A generalisation of renormalisation group methods for multiresolution image analysis

Abstract

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.<>