Efficient Globally Optimal Point Cloud Alignment using Bayesian Nonparametric Mixtures

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to describe the point cloud and surface normal densities, and the branch and bound (BB) paradigm to recover the optimal relative transformation. BB relies on a novel, refinable, approximately-uniform tessellation of the rotation space using 4D tetrahedra which leads to more efficient BB operation in comparison to the common axis-angle tessellation. For this novel tessellation, we provide upper and lower objective function bounds, and prove convergence and optimality of the BB approach under mild assumptions. Finally, we empirically demonstrate the efficiency of the proposed approach as well as its robustness to suboptimal real-world conditions such as missing data and partial overlap.