System and method for analyzing an image

A method for generating a Low Discrepancy Sequence on an image, comprising:

• receiving data describing an image, wherein the image is defined in a unit n-cube, wherein the image is embedded in an m-dimensional real space via an embedding function x( ), and wherein m>n;
• determining a diffeomorphism (f,g) of the unit n-cube;
• computing the inverse transform (f−1,g−1) of the determined diffeomorphism (f,g);
• selecting a Low Discrepancy Sequence in the unit n-cube;
• mapping the Low Discrepancy Sequence onto the image using x(f−1,g−1), thereby generating a Low Discrepancy Sequence on the image;
• and
• generating output comprising the mapped Low Discrepancy Sequence.

A system for analyzing an image, comprising:

• a sensor;
• and
• a computer which is operable to couple to said sensor, said computer comprising:
• a CPU;
• a memory medium which is operable to store program instructions;
• and
• an input for 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;
• wherein the CPU is operable to execute said program instructions to perform:
• determining a diffeomorphism f of the n-dimensional space;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a plurality of points in the n-dimensional space;
• mapping the plurality of points onto the image using x(f−1), thereby generating a mapped plurality of points on the image;
• wherein said computer and said sensor are operable to perform:
• sampling the image using at least a subset of the mapped plurality of points to generate samples of the image;
• and
• wherein the CPU is further operable to execute said program instructions to perform:
• analyzing the samples of the image to determine characteristics of the image.

A system for analyzing a image, comprising:

• a computer, comprising:
• a CPU;
• a memory medium which is operable to store program instructions;
• and
• an input for 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;
• wherein the CPU is operable to execute said program instructions to perform:
• determining a diffeomorphism f of the n-dimensional space;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a Low Discrepancy Sequence in the n-dimensional space;
• and
• mapping the Low Discrepancy Sequence onto the image using x(f−1), thereby generating a mapped Low Discrepancy Sequence on the image;
• sampling the image using at least a subset of the mapped Low Discrepancy Sequence to generate samples of the image;
• and
• analyzing the samples of the image to determine characteristics of the image.

A system for generating a Low Discrepancy Sequence on an image, comprising:

• a computer, comprising:
• a CPU;
• a memory medium which is operable to store program instructions;
• and
• an input for receiving data describing an n-dimensional image, wherein the image is defined in a unit n-cube, wherein the image is embedded in Rm via an embedding function x( ), and wherein m>n;
• wherein the CPU is operable to execute said program instructions to perform:
• determining a diffeomorphism f of the unit n-cube;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a Low Discrepancy Sequence in the unit n-cube;
• mapping the Low Discrepancy Sequence onto the embedded image using x(f−1), thereby generating a Low Discrepancy Sequence on the image;
• and
• generating output comprising the mapped Low Discrepancy Sequence.

A memory medium containing program instructions for analyzing an image, wherein said program instructions are executable to perform:

• 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;
• determining a diffeomorphism f of the n-dimensional space;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a plurality of points in the n-dimensional space;
• mapping the plurality of points onto the image using x(f−1), thereby generating a mapped plurality of points on the image;
• sampling the image using at least a subset of the mapped plurality of points to generate samples of the image;
• and
• analyzing the samples of the image to determine characteristics of the image.

A memory medium containing program instructions for analyzing an image, wherein said program instructions are executable to perform:

• receiving data describing an 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;
• determining a diffeomorphism f of the n-dimensional space;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a Low Discrepancy Sequence in the n-dimensional space;
• mapping the Low Discrepancy Sequence onto the image using x(f−1), thereby generating a mapped Low Discrepancy Sequence on the image;
• and
• sampling the image using at least a subset of the mapped Low Discrepancy Sequence to generate samples of the image;
• and
• analyzing the samples of the image to determine characteristics of the image.

A memory medium containing program instructions for generating a Low Discrepancy Sequence on an image, wherein said program instructions are executable to perform:

• selecting an image S, wherein S is defined in a unit n-cube, wherein S is embedded in Rm via an embedding function x( ), and wherein m>n.
• determining a diffeomorphism f of the unit n-cube;
• computing the inverse transform f−1 of the determined diffeomorphism f;
• selecting a Low Discrepancy Sequence in the unit n-cube;
• mapping the Low Discrepancy Sequence onto the embedded image S using x(f−1), thereby generating a Low Discrepancy Sequence on the image S;
• and
• generating output comprising the mapped Low Discrepancy Sequence.