Analytic Approximation of Gibbs Potentials to Model Stochastic Textures

Abstract

Gibbs random fields with multiple pairwise pixel interactionshave good potentialities in modeling natural image texturesbecause allow for learning both the structure and strengths ofpixel interactions from a given training sample. The learningscheme is based on the maximum likelihood estimate (MLE) ofGibbs potentials that specify the interaction strenghts. Thisscheme is amplified here by deducing an explicit, to scalingfactors, analytic form of the potentials from an additionalfeasible top rank principle. It suggests that the training samplemay possess a feasible top rank in its total Gibbs energy withinthe parent population. Under this condition, only the scaling factorshave to be learnt using their MLE. As a result, the introducedconditional MLE of the potentials extends capabilities of the Gibbsimage models under consideration.