Robust Generalized Point Cloud Registration with Orientational Data Based on Expectation Maximization

This paper introduces a robust generalized point cloud (PC) registration method that utilizes not only the positional but also the orientation information associated with each point. The proposed method solves the rigid PC registration problem in a probabilistic manner, which casts the problem into a maximum likelihood (ML) framework. A hybrid mixture model (HMM) is utilized to represent one generalized PC. In the HMM, a von-Mises-Fisher mixture model (FMM) is adopted to model the orientational uncertainty, while a Gaussian mixture model (GMM) is used to represent the positional uncertainty. An expectation-maximization (EM) algorithm is adopted to solve the optimization problem in an iterative manner to find the optimal rotation matrix and the translation vector between two generalized PCs. In both expectation step (E step) and maximization step (M step), orientational information is utilized, which can potentially improve the algorithm's robustness to noise and outliers. In the E step, the posterior probabilities that represent the degree of point correspondences in two PCs are computed. In the M step, an efficient closed-form solution to a rigid transformation matrix is developed. E and M steps will iterate until certain convergence criteria are satisfied. Extensive experiments under different noise levels and outlier ratios have been carried out on a data set of femur bone computed tomography images. Experimental results show that the proposed method outperforms the state-of-the-art ones in terms of accuracy, robustness, and convergence speed significantly. Note to Practitioners - This paper was motivated by solving the problem of registering two PCs. 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 for 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.