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In this paper, a globally optimal algorithm based on a maximum feasible subsystem framework is proposed for robust pairwise registration of point cloud data. Registration is formulated as a branch-and-bound problem with mixed-integer linear programming. Among the putative matches of three-dimensional (3D) features between two sets of range data, the proposed algorithm finds the maximum number of geometrically correct correspondences in the presence of incorrect matches, and it estimates the transformation parameters in a globally optimal manner. The optimization requires no initialization of transformation parameters. Experimental results demonstrated that the presented algorithm was more accurate and reliable than state-of-the-art registration methods and showed robustness against severe outliers/mismatches. This global optimization technique was highly effective, even when the geometric overlap between the datasets was very small.

A Maximum Feasible Subsystem for Globally Optimal 3D Point Cloud Registration