A Framework of Student's-t Mixture Model for Accurate and Robust Point Set Registration

Abstract

An accurate and robust point set registration framework using Student's-t mixture model is proposed in this paper due to the Gaussian mixture model being vulnerable by the outliers, noise and the data with longer than normal tails. The key idea of this point set registration framework is to theoretically consider Student's-t mixture model as a generalization of the well know Gaussian mixture model. In the proposed framework, we firstly model the correspondences of two point sets by using Student's-t mixture model, where one point set is considered as data observations and the other one as components of Student's-t mixture model respectively. Secondly, we separate parameters of registration parameters and transformation from the mixture model by using negative log-likelihood function for getting a simple optimization. Thirdly, we get general solutions of registration parameters and transformation in cases of rigid, affine, and non-rigid by EM method. Finally, we show the similarity of deformation parameters between Gaussian mixture model and the proposed framework based on Student's-t mixture models, and theoretically analyze the reason of similarity from the view of the Bayes method. We compare our framework with other state-of-the-art point set registration methods based on finite mixture models on both various 2D and 3D point sets identified from clinical medical images on rigid, affine, and non-rigid cases, where the proposed framework demonstrates its statistical accuracy and robustness, outperforming other competing methods.