Robust Generalized Point Cloud Registration with Expectation Maximization Considering Anisotropic Positional Uncertainties

Abstract

Alignment of two point clouds is an essential problem in medical robotics and computer-assisted surgery. In this paper, we first formally formulate the generalized point cloud registration problem in a probabilistic manner. Specifically, not only positional but also the orientational information are incorporated into registration. Notably, the positional error is assumed to obey a multivariate Gaussian distribution to accommodate anisotropic cases. Expectation conditional maximization framework is utilized to solve the problem. In E-step, the correspondence probabilities between points in two generalized point clouds are computed. In M -step, the constrained optimization problem with respect to the transformation matrix is re-formulated as an unconstrained one. Extensive experiments are conducted to compare the proposed algorithm with the state-of-the-art registration methods. The experimental results demonstrate the algorithm's robustness to noise and outliers, fast convergence speed.