Break and Splice: A Statistical Method for Non-Rigid Point Cloud Registration

3D object matching and registration on point clouds are widely used in computer vision. However, most existing point cloud registration methods have limitations in handling non-rigid point sets or topology changes (e.g. connections and separations). As a result, critical characteristics such as large inter-frame motions of the point clouds may not be accurately captured. This paper proposes a statistical algorithm for non-rigid point sets registration, addressing the challenge of handling topology changes without the need to estimate correspondence. The algorithm uses a novel Break and Splice framework to treat the non-rigid registration challenges as a reproduction process and a Dirichlet Process Gaussian Mixture Model (DPGMM) to cluster a pair of point sets. Labels are assigned to the source point set with an iterative classification procedure, and the source is registered to the target with the same labels using the Bayesian Coherent Point Drift (BCPD) method. The results demonstrate that the proposed approach achieves lower registration errors and efficiently registers point sets undergoing topology changes and large inter-frame motions. The proposed approach is evaluated on several data sets using various qualitative and quantitative metrics. The results demonstrate that the Break and Splice framework outperforms state-of-the-art methods, achieving an average error reduction of about 60% and a registration time reduction of about 57.8%.