Supplementary Material of LSG-GPD: Coherent Point Drift with Local Surface Geometry for Point Cloud Registration

Detailed derivations and experiment settings are provided in this supplementary material. In Sec. 1, the derivation of the EM algorithm is presented. In Sec. 2, we show the derivation of the outlier weight. In Sec. 3, concepts and definitions about Lie groups and Lie algebra are briefly reviewed. Then, the derivation of the gradient and the Hessian matrix are discussed. The update of the covariance multiplier σ is also derived in this section. In Sec. 4, detailed experiment settings are given. Finally, in Sec. 5, we provide a visualization of the point-to-plane penalization coefficient α on a point cloud data and more insights on the robustness of the method. The source code is available at https: //github.com/ChirikjianLab/LSG-CPD.git. 1. Derivation of EM Recall the negative log-likelihood function in Sec. 3.1 of the paper. The negative log-likelihood of the transformed observations g(xn) is: