Point set non-rigid registration using t-distribution mixture model

A robust non-rigid registration approach with a t-distribution Mixture Model (TMM) was proposed because point sets as Gaussian mixture model is vulnerable to the outliers and the data with longer than normal tails. The Gaussian mixture model was extended to the student's-t Mixture Model by full data definition in the Expectation Maximazation (EM) frame, then the closed solutions of the parameter set of the t-distribution mixture model were solved by re-parameterization of the t-distribution mixture model in the EM algorithm. The priori-weight of each float point was calculated in EM framework to reduce the effects of outliers and the data with longer than normal tails on the matching results. The degree of freedom of each float point in the t-distribution mixture model was calculated to change the probability density distribution, improve the robustness of the algorithm and avoid the effect of estimating the outlier level of point sets that may bring additional errors. The conditional expectation function in t-distribution mixture model was added a regular item of point set, so that the points have a feature of Coherent Point Drift (CPD). The simulation data show that the error from the TMM-CPD is only one tenth of that from comparison algorithms. When the point sets are approximate ellipse shape, tubular and three dimensions, the registration errors of TMM-CPD are only 42.0%, 80.1% and77.5% of those using comparison algorithms, respectively. The experiments show that this non-rigid registration approach using the t-distribution mixture model has features of high-accuracy, good robustness compared to other point set registration algorithms for point sets containing outliers and data with longer than normal tails.