Xiaoguang Wang, Yong-Qing Cheng, Robert Collins, and Allen Hanson,
"Determining Correspondences and Rigid Motion of 3-D Point Sets 
     with Missing Data,"
IEEE Computer Vision and Pattern Recognition,
San Francisco, CA, June 18-20. 1996, pp. 252-257.


This paper addresses the general 3D rigid motion problem, where the point correspondence and the motion parameters between two sets of 3D points are to be recovered. The existence of missing points in the two sets is the most difficult problem. We first show a mathematical symmetry in the solutions of rotation parameters and point correspondences. A closed-form solution based on the correlation matrix eigenstructure decomposition is proposed for correspondence recovery with no missing points. Using a heuristic measure of point pair affinity derived from the eigenstructure, a weighted bipartite matching algorithm is developed to determine the correspondences in general cases where missing points occur. The use of the affinity heuristic also leads to a fast outlier removal algorithm, which can be run iteratively to refine the correspondence recovery. Simulation results and experiments on real images are shown in both ideal and general cases.

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