We perform detailed theoretical analysis of an expectation-maximization-based algorithm recently proposed in for solving a variation of the 3D registration problem, named multi-model 3D registration. Despite having shown superior empirical results, did not theoretically justify the conditions under which the EM approach converges to the ground truth. In this project, we aim to close this gap by establishing such conditions. In particular, the analysis revolves around the usage of probabilistic tail bounds that are developed and applied in various instances throughout the course. The problem studied in this project stands as another example, different from those seen in the course, in which tail-bounds help advance our algorithmic understanding in a probabilistic way. We provide self-contained background materials on 3D Registration

翻译：本文对近期提出的用于解决三维配准问题变种——多模型三维配准的期望最大化算法进行详细理论分析。尽管该算法在实验中展现出优越性能，但其收敛至真实值的条件尚未得到理论论证。本研究旨在通过建立此类条件来填补这一空白。具体而言，分析围绕概率尾界的应用展开，这些尾界在本课程涉及的多种场景中已被开发并应用。本项目研究的问题作为课程中尚未出现的新实例，展示了尾界如何以概率方法推进我们对算法的理解。我们提供了关于三维配准的自包含背景材料。