LAUSR

Aligning different views or representations of anatomy is an essential task in both medical imaging computing (MIC) and computer-assisted interventions’ (CAIs’) communities. Motivated by simultaneously registering multiple point sets (PSs) and further improving the algorithm’s robustness to outliers and noise, in this paper, we propose a novel probabilistic approach to jointly register multiple generalized PSs. A generalized PS includes high-dimensional points consisting of both positional vectors and orientational information (or normal vectors). Hybrid mixture models (HMMs) combining Gaussian and von Mises–Fisher (VMF) distributions are used to model positional and orientational components of the generalized PSs. All generalized PSs are jointly registered using the expectation–maximization (EM) technique. In the E-step, the posterior probabilities representing point correspondence confidences are computed. In the M-step, the rigid transformation matrices, positional variances, and orientational concentration parameters are updated for each generalized PS. E and M steps will iterate until some termination condition is satisfied. We validate our algorithm using the surface points extracted from the human femur CT model. The experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art ones in terms of the accuracy, robustness, as well as convergence speed. In addition, our algorithm is able to recover a better central PS than the state-of-the-art one does in the case of registering multiple PSs. Our algorithm is very suitable for registering complex structures arising in medical imaging. Note to Practitioners—This paper was motivated by solving the problem of registering two or multiple point sets. Most existing approaches generally use only the positional information associated with each point and thus lack robustness to noise and outliers. This paper suggests a new robust method that also adopts the normal vectors associated with each point. The registration problem is cast into a maximum-likelihood (ML) problem and solved under the expectation–maximization (EM) framework. Closed-form solutions to estimating parameters in both expectation and maximization steps are provided in this paper. We have demonstrated through extensive experiments that the proposed registration algorithm achieves improved accuracy, robustness to noise and outliers, and faster convergence speed.