Bayesian joint estimation of the multifractality parameter of image patches using gamma Markov Random Field priors

Sébastien Combrexelle (1) , Herwig Wendt (1, 2) , Yoann Altmann (3) , Jean-Yves Tourneret (4, 5) , Stephen Mclaughlin (3) , Patrice Abry (6)

1 IRIT-SC - Signal et Communications
2 CNRS - Centre National de la Recherche Scientifique
3 UCLAN - School of Computing, Engineering and Physical Sciences, University of Central Lancashire, Preston
4 IRIT-MINDS - CoMputational imagINg anD viSion
5 Toulouse INP - Institut National Polytechnique (Toulouse)
6 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

Texture analysis can be embedded in the mathematical framework of multifractal (MF) analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, wavelet leaders. A statistical model for leaders was proposed permitting Bayesian estimation of MF parameters for images yielding improved estimation quality over linear regression based estimation. This present work proposes an extension of this Bayesian model for patch-wise MF analysis of images. Classical MF analysis assumes space homogeneity of the MF properties whereas here we assume MF properties may change between texture elements and we do not know where the changes are located. This paper proposes a joint Bayesian model for patches formulated using spatially smoothing gamma Markov Random Field priors to counterbalance the increased statistical variability of estimates caused by small patch sizes. Numerical simulations based on synthetic multi-fractal images demonstrate that the proposed algorithm outperforms previous formulations and standard estimators.

Mots clés: Wavelet leaders; Multifractal analysis; Gamma Markov random field; Texture analysis; Bayesian estimation

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

Sébastien Combrexelle, Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen Mclaughlin, et al.. Bayesian joint estimation of the multifractality parameter of image patches using gamma Markov Random Field priors. IEEE International Conference on Image Processing (ICIP 2016), Sep 2016, Phoenix, United States. pp. 4468-4472. ⟨hal-01447351⟩