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Journal of Electronic Imaging

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

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.

Paper Details

Date Published: 1 October 2005
PDF: 16 pages
J. Electron. Imaging. 14(4) 043011 doi: 10.1117/1.2139967
Published in: Journal of Electronic Imaging Volume 14, Issue 4
Show Author Affiliations
Patrice C. Brault, Univ. Paris Sud (France)
Ali Mohammad-Djafari, Lab. des signaux et systèmes (France)

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