Anisotropic Generalized Bayesian Coherent Point Drift for Point Set Registration

Abstract

of mixture distributions, the soft correspondence estimation, and the model parameters (i.e., the rotation matrix, translation vector, the covariance matrix with the anisotropic positional error, and the concentration parameter with the estimation of the normal vectors). Especially, the convergence is guaranteed at the theoretical level using the variational inference theory. The experimental results demonstrate the superiority of our algorithm on registration accuracy, convergence speed, and robustness to noise, outliers, and partial data.

Dataset of Finite Element Models of Normal and Deformed Thoracolumbar Spine

“…BCPD++ is an extension of the Bayesian Coherent Point Drift (BCPD) algorithm 33 , 34 . BCPD is a probabilistic method for point set registration 35 , as an extension of the Coherent Point Drift (CPD) algorithm 20 . The CPD algorithm models the transformation between two-point sets using a Gaussian Mixture Model (GMM) and iteratively solves for the optimal transformation parameters 20 .…”

“…The CPD algorithm models the transformation between two-point sets using a Gaussian Mixture Model (GMM) and iteratively solves for the optimal transformation parameters 20 . The GMM consists of K Gaussian distributions in the transformation space, and the probability density function of the GMM is defined as 35 : where Y is the transformed point set, X is the reference point set, Θ = {w j , µ j , Σj} is the set of parameters of the GMM, and N(µ j ,Σj) is the Gaussian distribution with mean µ j and covariance matrix Σj. Then, BCPD computes the correspondence probability between a point x in the reference point set and a point y in the transformed point set as 35 : where j is the index of the nearest centroid to y; and w j , µ j , and Σj are the parameters of the corresponding Gaussian distribution.…”

“…The CPD algorithm models the transformation between two-point sets using a Gaussian Mixture Model (GMM) and iteratively solves for the optimal transformation parameters 20 . The GMM consists of K Gaussian distributions in the transformation space, and the probability density function of the GMM is defined as 35 :…”

“…where Y is the transformed point set, X is the reference point set, Θ = {w j , µ j , Σj} is the set of parameters of the GMM, and N(µ j ,Σj) is the Gaussian distribution with mean µ j and covariance matrix Σj. Then, BCPD computes the correspondence probability between a point x in the reference point set and a point y in the transformed point set as 35 :…”