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

Abstract: 

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.

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Paper Details

Authors:
Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry
Submitted On:
24 March 2016 - 10:09pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Combrexelle Sébastien
Paper Code:
SPTM-L10.4
Document Year:
2016
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Document Files

Combrexelle_ICASSP_Shanghai_2016.pdf.zip

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[1] Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry, "A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1038. Accessed: Feb. 18, 2018.
@article{1038-16,
url = {http://sigport.org/1038},
author = {Herwig Wendt; Yoann Altmann; Jean-Yves Tourneret; Stephen McLaughlin; Patrice Abry },
publisher = {IEEE SigPort},
title = {A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation},
year = {2016} }
TY - EJOUR
T1 - A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation
AU - Herwig Wendt; Yoann Altmann; Jean-Yves Tourneret; Stephen McLaughlin; Patrice Abry
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1038
ER -
Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry. (2016). A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation. IEEE SigPort. http://sigport.org/1038
Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry, 2016. A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation. Available at: http://sigport.org/1038.
Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry. (2016). "A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation." Web.
1. Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, Patrice Abry. A Bayesian framework for the multifractal analysis of images using data augmentation and a Whittle approximation [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1038