Markov random fields model and applications to image processing

Boubaker Smii

doi:10.3934/math.2022248

Markov random fields model and applications to image processing

Boubaker Smii^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	4459-4471
Number of pages	13
Journal	AIMS Mathematics
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/math.2022248
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press.

Keywords

Feynman graphs and rules
Gibbs distribution
Lévy processes
Markov random fields
Stochastic differential equations

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2022248

Cite this

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AB - 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 Xv of the SDE is a MRF satisfying the Markov property. We will prove that the Gibbs distribution of the process Xv 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.

KW - Feynman graphs and rules

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KW - Lévy processes

KW - Markov random fields

KW - Stochastic differential equations

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ER -

Markov random fields model and applications to image processing

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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