In this note, we propose an approach to initialize the Iterative Closest Point (ICP) algorithm to match unlabelled point clouds related by rigid transformations. The method is based on matching the ellipsoids defined by the points' covariance matrices and then testing the various principal half-axes matchings that differ by elements of a finite reflection group. We derive bounds on the robustness of our approach to noise and numerical experiments confirm our theoretical findings.

翻译：本文提出一种迭代最近点（ICP）算法的初始化方法，用于匹配由刚性变换关联的无标签点云。该方法基于匹配由点云协方差矩阵定义的椭球体，随后测试通过有限反射群元素区分的各种主半轴匹配组合。我们推导了该方法对噪声鲁棒性的理论界限，数值实验验证了理论结果。