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

### Barbara Caputo, Heinrich Niemann

#### University of Erlangen-Nuremberg

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 make 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 Glass-- Markov Random Field (SG--MRF).
Experiments on textures and objects database show
the correctness and effectiveness of the proposed model.