Accurate and Robust Non-rigid Point Set Registration using Student\u2019s-t Mixture Model with Prior Probability Modeling

Abstract

A new accurate and robust non-rigid point set registration method, named DSMM, is proposed for non-rigid point set registration in the presence of significant amounts of missing correspondences and outliers. The key idea of this algorithm is to consider the relationship between the point sets as random variables and model the prior probabilities via Dirichlet distribution. We assign the various prior probabilities of each point to its correspondences in the Student’s-t mixture model. We later incorporate the local spatial representation of the point sets by representing the posterior probabilities in a linear smoothing filter and get closed-form mixture proportions, leading to a computationally efficient registration algorithm comparing to other Student’s-t mixture model based methods. Finally, by introducing the hidden random variables in the Bayesian framework, we propose a general mixture model family for generalizing the mixture-model-based point set registration, where the existing methods can be considered as members of the proposed family. We evaluate DSMM and other state-of-the-art finite mixture models based point set registration algorithms on both artificial point set and various 2D and 3D point sets, where DSMM demonstrates its statistical accuracy and robustness, outperforming the competing algorithms.