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A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation

Combrexelle, Sébastien and Wendt, Herwig and Altmann, Yoann and Tourneret, Jean-Yves and Mclaughlin, Stephen and Abry, Patrice A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation. (2016) In: 41st IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016), 20 March 2016 - 25 March 2016 (Shanghai, China).

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Official URL: http://dx.doi.org/10.1109/ICASSP.2016.7472473


Texture analysis is an image processing task that can be conducted using the mathematical framework of multifractal analysis to study the regularity fluctuations of image intensity and the practical tools for their assessment, such as (wavelet) leaders. A recently introduced statistical model for leaders enables the Bayesian estimation of multifractal parameters. It significantly improves performance over standard (linear regression based) estimation. However, the computational cost induced by the associated nonstandard posterior distributions limits its application. The present work proposes an alternative Bayesian model for multifractal analysis that leads to more efficient algorithms. It relies on three original contributions: A novel generative model for the Fourier coefficients of log-leaders; an appropriate reparametrization for handling its inherent constraints; a data-augmented Bayesian model yielding standard conditional posterior distributions that can be sampled exactly. Numerical simulations using synthetic multifractal images demonstrate the excellent performance of the proposed algorithm, both in terms of estimation quality and computational cost.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of ICASSP 2016. Electronic ISBN: 978-1-4799-9988-0 ISSN: 2379-190X The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/7472473/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01511897
Audience (conference):International conference proceedings
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 > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Heriot-Watt University (UNITED KINGDOM)
Laboratory name:
Deposited On:22 Mar 2017 15:13

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