime, the target image is received, and the UST is applied at the generalized frequency to the target image to calculate a corresponding GFCV. The UST may be applied to pixel subsets of the template and target images. A best match is determined between the GFCV of the target image and the GFCVs of each template image. Finally, information indicating the best match template image from the set of template images is output.

Abstract: A system and method for selecting a best match of a received input signal from a set of candidate signals, wherein two or more of the candidate signals are uncorrelated. In a preprocessing phase a unified signal transform (UST) is determined from the candidate signals. The UST converts each candidate signal to a generalized frequency domain. The UST is applied at a generalized frequency to each candidate signal to calculate corresponding generalized frequency component values (GFCVs) for each candidate signal. At runtime, the input signal of interest is received, and the UST is applied at the generalized frequency to the input signal of interest to calculate a corresponding GFCV. The best match is determined between the GFCV of the input signal of interest and the GFCVs of each of the set of candidate signals. Finally, information indicating the best match candidate signal from the set of candidate signals is output.

Abstract: A system and method for scanning for an object within a region using a conformal scanning scheme. The system may comprise a computer which includes a CPU and a memory medium which is operable to store one or more programs executable by the CPU to perform the method. The method may: 1) determine the characteristic geometry of the region; 2) generate a conformal scanning curve based on the characteristic geometry of the region by performing a conformal mapping between the characteristic geometry and a first scanning curve to generate the conformal scanning curve, i.e., mapping points of the first scanning curve to the characteristic geometry of the region; and 3) scan the region using the conformal scanning curve. These measurements of the region produce data indicative of one or more characteristics of the object. The method may also generate output indicating the one or more characteristics of the object.

Abstract: A system and method for scanning for an object within a region using a Low Discrepancy Sequence scanning scheme. The system may comprise a computer which includes a CPU and a memory medium which is operable to store one or more programs executable by the CPU to perform the method. The method may: 1) calculate a Low Discrepancy Sequence of points in the region; 2) generate a motion control trajectory from the Low Discrepancy Sequence of points (e.g., by generating a Traveling Salesman Path (TSP) from the Low Discrepancy Sequence of points and then re-sampling the TSP to produce a sequence of motion control points comprising the motion control trajectory); 3) scan the region along the motion control trajectory to determine one or more characteristics of the object in response to the scan. The method may also generate output indicating the one or more characteristics of the object.