LieTrICP: An improvement of trimmed iterative closest point algorithm

We propose a robust registration method for two point sets using Lie group parametrization. Our algorithm is termed as LieTrICP, as it combines the advantages of the Trimmed Iterative Closest Point (TrICP) algorithm and Lie group representation. Given two low overlapped point sets, we first find the correspondence for every point, then select the overlapped point pairs, and use Lie group representation to estimate the geometric transformation from the selected point pairs. These three steps are conducted iteratively to obtain the optimal transformation. The novelties of this algorithm are twofold: (1) it generalizes the TrICP to the anisotropic case; and (2) it gives a unified Lie group framework for point set registration, which can be extended to more complicated transformations and high dimensional problems. We conduct extensive experiments to demonstrate that our algorithm is more accurate and robust than several other algorithms in a variety of situations, including missing points, perturbations and outliers.