Probabilistic Methods for Point Cloud Registration Problem

Abstract

Over the past few decades, probabilistic methods have been one of the popular approaches for registering point clouds generated by LiDAR systems. Such methods consist of two major steps, i.e., using probabilistic models to represent point clouds and finding optimal transformation to align point clouds with the help of some statistical distances. In this thesis, a theoretical framework of probabilistic methods is studied, which provides a foundation for understanding and implementing point cloud registration with some specific probabilistic models and distance measures. Specifically, the concepts of Gaussian Mixture Models and Kernel Density Estimation are explored, with a detailed discussion of their practical implementation. Furthermore, Kullback-Leibler divergence and Wasserstein distance, including the computation of Wasserstein distance through Kantorovich-Rubinstein duality, are also studied. An approximation of Wasserstein distance that preserves differentiability through linear programming techniques is proposed, which enables the use of gradient-based methods on Wasserstein distance to find the optimal transformation that aligns two point clouds. The algorithms that contribute to a complete procedure for solving point cloud registration problem with our proposed methods are also discussed and demonstrated.