Generalized Point Set Registration With Fuzzy Correspondences Based on Variational Bayesian Inference

Point set registration (PSR) is an essential problem in surgical navigation and computer-assisted surgery (CAS). In CAS, PSR can be used to map the intraoperative surgical space with the preoperative volumetric image space. The performances of PSR in real-world surgical scenarios are sensitive to noise and outliers. This article proposes a novel point set registration approach where the additional features (i.e., the normal vectors) extracted from the point sets are utilized and the convergence of the algorithm is guaranteed from the theoretical perspective. More specifically, we formulate the PSR with normal vectors by generalizing the Bayesian coherent point drift (BCPD) into the 6-D scenario. The proposed algorithm is more accurate and robust to noise and outliers, and the theoretical convergence of the proposed approach is guaranteed. Our contributions of this article are summarized as follows. 1) The PSR problem with normal vectors is formally formulated through generalizing the BCPD approach. 2) The formulas for updating the parameters during the algorithm’s iterations are given in closed forms. 3) Extensive experiments have been done to verify the proposed approach and specifically its significant improvements over the BCPD has been validated.