  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.
