5.2. MRFs Background

In this section, we first introduce the concept of MRFs and the associated notation. Then, we present the Gibbs fields and their properties. Finally, we present the interplay between MRFs and Gibbs distributions, highlighting how they are used in practical applications.

5.2.1. MRFs

MRFs are a branch of probability theory with important theoretical properties and practical applications. Most prominent applications of MRFs lie in the areas of statistical physics [136], image processing [83,228], and coordination of autonomous robots [206] until now. A MRF is a stochastic process that generalizes the Markov process in the sense that the time index of the original Markov process (characterized by the memoryless property) is substituted ...

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