Constrained multiscale Markov random fields and the analysis of visual motion

The use of markov random field (MRF) models within the framework of global bayesian decision has recently brought new powerful solutions to most of static and dynamic image analysis issues. Use of MRF models with the maximum a posteriori criterion leads to the minimization of a global energy function which may exhibit local minima. This minimization is generally performed using deterministic or stochastic relaxation algorithms which can be sped up significantly by using multigrid techniques. In this paper we investigate a new approach to multigrid image analysis based on MRF models. The multigrid algorithm under concern relies on constrained optimization. The global optimization problem associated to MRF modeling is solved over a sequence of nested subsets of the original configuration space. Those subsets consist of allowed configurations constraining the desired solution at different scales. The constrained optimization can be implemented via a coarse-to-fine multigrid algorithm defined on a sequence of consistent multiscale MRF models. The proposed multiscale paradigm yields fast convergence towards high quality estimates when compared to standard monoresolution or multigrid relaxation schemes. It reveals also far less sensitive to local minima than standard relaxation algorithms. The efficiency of the approach is demonstrated on several relevant problems in image sequence analysis : motion detection, optical flow measurement and motion-based segmentation. Results are presented on real world sequences including several moving objects and camera motion.