Rigid and Articulated Point Registration with Expectation Conditional Maximization

TL;DR

This paper introduces a probabilistic framework and an EM-like algorithm for rigid and articulated point registration, improving robustness and flexibility over existing methods by handling covariance matrices and outliers.

Contribution

It presents the ECMPR algorithm for point registration, extending to articulated shapes, with enhanced covariance modeling and outlier rejection capabilities.

Findings

The ECMPR algorithm outperforms existing methods in accuracy.

Incorporating general covariance matrices improves registration flexibility.

The method effectively detects and rejects outliers.

Abstract

This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration.