Image registration methods and apparatus using random projections
According to some aspects, a computer-implemented method of registering a first image and a second image is provided. The method comprises computer-implemented acts of logically dividing the first image into a first plurality of regions, logically dividing the second image into a second plurality of regions, projecting the first plurality of regions and the second plurality of regions into a lower dimensional space using random projections, determining, for each of the projected first plurality of regions, at least one of the projected second plurality of regions that is closest according to first criteria, and determining a transform that brings each of the projected first plurality of regions into a closest correspondence with the respective at least one of the projected second plurality of regions according to second criteria, the transform indicating the registration of the first image and the second image. According to some aspects, at least one computer readable medium encoding instructions that when executed perform such a method and/or a system for providing such a method is provided.
1. A computer-implemented method of registering a first image and a second image, the method comprising computer-implemented acts of:
logically dividing the first image into a first plurality of regions;
logically dividing the second image into a second plurality of regions;
projecting the first plurality of regions and the second plurality of regions into a lower dimensional space using random projections;
determining, for each of the projected first plurality of regions, at least one of the projected second plurality of regions that is closest according to first criteria; and
determining a transform that brings each of the projected first plurality of regions into a closest correspondence with the respective at least one of the projected second plurality of regions according to second criteria, the transform indicating the registration of the first image and the second image.
2. The method of claim 1 , wherein the lower dimensional space has a dimensionality k, wherein k=O(log n), wherein n is a number of data points of a region of the first or second plurality of regions.
3. The method of claim 2 , wherein k =O(ε −2 log n), and wherein the projecting expands or contracts pairwise distances between data points in a region of the first or second plurality of regions by a factor of at most 1+ε.
4. The method of claim 1 , wherein the projecting comprises applying a projection matrix of random variables taking values of 1, 0 or −1.
5. The method of claim 1 , wherein the first criteria are based at least in part on an approximate nearest neighbor formulation.
6. The method of claim 1 , wherein the determining acts are performed using an expectation maximization iterative closest point procedure.
7. The method of claim 1 , further comprising transforming at least one of the first plurality of regions prior to projecting the first plurality of regions into the lower dimensional space.
8. At least one non-transitory computer readable medium encoded with instructions that, when executed by at least one processor, perform a method of registering a first image and a second image, the method comprising:
logically dividing the first image into a first plurality of regions;
logically dividing the second image into a second plurality of regions;
projecting the first plurality of regions and the second plurality of regions into a lower dimensional space using random projections;
determining, for each of the projected first plurality of regions, at least one of the projected second plurality of regions that is closest according to first criteria; and
determining a transform that brings each of the projected first plurality of regions into a closest correspondence with the respective at least one of the projected second plurality of regions according to second criteria, the transform indicating the registration of the first image and the second image.
9. The at least one non-transitory computer readable medium of claim 8 , wherein the lower dimensional space has a dimensionality k, wherein k=O(log n), wherein n is a number of data points of a region of the first or second plurality of regions.
10. The at least one non-transitory computer readable medium of claim 9 , wherein k =O(ε −2 log n), and wherein the projecting expands or contracts pairwise distances between data points in a region of the first or second plurality of regions by a factor of at most 1 +ε.
11. The at least one non-transitory computer readable medium of claim 8 , wherein the projecting comprises applying a projection matrix of random variables taking values of 1, 0 or −1.
12. The at least one non-transitory computer readable medium of claim 8 , wherein the first criteria are based at least in part on an approximate nearest neighbor formulation.
13. The at least one non-transitory computer readable medium of claim 8 , wherein the determining acts are performed using an expectation maximization iterative closest point procedure.
14. The at least one non-transitory computer readable medium of claim 8 , wherein the method further comprises transforming at least one of the first plurality of regions prior to projecting the first plurality of regions into the lower dimensional space.
15. A system for registering a first image and a second image, the system comprising:
an input to receive the first image and the second image; and
at least one processor coupled to the input, the at least one processor programmed to perform a method comprising:
logically dividing the first image into a first plurality of regions;
logically dividing the second image into a second plurality of regions;
projecting the first plurality of regions and the second plurality of regions into a lower dimensional space using random projections;
determining, for each of the projected first plurality of regions, at least one of the projected second plurality of regions that is closest according to first criteria; and
determining a transform that brings each of the projected first plurality of regions into a closest correspondence with the respective at least one of the projected second plurality of regions according to second criteria, the transform indicating the registration of the first image and the second image.
16. The system of claim 15 , wherein the lower dimensional space has a dimensionality k, wherein k=O(log n), wherein n is a number of data points of a region of the first or second plurality of regions.
17. The system of claim 16 , wherein k =O(ε −2 log n), and wherein the projecting expands or contracts pairwise distances between data points in a region of the first or second plurality of regions by a factor of at most 1+ε.
18. The system of claim 15 wherein the first criteria are based at least in part on an approximate nearest neighbor formulation.
19. The system of claim 15 , wherein the determining acts are performed using an expectation maximization iterative closest point procedure.
20. The system of claim 15 , wherein the method further comprises transforming at least one of the first plurality of regions prior to projecting the first plurality of regions into the lower dimensional space.