Rigid and Articulated Point Registration with Expectation Conditional Maximization

Radu Horaud (1) , Florence Forbes (2) , Manuel Yguel (3) , Guillaume Dewaele (1, 4) , Jian Zhang (5)

1 PERCEPTION - Interpretation and Modelling of Images and Videos
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
3 E-MOTION - Geometry and Probability for Motion and Action
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
5 EEE - Department of Electrical and Electronic Engineering

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.

Mots clés: EM; Gaussian mixture models; ICP; Point registration; SDP relaxation; articulated object tracking; convex optimization; expectation maximization; feature matching; hand tracking; object pose; outlier detection; robust statistics

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Radu Horaud, Florence Forbes, Manuel Yguel, Guillaume Dewaele, Jian Zhang. Rigid and Articulated Point Registration with Expectation Conditional Maximization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33 (3), pp.587-602. ⟨10.1109/TPAMI.2010.94⟩. ⟨inria-00590265⟩