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Probabilistic point cloud registration methods are becoming more popularbecause of their robustness. However, unlike point-to-plane variants ofiterative closest point (ICP) which incorporate local surface geometricinformation such as surface normals, most probabilistic methods (e.g., coherentpoint drift (CPD)) ignore such information and build Gaussian mixture models(GMMs) with isotropic Gaussian covariances. This results in sphere-like GMMcomponents which only penalize the point-to-point distance between the twopoint clouds. In this paper, we propose a novel method called CPD with LocalSurface Geometry (LSG-CPD) for rigid point cloud registration. Our methodadaptively adds different levels of point-to-plane penalization on top of thepoint-to-point penalization based on the flatness of the local surface. Thisresults in GMM components with anisotropic covariances. We formulate pointcloud registration as a maximum likelihood estimation (MLE) problem and solveit with the Expectation-Maximization (EM) algorithm. In the E step, wedemonstrate that the computation can be recast into simple matrix manipulationsand efficiently computed on a GPU. In the M step, we perform an unconstrainedoptimization on a matrix Lie group to efficiently update the rigidtransformation of the registration. The proposed method outperformsstate-of-the-art algorithms in terms of accuracy and robustness on variousdatasets captured with range scanners, RGBD cameras, and LiDARs. Also, it issignificantly faster than modern implementations of CPD. The source code isavailable at https://github.com/ChirikjianLab/LSG-CPD.git.

LSG-CPD: Coherent Point Drift with Local Surface Geometry for Point Cloud Registration