Markov/Gibbs texture modeling: aura matrices and temperature effects

Rosalind W. Picard, Ibrahim M. Elfadel, Alex Pentland

Abstract: An 'aura' framework is used to rewrite the nonlinear energy function of a homogeneous anisotropic Markov/Gibbs random field (MRF) as a linear sum of aura measures. The formulation relates MRFs to co-occurrence matrices. It also provides a physical interpretation of MRF textures in terms of the mixing and separation of gray-level sets, and in terms of boundary maximization and minimization. Within this framework, the authors introduce the use of temperature for texture modeling and show how the parameters of the MRF can be interpreted as temperature annealing rates. In particular, they show evidence for a transition temperature, above which all patterns generated will be visually similar, and below which a pattern evolves down to its ground state. Results which characterize the ground state patterns are described.<