Multi-temperature annealing: a new approach for the energy-minimization of hierarchical Markov random field models

As it is well known, optimization of the energy function of Markov random fields is very expensive. Hierarchical models have usually much more communication per pixel than monogrid ones. This is why classical annealing schemes are too slow, even on a parallel machine, to minimize the energy associated with such a model. However, taking benefit of the pyramidal structure of the model, we can define a new annealing scheme: the multitemperature annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalisation of the annealing theorem of Geman and Geman (1984). We have applied the algorithm to image classification and tested it on synthetic and real images.