Bi-Stage Large Point Set Registration Using Gaussian Mixture Models

Abstract

Point set registration is to determine correspondences between two different point sets, then recover the spatial transformation between them. Many current methods, become extremely slow as the cardinality of the point set increases; making them impractical for large point sets. In this paper, we propose a bi-stage method called bi-GMM-TPS, based on Gaussian Mixture Models and Thin-Plate Splines (GMM-TPS). The first stage deals with global deformation. The two point sets are grouped into clusters independently using K-means clustering. The cluster centers of the two sets are then registered using a GMM based method. The point sets are subsequently aligned based on the transformation obtained from cluster center registration. At the second stage, the GMM based registration method is again applied, to fine tune the alignment between the two clusters to address local deformation. Experiments were conducted on eight publicly available datasets, including large point clouds. Comparative experimental results demonstrate that the proposed method, is much faster than state-of-the-art methods GMM-TPS and QPCCP (Quadratic Programming based Cluster Correspondence Projection); especially on large non-rigid point sets, such as the swiss roll, bunny and USF face datasets, and challenging datasets with topological ambiguity such as the banana dataset. Although the Coherent Point Drift (CPD) method has comparable computational speed, it is less robust than bi-GMM-TPS. Especially for large point sets, under conditions where the number of clusters is not extreme, a complexity analysis shows that bi-GMM-TPS is more efficient than GMM-TPS.