REM-Seg: A robust EM algorithm for parallel segmentation and registration of point clouds

For purposes of real-time 3D sensing, it is important to be able to quickly register together incoming point cloud data. In this paper, we devise a method to quickly and robustly decompose large point clouds into a relatively small number of meaningful surface patches from which we register new data points. The surface patch representation sidesteps the costly problem of matching points to points since incoming data only need to be compared with the patches. The chosen parametrization of the patches (as Gaussians) leads to a smooth data likelihood function with a well-defined gradient. This representation thus forms the basis for a robust and efficient registration algorithm using a parallelized gradient descent implemented on a GPU using CUDA. We use a modified Gaussian Mixture Model (GMM) formulation solved by Expectation Maximization (EM) to segment the point cloud and an annealing gradient descent method to find the 6-DOF rigid transformation between the incoming point cloud and the segmented set of surface patches. We test our algorithm, Robust EM Segmentation (REM-Seg), against other GPU-accelerated registration algorithms on simulated and real data and show that our method scales well to large numbers of points, has a wide range of convergence, and is suitably accurate for 3D registration.