Markov random fields model and applications to image processing

Abstract

<abstract><p>Markov random fields (MRFs) are well studied during the past 50 years. Their success are mainly due to their flexibility and to the fact that they gives raise to stochastic image models. In this work, we will consider a stochastic differential equation (SDE) driven by Lévy noise. We will show that the solution $ X_v $ of the SDE is a MRF satisfying the Markov property. We will prove that the Gibbs distribution of the process $ X_v $ can be represented graphically through Feynman graphs, which are defined as a set of cliques, then we will provide applications of MRFs in image processing where the image intensity at a particular location depends only on a neighborhood of pixels.</p></abstract>

Improving the Accuracy of Brain Tumor Identification in Magnetic Resonanceaging using Super-pixel and Fast Primal Dual Algorithm

“…MRFs can be optimized in multi-phrase time functions. For example, an overall optimizer is computed [36]. More simply, if each binary potential function of 𝑑(𝑥 𝑝 .…”

A Graphical Representation of the Truncated Moment of the Solution of a Nonlinear SPDE

“…A suitable way to take care of stochastic influence, complexity and randomness is to generalize such class of SPDEs by adding more factors that describe models in financial market, weather forecast, climatic changes, neurobiological process. It is therefore the aim of this paper to study a class of nonlinear SPDEs driven by Lévy noise, which is more general than the previous studied models in [17] and [25,26]. We shall adopt methods based on Feynman graphs and rules to represent the solution of a given class of a nonlinear SPDE, as well as its truncated moments.…”