Publications about finite mixture models

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• 1 Article
• 2 Conference articles
• 2 Technical and Research Reports

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Article

1 - Enhanced Dictionary-Based SAR Amplitude Distribution Estimation and Its Validation With Very High-Resolution Data. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. IEEE-Geoscience and Remote Sensing Letters, 8(1): pages 148-152, January 2011. Keywords : finite mixture models, parametric estimation, probability-density-function estimation, Stochastic EM (SEM), synthetic aperture radar. Copyright : IEEE @ARTICLE{krylovGRSL2011, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Enhanced Dictionary-Based SAR Amplitude Distribution Estimation and Its Validation With Very High-Resolution Data}, year = {2011}, month = {January}, journal = {IEEE-Geoscience and Remote Sensing Letters}, volume = {8}, number = {1}, pages = {148-152}, url = {http://dx.doi.org/10.1109/LGRS.2010.2053517}, pdf = {http://hal.archives-ouvertes.fr/inria-00503893/en/}, keyword = {finite mixture models, parametric estimation, probability-density-function estimation, Stochastic EM (SEM), synthetic aperture radar} } Abstract : In this letter, we address the problem of estimating the amplitude probability density function (pdf) of single-channel synthetic aperture radar (SAR) images. A novel flexible method is developed to solve this problem, extending the recently proposed dictionary-based stochastic expectation maximization approach (developed for a medium-resolution SAR) to very high resolution (VHR) satellite imagery, and enhanced by introduction of a novel procedure for estimating the number of mixture components, that permits to reduce appreciably its computational complexity. The specific interest is the estimation of heterogeneous statistics, and the developed method is validated in the case of the VHR SAR imagery, acquired by the last-generation satellite SAR systems, TerraSAR-X and COSMO-SkyMed. This VHR imagery allows the appreciation of various ground materials resulting in highly mixed distributions, thus posing a difficult estimation problem that has not been addressed so far. We also conduct an experimental study of the extended dictionary of state-of-the-art SAR-specific pdf models and consider the dictionary refinements.

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2 Conference articles

1 - Synthetic Aperture Radar Image Classification via Mixture Approaches. V. Krylov and J. Zerubia. In Proc. IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS), Tel Aviv, Israel, November 2011. Keywords : Synthetic Aperture Radar (SAR), remote sensing, high resolution, Classification, finite mixture models, generalized gamma distribution. Copyright : IEEE @INPROCEEDINGS{krylovCOMCAS11, author = {Krylov, V. and Zerubia, J.}, title = {Synthetic Aperture Radar Image Classification via Mixture Approaches}, year = {2011}, month = {November}, booktitle = {Proc. IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS)}, address = {Tel Aviv, Israel}, url = {http://www.ortra.biz/comcas/}, pdf = {http://hal.archives-ouvertes.fr/inria-00625551/en/}, keyword = {Synthetic Aperture Radar (SAR), remote sensing, high resolution, Classification, finite mixture models, generalized gamma distribution} } Abstract : In this paper we focus on the fundamental synthetic aperture radars (SAR) image processing problem of supervised classification. To address it we consider a statistical finite mixture approach to probability density function estimation. We develop a generalized approach to address the problem of mixture estimation and consider the use of several different classes of distributions as the base for mixture approaches. This allows performing the maximum likelihood classification which is then refined by Markov random field approach, and optimized by graph cuts. The developed method is experimentally validated on high resolution SAR imagery acquired by Cosmo-SkyMed and TerraSAR-X satellite sensors.

2 - Dictionary-based probability density function estimation for high-resolution SAR data. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. In Proc. of SPIE (IS&T/SPIE Electronic Imaging 2009), Vol. 7246, pages 72460S, San Jose, USA, January 2009. Keywords : SAR image, Probability density function, parametric estimation, finite mixture models, Stochastic EM (SEM). Copyright : SPIE @INPROCEEDINGS{KrylovSPIE09, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Dictionary-based probability density function estimation for high-resolution SAR data}, year = {2009}, month = {January}, booktitle = {Proc. of SPIE (IS&T/SPIE Electronic Imaging 2009)}, volume = {7246}, pages = {72460S}, address = {San Jose, USA}, url = {http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=812524}, pdf = {http://hal.archives-ouvertes.fr/inria-00361384/en/}, keyword = {SAR image, Probability density function, parametric estimation, finite mixture models, Stochastic EM (SEM)} } Abstract : In the context of remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of pixel intensities. In this work, we develop a parametric finite mixture model for the statistics of pixel intensities in high resolution synthetic aperture radar (SAR) images. This method is an extension of previously existing method for lower resolution images. The method integrates the stochastic expectation maximization (SEM) scheme and the method of log-cumulants (MoLC) with an automatic technique to select, for each mixture component, an optimal parametric model taken from a predefined dictionary of parametric probability density functions (pdf). The proposed dictionary consists of eight state-of-the-art SAR- specific pdfs: Nakagami, log-normal, generalized Gaussian Rayleigh, Heavy-tailed Rayleigh, Weibull, K-root, Fisher and generalized Gamma. The designed scheme is endowed with the novel initialization procedure and the algorithm to automatically estimate the optimal number of mixture components. The experimental results with a set of several high resolution COSMO-SkyMed images demonstrate the high accuracy of the designed algorithm, both from the viewpoint of a visual comparison of the histograms, and from the viewpoint of quantitive accuracy measures such as correlation coefficient (above 99,5%). The method proves to be effective on all the considered images, remaining accurate for multimodal and highly heterogeneous scenes.

