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Point Registration with Expectation-Maximization

Rigid and Articulated Point Registration with Expectation Conditional Maximization

Radu Horaud, Florence Forbes, Manuel Yguel, Guillaume Dewaele, and Jian Zhang

IEEE Transactions on Pattern Analysis and Machine Intelligence, 33 (3), 587-602, March 2011

Abstract  | code | pdf from HAL | IEEEXplore | Bibtex | Video of a toy example

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.

A follow-up paper of this work was presented at ECCV’14: A Generative Model for the Joint Registration of Multiple Point Sets

Video of a toy example:

ECMPR code and example:  The file contains two point clouds: pointCloudX.txt (3000 points) and pointCloudY.txt (4000 points), the Matlab code and an example using the two point clouds. The example ecmpr_demo.m is set to perform 70 EM iterations.