From Markov Random Fields to Associative Memories and Back: Spin-Glass Markov Random Fields

In this paper we propose a fully connected energy function for Markov Random Field (MRF) modeling which is inspired by Spin-Glass Theory (SGT). Two major tasks in MRF modeling are how to define the neighborhood system for irregular sites and how to choose the energy function for a proper encoding of constraints. The proposed energy function offers two major advantages that makes it possible to avoid MRF modeling problems in the case of irregular sites. First, full connectivity makes the neighborhood definition irrelevant, and second, the energy function is defined independently of the considered application. A basic assumption in SGT is the infinite dimension of the configuration space in which the energy is defined; the choice of a particular energy function, which depends on the scalar product between configurations, allows us to use a kernel function in the energy formulation; this solves the problem of high dimensionality and makes it possible to use SGT results in an MRF framework. We call this new model Spin GlassMarkov Random Field (SG-MRF). Experiments on textures and objects database show the correctness and effectiveness of the proposed model.