Section: New Results
Statistical approaches for computer animation
This research area is quite recent and very promising. This work has been done in close collaboration with the team EVASION of INRIA. We first addressed the problem of inverse kinematics, which is classically solved using deterministic numerical approaches. We proposed an original modelisation of the problem via a hidden Markov chain. Therefor, we provided a new algorithm based on a Monte Carlo filter that allows to solve sequentially the inverse kinematics problem. The work presented in  concerns the compression of motion capture sequences. We propose a novel, lossy compression algorithm that exploits both temporal and spatial coherence. This algorithm is based on approximation of pose manifold computed using a principal geodesics analysis.
Theoretical result on Sequential Monte Carlo
Sequential Monte Carlo approaches, also known as particle filters, are well-know tools for tracking appplications in computer vision. A longstanding problem in sequential Monte Carlo (SMC) is to mathematically prove the popular belief that resampling does improve the performance of the estimation (this of course is not always true, and the real question is to clarify classes of problems where resampling helps). A more pragmatic answer to the problem is to use adaptive procedures that have been proposed on the basis of heuristic considerations, where resampling is performed only when it is felt necessary, i.e. when some criterion (effective number of particles, entropy of the sample, etc.) reaches some prescribed threshold. It still remains to mathematically prove the efficiency of such adaptive procedures. The contribution of the paper  is to propose an approach, based on a representation in terms of multiplicative functionals (in which importance weights are treated as particles, roughly speaking) to obtain the asymptotic variance of adaptive resampling procedures, when the sample size goes to infinity. It is then possible to see the impact of the threshold on the asymptotic variance, at least in the Gaussian case, where the resampling criterion has an explicit expressions in the large sample asymptotics.
Geometric Video Projector Auto-Calibration.
We have developed several methods for the calibration and self-calibration of projector–camera system  ,  ,  . Typical classical methods have to augment the projection screen with markers. Our methods can do without this, but require moving the projector for the self-calibration procedure. In many cases, this is arguably less cumbersome to do. Our methods are based on the fact that projectors can be modeled like cameras, and adapt self-calibration methods designed for cameras, to projector–camera systems. This is joint work with Sébastien Roy from the University of Montréal.
Critical motions for camera self-calibration.
This is one of our historic topics in structure-from-motion research. This year, we have extended the existing results in two main ways  . First, a more general framework than previously was used, based on confocal quadric theory; this makes several results easier to obtain than previously. Second, we analyzed so-called artificial critical motions, i.e. degeneracies that arise due to the specific self-calibration method used and not due to a generic degeneracy. We have shown the artificial critical motions for the most representative family of self-calibration methods, which neglect a rank-constraint on the dual absolute quadric. We have also shown that enforcing that rank constraint a posteriori , allows to resolve all artificial degeneracies, i.e. allows self-calibration to be successful on more cases than previously possible with the considered methods. This is joint work with Pierre Gurdjos from IRI Toulouse and Adrien Bartoli from LASMEA, Clermont-Ferrand.