A generalisation of renormalisation group methods for multiresolution image analysis

The application of multigrid methods to accelerating the minimisation of a nonconvex Gibbs potential requires that Gibbs parameters (GP´s) be chosen at each level of coarsening in such a way that the long-range conditional probabilities of the associated 2D Markov random field are unchanged by coarsening. Formulae specifying how GP´s transform from fine to coarse resolution exist for a restricted set of computationaly tractable cost functions and, while numerical routines solve the problem in principle, they are hopelessly slow for that class of spatially inhomogeneous GP´s (site parameters) which depend on the image data. The authors provide a general theorem which specifies how site parameters coarsen for deterministic linear block coarsening. The theorem can be used to accelerate the annealing of realistic image models