Efficient re-sampling of discrete curves

A computer readable medium which stores program instructions for re-sampling discrete curves, wherein the discrete curves correspond to data, wherein the program instructions are executable by a processor to perform:

• normalizing a plurality of discrete curves, wherein each discrete curve comprises a respective sequence of points;
• computing a weight function based on the plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• determining a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of basis functions;
• determining values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• re-sampling each of the plurality of discrete curves based on the determined values of the plurality of zeros, thereby generating re-sampled discrete curves;
• wherein the re-sampled discrete curves are usable to analyze the data.

A system for re-sampling discrete curves, comprising:

• a computer system, comprising:
• a processor;
• and
• a memory medium coupled to the processor;
• and
• wherein the memory medium stores program instructions which are executable by the processor to:
• normalize a plurality of discrete curves, wherein each discrete curve comprises a respective sequence of points, and wherein the discrete curves correspond to data;
• compute a weight function based on the plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• determine a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of basis functions;
• determine values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• re-sample each of the plurality of discrete curves based on the determined values of the plurality of zeros, thereby generating re-sampled discrete curves;
• wherein the re-sampled discrete curves are usable to analyze the data.

A system for re-sampling discrete curves, comprising:

• means for normalizing a plurality of discrete curves, wherein each discrete curve comprises a respective sequence of points;
• means for computing a weight function based on the plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• means for determining a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of basis functions;
• means for determining values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• means for re-sampling each of the plurality of discrete curves based on the determined values of the plurality of zeros.

A computer-implemented method for re-sampling discrete curves, the method comprising:

• receiving one or more images, wherein each image contains one or more image objects;
• determining a plurality of discrete curves from the one or more images, wherein each of the discrete curves corresponds to one of the one or more image objects, and wherein each discrete curve comprises a respective sequence of points;
• normalizing each of the plurality of discrete curves,
• computing a weight function based on the plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• determining a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of basis functions;
• determining values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• re-sampling each of the plurality of discrete curves based on the determined values of the plurality of zeros, thereby generating re-sampled discrete curves;
• wherein the re-sampled discrete curves are usable to analyze the one or more images.

A computer-implemented method for re-sampling discrete curves, the method comprising:

• receiving one or more data sets, wherein each data set contains one or more data objects;
• determining a plurality of discrete curves from the one or more data sets, wherein each of the discrete curves corresponds to one of the one or more data objects, and wherein each discrete curve comprises a respective sequence of points;
• normalizing each of the plurality of discrete curves,
• computing a weight function based on the plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• determining a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of basis functions;
• determining values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• re-sampling each of the plurality of discrete curves based on the determined values of the plurality of zeros;
• thereby generating re-sampled discrete curves;
• wherein the re-sampled discrete curves are usable to analyze the one or more data sets.

A computer-implemented method for re-sampling discrete curves, wherein the discrete curves correspond to data, the method comprising:

• computing a weight function based on a plurality of discrete curves, wherein the weight function enhances differences between weighted discrete curves;
• determining a set of orthonormal polynomials based on the computed weight function, wherein the set of orthonormal polynomials comprises a set of orthogonal eigenfunctions of a Sturm-Liouville differential equation;
• determining values for a plurality of zeros for one of the set of orthonormal polynomials, wherein the values for the plurality of zeros comprise re-sampling points for the plurality of discrete curves;
• and
• re-sampling each of the plurality of discrete curves based on the determined values of the plurality of zeros, thereby generating re-sampled discrete curves;
• wherein the re-sampled discrete curves are usable to analyze the data.