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Unsupervised Bayesian wavelet domain segmentation using Potts-Markov random field modeling

[+] Author Affiliations
Patrice Brault

Université Orsay Paris-Sud, Institut d’Electronique Fondamentale, CNRS UMR-8622, 91405 Orsay Cedex, France

Ali Mohammad-Djafari

Laboratoire des Signaux et Systèmes, CNRS UMR-8506, Supelec, Plateau du Moulon, 91192 Gif sur Yvette Cedex, France

J. Electron. Imaging. 14(4), 043011 (December 19, 2005). doi:10.1117/1.2139967
History: Received January 10, 2005; Revised June 14, 2005; Accepted June 14, 2005; Published December 19, 2005; Online December 19, 2005
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We describe a new fully unsupervised image segmentation method based on a Bayesian approach and a Potts-Markov random field (PMRF) model that are performed in the wavelet domain. A Bayesian segmentation model, based on a PMRF in the direct domain, has already been successfully developed and tested. This model performs a fully unsupervised segmentation, on images composed of homogeneous regions, by introducing a hidden Markov model (HMM) for the regions to be classified, and Gaussian distributions for the noise and for the pixels pertaining to each region. The computation of the posterior laws, deduced from these a priori distributions for the pixels, is done by a Markov chain Monte Carlo (MCMC) approach and uses a Gibbs sampling algorithm. The use of a high number of iterations to reach convergence in a segmentation, where the number of segments, or “classes” labels, is important, makes the algorithm rather slow for the processing of a large quantity of data like image sequences. To overcome this problem, we take advantage of the property of the wavelet coefficients, in an orthogonal decomposition, to be modeled by a mixture of two Gaussians. Thus, by projecting an observable noisy image in the wavelet domain, we are able to segment, in this same domain, the wavelet subbands in only two classes. After a decomposition up to a scale J, the main idea is to segment the coarse, and small, approximation subband with a high number of classes, and to segment all the detail (wavelet) subbands with only two classes. The segmented wavelet domain coefficients are then reconstructed to obtain a final segmented image in the direct domain. Our tests on synthetic and natural images show that the segmentation quality stays good, even with noisy images, and shows that the segmentation times can be significantly reduced.

© 2005 SPIE and IS&T

Topics

Wavelets ; Modeling

Citation

Patrice Brault and Ali Mohammad-Djafari
"Unsupervised Bayesian wavelet domain segmentation using Potts-Markov random field modeling", J. Electron. Imaging. 14(4), 043011 (December 19, 2005). ; http://dx.doi.org/10.1117/1.2139967


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