System and method for analyzing an image

1. A method for analyzing an image, comprising:

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,g) of the n-dimensional space;

computing the inverse transform (f −1 ,g −1 ) of the determined diffeomorphism (f,g);

selecting a plurality of points in the n-dimensional space;

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

analyzing the mapped plurality of points to determine characteristics of the image.

2. The method of claim 1 ,

wherein the plurality of points comprise a Low Discrepancy Sequence;

wherein the mapped plurality of points comprises a mapped Low Discrepancy Sequence.

3. The method of claim 1 , further comprising:

generating output comprising the mapped plurality of points.

4. The method of claim 1 , wherein said analyzing comprises detecting one or more edges in the image.

5. The method of claim 1 , wherein the bounded n-dimensional space comprises a unit n-cube.

6. The method of claim 5 , wherein n=2, and wherein the n-cube comprises a unit square.

7. The method of claim 5 , wherein n=3, and wherein the n-cube comprises a unit cube.

8. The method of claim 5 , wherein n>3, and wherein the n-cube comprises a hyper-cube of dimensionality greater than 3.

9. The method of claim 1 ,

wherein the image comprises a Riemannian manifold, and wherein the received data comprises a Riemannian metric of the image.

10. The method of claim 1 ,

wherein the received data comprises an intensity function of the image.

11. The method of claim 1 ,

wherein the image comprises a 3-dimensional image;

wherein said analyzing comprises analyzing the mapped plurality of points to determine one or more characteristics of the 3-dimensional image.

12. The method of claim 1 ,

wherein the image comprises an n-dimensional image, wherein n is greater than 3; and

wherein said analyzing comprises analyzing the mapped plurality of points to determine one or more characteristics of the n-dimensional image.

13. The method of claim 1 ,

wherein said analyzing the mapped plurality of points to determine characteristics of the image comprises performing pattern recognition on the image.

14. 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.

15. The method of claim 14 , further comprising:

analyzing the mapped Low Discrepancy Sequence to determine one or more characteristics of the image.

16. The method of claim 15 ,

wherein said analyzing comprises detecting one or more edges in the image.

17. The method of claim 15 ,

wherein said analyzing comprises performing pattern recognition on the image.

18. The method of claim 15 ,

wherein the image comprises a 3-dimensional image;

wherein said analyzing comprises analyzing the mapped plurality of points to determine one or more characteristics of the 3-dimensional image.

19. The method of claim 15 ,

wherein the image comprises an n-dimensional image, wherein n is greater than 3; and

wherein said analyzing comprises analyzing the mapped plurality of points to determine one or more characteristics of the n-dimensional image.

20. The method of claim 14 , wherein n=2, and wherein the unit n-cube comprises a unit square.

21. The method of claim 14 , wherein n=3, and wherein the unit n-cube comprises a unit cube.

22. The method of claim 14 , wherein n>3, and wherein the unit n-cube comprises a unit hyper-cube of dimensionality greater than 3.

23. The method of claim 14 ,

wherein the received data comprises an intensity function of the image.

24. The method of claim 14 ,

wherein the image comprises a Riemannian manifold, and wherein the received data comprises a Riemannian metric of the image.

25. 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.

26. The system of claim 25 ,

wherein the plurality of points comprises a Low Discrepancy Sequence;

wherein the mapped plurality of points comprises a mapped Low Discrepancy Sequence.

27. The system of claim 25 , wherein the CPU is further operable to execute said program instructions to perform:

generating output comprising the mapped plurality of points.

28. The system of claim 25 , wherein the bounded n-dimensional space comprises a unit n-cube.

29. 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.

30. The system of claim 29 ,

wherein the image comprises an image of an object;

wherein said analyzing comprises analyzing the samples of the image to determine one or more characteristics of the object.

31. 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 R m 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.

32. 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.

33. The method of claim 32 ,

wherein the plurality of points comprises a Low Discrepancy Sequence;

wherein the mapped plurality of points comprises a mapped Low Discrepancy Sequence.

34. 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.

35. The memory medium of claim 34 ,

wherein the image comprises a image of an object;

wherein said analyzing comprises analyzing the samples of the image to determine one or more characteristics of the object.

36. 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 R m 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.