Multiscale Markov random field models for parallel image classification

The authors consider multiscale Markov random field (MRF) models. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. A hierarchical model is proposed, which consists of a label pyramid and a whole observation field. The parameters of the coarse grid can be derived by simple computation from the finest grid. In the label pyramid, a new local interaction is introduced between two neighbor grids. This model gives a relaxation algorithm which can be run in parallel on the entire pyramid. The model allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price