Coherent point drift with Skewed Distribution for accurate point cloud registration

Point cloud registration methods based on Gaussian Mixture Models (GMMs) exhibit high robustness. However, GMM cannot precisely depict point clouds, because the Gaussian distribution is spatially symmetric and local surfaces of point clouds are typically non-symmetric. In this paper, we propose a novel method for rigid point cloud registration, termed coherent point drift with Skewed Distribution (Skewed CPD). Our method employs an asymmetric distribution constructed from the local surface normals and curvature radii. Compared to the Gaussian distribution, this skewed distribution provides a more accurate spatial description of points on local surfaces. Additionally, we integrate an adaptive multiplier to the covariance, which reallocates the weight of the covariance for different components in the probabilistic mixture model. We employ the EM algorithm to address this maximum likelihood estimation (MLE) issue and leverage GPU acceleration. In the M-step, we adopt an unconstrained optimization technique rooted in a Lie group and Lie algebra to attain the optimal transformation. Experimental results indicate that our method outperforms state-of-the-art methods in both accuracy and robustness. Remarkably, even without loop closure detection, the cumulative error of our approach remains minimal.