Research On Hierarchical Probabilistic Mixture Model Via Finite Heavy-tailed Distribution Based Non-rigid Point Set Registration

Non-rigid point set registration is fundamental research in computer vision and pattern recognition.When the source point set contains problems of outliers,noise,occlusion,rotation and deformation,biases of registration will increase.In this research,we construct a hierarchical probabilistic model based non-rigid point set registration(HPMR)algorithm using finite heavy-tailed distributions under a variational Bayes framework to improve the precision of registraion.irst of all,the hesitant fuzzy Einstein weighted averaging(HFEWA)operator and the symmetric cross entropy are used to estimate putative inliers in the hesitant fuzzy environment.Then,the student-t mixture model(SMM)based a hierarchical probabilistic model(HPM)is constructed,which is divided into a correspondence estimation component and an outlier component,which are used to estimate correspondences and cluster outliers between two point sets according to posterior probabilities.Besides,the Gamma prior distribution and Dirichlet prior distribution are used to automatically adjust the model tail and mixture proportion of each subcomponent in SMM to further solving the problem of outliers and occlusion.Finally,model parameters and latent variables are updating until an objective equation converges under the variational Bayes expectation maximization(VBEM)framework,at that time an optimal spatial transformation function is obtained that can fit the target point set correctly.In the E step,values of model parameters in the current step are used to calculate the posterior distribution of the latent variable.In the M step,the values of the hidden variables are used to update the model parameters using the tree-structured mean-field factorization to obtain a tighter variational lower bound.The performances of HPMR in synthetic point sets,3D point set,Oxford pubic image,and SUIRD pubic image against 11 state-of-the-art methods are evaluated,in which HPMR can obtain the best performance in most scenarios.