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 analyze in detail the associated consequences in terms of estimation of the registration parameters, and propose an optimal method for estimating the rotational and translational parameters based on semidefinite 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 compare it both theoretically and experimentally with other robust methods for point registration.

Project co-funded by the European Commission within the Sixth Framework Programme (2002-2006) Dissemination Level PU Public X PP Restricted to other program participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

Building occupancy grids (OGs) in order to model the surrounding environment of a vehicle implies to fusion occupancy information provided by the different embedded sensors in the same grid. The principal difficulty comes from the fact that each can have a different resolution, but also that the resolution of some sensors varies with the location in the field of view. In this article we present a new efficient approach to this issue based upon a graphical processor unit (GPU). In that perspective, we explain why the problem of switching coordinate systems is an instance of the texture mapping problem in computer graphics. We also present an exact algorithm in order to evaluate the accuracy of such a device, which is not precisely known due to the several approximations made by the hardware. To validate our method, the results with GPU are also compared to results obtained through the exact approach and the GPU precision is shown to be good enough for robotic applications. Therefore we describe a whole and general calculus architecture to build occupancy grids for any kind of range-finder with a graphical processor unit (GPU). And we present computational time results that can allow to compute occupancy grids for 50 sensors at frame rate even for a very fine grid.