Anisotropic Generalized Bayesian Coherent Point Drift for Point Set Registration

Abstract

Registration is highly demanded in many real-world scenarios such as robotics and automation. Registration is challenging partly due to the fact that the acquired data is usually noisy and has many outliers. In addition, in many practical applications, one point set (PS) usually only covers a partial region of the other PS. Thus, most existing registration algorithms cannot guarantee theoretical convergence. This article presents a novel, robust, and accurate three-dimensional (3D) rigid point set registration (PSR) method, which is achieved by generalizing the state-of-the-art (SOTA) Bayesian coherent point drift (BCPD) theory to the scenario that high-dimensional point sets (PSs) are aligned and the anisotropic positional noise is considered. The high-dimensional point sets typically consist of the positional vectors and normal vectors. On one hand, with the normal vectors, the proposed method is more robust to noise and outliers, and the point correspondences can be found more accurately. On the other hand, incorporating the registration into the BCPD framework will guarantee the algorithm’s theoretical convergence. Our contributions in this article are three folds. First, the problem of rigidly aligning two general PSs with normal vectors is incorporated into a variational Bayesian inference framework, which is solved by generalizing the BCPD approach while the anisotropic positional noise is considered. Second, the updated parameters during the algorithm’s iterations are given in closed-form or with iterative solutions. Third, extensive experiments have been done to validate the proposed approach and its significant improvements over the BCPD. Note to Practitioners—This paper was motivated by the problem of 3D rigid PSR for computer-assisted surgery (CAS), especially in orthopedic applications. The proposed algorithm is also suitable for other scenarios where the initial coarse registration is conducted. The traditional registration methods are susceptible to noise (especially anisotropic noise), outliers, and incomplete partial data. This paper generalizes the recently proposed BCPD method to the six-dimensional scenario where anisotropic positional noise is considered and normal vectors are incorporated. The proposed noise model is decomposed into three parts to be solved alternately: the membership probability of mixture distributions, the soft correspondence estimation, and the model parameters (i.e., the rotation matrix, translation vector, the covariance matrix with the anisotropic positional error, and the concentration parameter with the estimation of the normal vectors). Especially, the convergence is guaranteed at the theoretical level using the variational inference theory. The experimental results demonstrate the superiority of our algorithm on registration accuracy, convergence speed, and robustness to noise, outliers, and partial data.