Joint Registration of Multiple Generalized Point Sets

Abstract

To align different views or representations of anatomy is an essential task in computer-assisted surgery (CAS). In this paper, we propose a probabilistic approach to the joint rigid registration problem of multiple generalized point sets. A generalized point set consist of high-dimensional points which include both positional and orientational information (normal vector). A hybrid mixture model (HMM) combining Gaussian and Von-Mises-Fisher distributions is used to model the positional and orientational components of the generalized point sets, respectively. All generalized point sets are jointly registered under the expectation maximization framework. In E-step, the posterior probabilities representing point correspondence confidences are computed. In M-step, the transformation matrices, positional variances and orientational concentration parameters are updated for each point set. We validate the proposed algorithm using the human femur bone surface points extracted from the CT data. The experimental results show that the proposed algorithm outperforms the state-of-the-art ones in terms of the registration accuracy, the robustness to noise and outliers, and the convergence speed.