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Multifractal Analysis of Multivariate Images Using Gamma Markov Random Field Priors

Wendt, Herwig and Combrexelle, Sébastien and Altmann, Yoann and Tourneret, Jean-Yves and Mclaughlin, Stephen and Abry, Patrice Multifractal Analysis of Multivariate Images Using Gamma Markov Random Field Priors. (2018) SIAM Journal on Imaging Sciences, 11 (2). 1294-1316. ISSN 1936-4954

(Document in English)

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Official URL: https://doi.org/10.1137/17M1151304


Texture characterization of natural images using the mathematical framework of multifractal analysis (MFA) enables the study of the fluctuations in the regularity of image intensity. Although successfully applied in various contexts, the use of MFA has so far been limited to the independent analysis of a single image, while the data available in applications are increasingly multivariate. This paper addresses this limitation and proposes a joint Bayesian model and associated estimation procedure for multifractal parameters of multivariate images. It builds on a recently introduced generic statistical model that enabled the Bayesian estimation of multifractal parameters for a single image and relies on the following original key contributions: First, we develop a novel Fourier domain statistical model for a single image that permits the use of a likelihood that is separable in the multifractal parameters via data augmentation. Second, a joint Bayesian model for multivariate images is formulated in which prior models based on gamma Markov random fields encode the assumption of the smooth evolution of multifractal parameters between the image components. The design of the likelihood and of conjugate prior models is such that exploitation of the conjugacy between the likelihood and prior models enables an efficient estimation procedure that can handle a large number of data components. Numerical simulations conducted using sequences of multifractal images demonstrate that the proposed procedure significantly outperforms previous univariate benchmark formulations at a competitive computational cost.

Item Type:Article
HAL Id:hal-01925387
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Heriot-Watt University (UNITED KINGDOM)
Laboratory name:
Agence Nationale de la Recherche (FRANCE) - Agence Nationale de la Recherche (FRANCE) - Direction Générale de l'Armement - DGA (FRANCE) - Engineering and Physical Sciences Research Council - EPSRC (UK)
Deposited On:16 Nov 2018 15:18

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