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

Patrice C. Brault; Ali Mohammad-Djafari

doi:10.1117/1.2139967

1 October 2005 Unsupervised Bayesian wavelet domain segmentation using Potts-Markov random field modeling

Patrice C. Brault, Ali Mohammad-Djafari

Author Affiliations +

Journal of Electronic Imaging, Vol. 14, Issue 4, 043011 (October 2005). https://doi.org/10.1117/1.2139967

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.

©(2005) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Patrice C. Brault and Ali Mohammad-Djafari "Unsupervised Bayesian wavelet domain segmentation using Potts-Markov random field modeling," Journal of Electronic Imaging 14(4), 043011 (1 October 2005). https://doi.org/10.1117/1.2139967

Published: 1 October 2005

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