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2 Technical and Research Reports

1 - Classification of very high resolution SAR images of urban areas. A. Voisin and V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. Rapport de recherche 7758, INRIA, October 2011. Keywords : Synthetic Aperture Radar (SAR) image, Supervised classification, Bayesian, finite mixture models, hierarchical Markov random fields, wavelet. @TECHREPORT{RR-7758, author = {Voisin, A. and Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Classification of very high resolution SAR images of urban areas}, year = {2011}, month = {October}, institution = {INRIA}, type = {Rapport de recherche}, number = {7758}, url = {http://hal.inria.fr/docs/00/63/10/38/PDF/RR-7758.pdf}, keyword = {Synthetic Aperture Radar (SAR) image, Supervised classification, Bayesian, finite mixture models, hierarchical Markov random fields, wavelet} } Résumé : Dans le cadre d’une approche face aux risques environnementaux, nous proposons une nouvelle méthode de classification bayésienne supervisée. Celle-ci combine une modélisation statistique des images avec une prise en compte contextuelle via des champs de Markov hiérarchiques. Ce rapport de recherche vise à détailler plus amplement cette modélisation contextuelle, à savoir expliciter le modèle mathématique sur quad-arbre et l’obtention des observations par décomposition en ondelettes de l’image originale. Il met également en exergue certaines modifications apportées en vue d’améliorer la classification finale. Abstract : In the framework of the assessment of environmental risks, we propose herein a new supervised Bayesian classification method. It combines statistical image modeling with a contextual approach via hierarchical Markov random fields. This research report aims to further focus on this kind of contextual classification approach by detailing both the quad-tree mathematical model and the statistics of the observations, obtained by wavelet transform. We therefore introduce modifications to a classical Markovian single-scale algorithm that lead to more accurate classification results.

2 - Modeling the statistics of high resolution SAR images. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. Research Report 6722, INRIA, November 2008. Keywords : Synthetic Aperture Radar (SAR) image, Probability density function, parametric estimation, finite mixture models, Stochastic EM (SEM). Copyright : INRIA/ARIANA, 2008 @TECHREPORT{krylovDSEM08, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Modeling the statistics of high resolution SAR images}, year = {2008}, month = {November}, institution = {INRIA}, type = {Research Report}, number = {6722}, url = {http://hal.archives-ouvertes.fr/inria-00342681/en/}, pdf = {http://hal.archives-ouvertes.fr/docs/00/35/76/27/PDF/RR-6722.pdf}, keyword = {Synthetic Aperture Radar (SAR) image, Probability density function, parametric estimation, finite mixture models, Stochastic EM (SEM)} } Abstract : In the context of remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of pixel intensities. In this work, we develop a parametric finite mixture model for modelling the statistics of intensities in high resolution Synthetic Aperture Radar (SAR) images. Along with the models we design an efficient parameter estimation scheme by integrating the Stochastic Expectation Maximization scheme and the Method of log-cumulants with an automatic technique to select, for each mixture component, an optimal parametric model taken from a predefined dictionary of parametric probability density functions (pdf). In particular, the proposed dictionary consists of eight most efficient state-of-the-art SAR-specific pdfs: Nakagami, log-normal, generalized Gaussian Rayleigh, Heavy-tailed Rayleigh, Weibull, K-root, Fisher and generalized Gamma. The experiment results with a set of several real SAR (COSMO-SkyMed) images demonstrate the high accuracy of the designed algorithm, both from the viewpoint of a visual comparison of the histograms, and from the viewpoint of quantitive measures such as correlation coefficient (always above 99,5%) . We stress, in particular, that the method proves to be effective on all the considered images, remaining accurate for multimodal and highly heterogeneous images.

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