Generalized Point Set Registration with the Kent Distribution

Abstract

Point set registration (PSR) is an essential problem in communities of computer vision, medical robotics and biomedical engineering. This paper is motivated by considering the anisotropic characteristics of the error values in estimating both the positional and orientational vectors from the PSs to be registered. To do this, the multi-variate Gaussian and Kent distributions are utilized to model the positional and orientational uncertainties, respectively. Our contributions of this paper are three-folds: (i) the registration problem using the normal vectors is formulated as a maximum likelihood problem, where the anisotropic characteristics in both positional and normal vectors are considered; (ii) the matrix forms of the objective function and its associated gradients with respect to the desired parameters are provided, which can facilitate the computational process; (iii) two approaches of computing the normalizing constant in the Kent distribution are compared. We verify our proposed registration method on various pre-operative and intra-operative PSs (pelvis and femur bones) in computer-assisted surgery (CAS). Extensive experimental results demonstrate that our proposed method outperforms the state-of-the-art methods in terms of the registration accuracy and the robustness.