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

Marcelo Alejandro Pereyra (1) , Nicolas Dobigeon (2, 3) , Hadj Batatia (4) , Jean-Yves Tourneret (2, 3)

1 School of Mathematics [Bristol]
2 IRIT-SC - Signal et Communications
3 Toulouse INP - Institut National Polytechnique (Toulouse)
4 IRIT-TCI - Traitement et Compréhension d’Images

This paper addresses the problem of estimating the Potts parameter β 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 β requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method, the estimation of β is conducted using a likelihood-free Metropolis–Hastings algorithm. Experimental results obtained for synthetic data show that estimating β jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of β. On the other hand, choosing an incorrect value of β can degrade estimation performance significantly. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.

Mots clés: Bayesian estimation; Gibbs sampler; Intractable normalizing constants; Mixture model; Potts-Markov field

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Intelligence artificielle [cs.AI]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Marcelo Alejandro Pereyra, Nicolas Dobigeon, Hadj Batatia, Jean-Yves Tourneret. Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm. IEEE Transactions on Image Processing, 2013, 22 (6), pp.2385-2397. ⟨10.1109/TIP.2013.2249076⟩. ⟨hal-01130731⟩