Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

TL;DR

This paper introduces a likelihood-free MCMC method to jointly estimate the Potts model's granularity coefficient and other parameters, improving segmentation accuracy in image analysis.

Contribution

It proposes a novel likelihood-free Metropolis-Hastings algorithm for estimating the Potts parameter within a Bayesian framework, addressing intractable normalizing constants.

Findings

Joint estimation of B improves accuracy over assuming known B.

Incorrect B values can significantly degrade estimation performance.

Method successfully applied to real SAR and ultrasound images.

Abstract

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.