Generalized Coherent Point Drift With Multi-Variate Gaussian Distribution and Watson Distribution

Abstract

This letter introduces a novel rigid point set registration (PSR) approach that accurately aligns the pre-operative space and the intra-operative space together in the scenario of computer-assisted orthopedic surgery (CAOS). Motivated by considering anisotropic positional localization noise and utilizing undirected normal vectors in the point sets (PSs), the multi-variate Gaussian distribution and the Watson distribution are utilized to model positional and normal vectors’ error distributions respectively. In the proposed approach, with the above probability distributions, the PSR problem is then formulated as a maximum likelihood estimation (MLE) problem and solved under the expectation maximization (EM) framework. Our contributions are three folds. First, the rigid registration problem of aligning generalized points with undirected normal vectors is formally formulated in a probabilistic manner. Second, the MLE problem is solved under the EM framework. Third, the gradients of associated objective functions with respect to desired parameters are computed and provided. Experimental results on both the human pelvis and femur models demonstrate the potential clinical values and that the proposed approach owns significantly improved performances compared with existing methods.