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 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 scanning system and method for scanning for an object within a region, or for locating a point within a region. Embodiments of the invention include a method for scanning for an object within a region using a Low Discrepancy Curve (LDC) scanning scheme. The method may: 1) generate a Low Discrepancy Sequence (LDS) of points in the region; 2) calculate an LDC in the region based on the LDS of points; and 3) scan the region along the LDC to determine one or more characteristics of the object in response to the scan. In calculating the LDC in the region based on the LDS of points, the method may connect sequential pairs of the LDS with contiguous orthogonal line segments (each parallel to a respective axis of the region), then sample the segments, generating points which may be used to generate the LDC, such as by a curve fit.

Abstract: A system and method for generating a curve, such as a Low Discrepancy Curve, on a surface, such as an abstract surface with a Riemannian metric. 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) parameterize the surface; 2) select a curve, such as a Low Discrepancy Curve, in a parameter space, for example, a simple space such as a unit square; 3) re-parameterize the surface, for example, re-parameterize the surface such that a ratio of line and area elements of the surface based on a Riemannian metric is constant; and 4) map the curve onto the surface using the re-parameterization. The method may also generate output comprising information regarding the mapped curve, for example, displaying the mapped curve on a display device.

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 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 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: 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 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 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: 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 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: 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.