### AIMS Mathematics

2022, Issue 3: 4459-4471. doi: 10.3934/math.2022248
Research article

# Markov random fields model and applications to image processing

• Received: 18 October 2021 Revised: 15 December 2021 Accepted: 15 December 2021 Published: 22 December 2021
• MSC : 60G20, 60H10, 60K35, 81T15, 81T18

• 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.

Citation: Boubaker Smii. Markov random fields model and applications to image processing[J]. AIMS Mathematics, 2022, 7(3): 4459-4471. doi: 10.3934/math.2022248

### Related Papers:

• 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.

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