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Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

Combrexelle, Sébastien and Wendt, Herwig and Dobigeon, Nicolas and Tourneret, Jean-Yves and Mclaughlin, Stephen and Abry, Patrice Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation. (2015) IEEE Transactions on Image Processing, 24 (8). 2540-2551. ISSN 1057-7149

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Official URL: http://dx.doi.org/10.1109/TIP.2015.2426021

Abstract

Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF of the article can be found at IEEE website : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7094286
HAL Id:hal-01187463
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 - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (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:
Funders:
Agence Nationale de la Recherche (ANR) - Direction générale de l’Armement - Engineering and Physical Sciences Research Council
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Deposited By: Nicolas DOBIGEON
Deposited On:26 Aug 2015 15:30

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