Determining Correspondences and Rigid Motion of 3-D Point Sets with Missing Data

This paper addresses the general 3-D rigid motion problem, where the point correspondences and the motion parameters between two sets of 3-D points are to be recovered. The existence of missing points in the two sets is the most di cult problem. We rst 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 a nity 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 a nity heuristic also leads to a fast outlier removal algorithm, which can be run iteratively to re ne the correspondence recovery. Simulation results and experiments on real images are shown in both ideal and general cases.