Theoretical Analysis for Expectation-Maximization-Based Multi-Model 3D Registration

TL;DR

This paper provides a theoretical foundation for an EM-based algorithm in multi-model 3D registration, establishing convergence conditions and enhancing understanding of its probabilistic behavior.

Contribution

It offers the first theoretical analysis and convergence conditions for the EM-based multi-model 3D registration algorithm, bridging empirical success with rigorous justification.

Findings

Established convergence conditions for the EM algorithm

Applied probabilistic tail bounds to analyze algorithm behavior

Enhanced theoretical understanding of multi-model 3D registration

Abstract

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