Method and system for filtering, registering, and matching 2.5D normal maps
An iterative approach to vector median filtering wherein the resulting median vector need not be a member of the original data set. The iterative vector median filtering allows for fast convergence for complex computations and an output which is approximate to the mean, particularly for small data sets. In addition, a method and system for registering and matching 2.5 normal maps is provided. Registration of two maps is performed by optimally aligning their normals through 2-D warping in the image plane in conjunction with a 3-D rotation of the normals. Once aligned, the average dot-product serves as a matching metric for automatic target recognition (ATR).
1. A method of registering normal maps, comprising the steps of:
converting observed object data to an observed normal map;
calculating a 3-D rotation matrix for a first normal map and a second normal map;
producing 2-D planar transform weights by warping a 2-D position of surface normals of at least one of the observed normal map and each reference normal map in an image plane; and
jointly optimizing the 3-D rotation matrix and the 2-D planar transform weights of the first and second normal maps until convergence to a registered normal map pair.
2. The method of claim 1 , further comprising the step of setting an optimization criteria for registration, said setting including determining the L 2 -norm of a difference between corresponding surface normals of the first normal map and the second normal map.
3. The method of claim 1 , further comprising the step of estimating a pose of the observed normal map, wherein the pose is estimated using a gnomonic projection.
4. The method of claim 3 , wherein the step of estimating comprises generating at least one cluster center using a K-means clustering method, and extracting the pose from the at least one cluster center through the gnomonic projection.
5. The method of claim 1 , further comprising the step of warping in the image plane the 2-D position of the surface normals of one at least one of the first normal map and the second normal map.
6. The method of claim 1 , wherein said step of calculating a 3-D rotation matrix includes finding orthogonal matrices U,V such that the 3-D rotation matrix R is equal to R=UV T where U and V are derived from the singular value decomposition of the outer product of a plurality of surface normals of at least one of the first normal map and the second normal map.
7. The method of claim 1 , wherein the 2-D planar transformation weights are optimized according to an iterative method.
8. The method of claim 7 , wherein the iterative method includes a Gauss-Newton method.
9. The method of claim 7 , wherein the iterative method includes a model-trust region approach, whereby a scaled diagonal matrix is added to the Hessian matrix.
10. The method of claim 9 , wherein the optimal value of a scaling factor is determined using a line-search technique.
11. The method of claim 7 , further comprising the step of interpolating the warped versions of the at least one of the observed normal map and each reference normal map at non-integer planar coordinates.
12. The method of claim 11 , wherein said step of interpolating further includes independently interpolating using nearest neighbor, bi-linear, and highest-order non-linear methods followed by renormalization.
13. The method of claim 2 , wherein jointly optimizing the 3-D rotation matrix and the 2-D planar transform weights proceeds by alternating between calculating of the 3-D rotation matrix and iterative optimization of the 2-D planar transformation weights.
14. The method of claim 13 , wherein the step of jointly optimizing further includes the steps of:
(a) optimizing the 2-D planar transformation weights until at least one of no further improvement in the optimization criteria is observed and up to a maximum number of iterations are executed;
(b) recalculating the rotation matrix using the latest alignment between two images, and
(c) repeating steps (a) and (b) until no further improvement in the criteria is observed between successive recalculations of the rotation matrix.
15. The method of claim 1 , wherein said calculating, producing, and jointly optimizing steps are performed at multiple image scales, from course to fine scale.
16. The method of claim 15 , wherein alignment parameters at a next higher scale are used as a seed for the next lower scale.
17. The method of claim 1 , wherein said calculating, producing, and jointly optimizing steps include optical flow.
18. A non-transient computer-readable storage medium storing computer code for registering normal maps, wherein the computer code comprises:
code for converting observed object data to an observed normal map;
code for calculating a 3-D rotation matrix for a first normal map and a second normal map;
code for producing 2-D planar transform weights by warping a 2-D position of surface normals of at least one of the observed normal map and each reference normal map in an image plane; and
code for jointly optimizing the 3-D rotation matrix and the 2-D planar transform weights of the first and second normal maps until convergence to a registered normal map pair.
19. The computer-readable medium of claim 18 , further comprising code for setting an optimization criteria for registration, said setting including determining the L2-norm of a difference between corresponding surface normals of the first normal map and the second normal map.
20. The computer-readable medium of claim 18 , wherein code for calculating a 3-D rotation matrix includes code for finding orthogonal matrices U,V such that the 3-D rotation matrix R is equal to R=UV T where U and V are derived from the singular value decomposition of the outer product of a plurality of surface normals of at least one of the first normal map and the second normal map.
21. The computer-readable medium of claim 18 , wherein the 2-D planar transformation weights are optimized according to an iterative method.
22. The computer-readable medium of claim 21 , wherein the iterative method includes a Gauss-Newton method.
23. The computer-readable medium of claim 19 , wherein jointly optimizing the 3-D rotation matrix and the 2-D planar transform weights proceeds by alternating between calculating of the 3-D rotation matrix and iterative optimization of the 2-D planar transformation weights.
24. The computer-readable medium of claim 23 , wherein code for jointly optimizing further includes:
code for (a) optimizing the 2-D planar transformation weights are optimized until at least one of no further improvement in the optimization criteria is observed and up to a maximum number of iterations are executed;
code for (b) recalculating the rotation matrix using the latest alignment between two images; and
code for (c) repeating (a) and (b) until no further improvement in the criteria is observed between successive recalculations of the rotation matrix.
25. The computer-readable medium of claim 18 , wherein said calculating, producing, and jointly optimizing steps are performed at multiple image scales, from course to fine scale.