Publications about Stochastic EM (SEM)

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• 2 Articles
• 3 Conference articles
• 4 Technical and Research Reports

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2 Articles

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.

2 - Dictionary-Based Stochastic Expectation-Maximization for SAR Amplitude Probability Density Function Estimation. G. Moser and J. Zerubia and S.B. Serpico. IEEE Trans. Geoscience and Remote Sensing, 44(1): pages 188-200, January 2006. Keywords : SAR Images, Stochastic EM (SEM), Dictionary. Copyright : IEEE @ARTICLE{moser_ieeetgrs_05, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {Dictionary-Based Stochastic Expectation-Maximization for SAR Amplitude Probability Density Function Estimation}, year = {2006}, month = {January}, journal = {IEEE Trans. Geoscience and Remote Sensing}, volume = {44}, number = {1}, pages = {188-200}, url = {http://dx.doi.org/10.1109/TGRS.2005.859349}, pdf = {http://hal.archives-ouvertes.fr/inria-00561369/en/}, keyword = {SAR Images, Stochastic EM (SEM), Dictionary} } Abstract : In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SAR-specific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation–maximization iterative methodology with the recently developed “method-of-log-cumulants” for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data.

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3 Conference articles

1 - Parameter estimation for a marked point process within a framework of multidimensional shape extraction from remote sensing images. S. Ben Hadj and F. Chatelain and X. Descombes and J. Zerubia. In Proc. ISPRS Technical Commission III Symposium on Photogrammetry Computer Vision and Image Analysis (PCV), Paris, France, September 2010. Keywords : Shape extraction, Marked point process, RJMCMC, Simulated Annealing, Stochastic EM (SEM). @INPROCEEDINGS{sbenhadj10a, author = {Ben Hadj, S. and Chatelain, F. and Descombes, X. and Zerubia, J.}, title = {Parameter estimation for a marked point process within a framework of multidimensional shape extraction from remote sensing images}, year = {2010}, month = {September}, booktitle = {Proc. ISPRS Technical Commission III Symposium on Photogrammetry Computer Vision and Image Analysis (PCV)}, address = {Paris, France}, url = {http://hal.archives-ouvertes.fr/docs/00/52/63/45/PDF/ISPRS_SBH_FC_XD_JZ_Final2.pdf}, keyword = {Shape extraction, Marked point process, RJMCMC, Simulated Annealing, Stochastic EM (SEM)} }

2 - High resolution SAR-image classification by Markov random fields and finite mixtures. G. Moser and V. Krylov and S.B. Serpico and J. Zerubia. In Proc. of SPIE (IS&T/SPIE Electronic Imaging 2010), Vol. 7533, pages 753308, San Jose, USA, January 2010. Keywords : SAR image classification, Dictionary, amplitude probability density, Stochastic EM (SEM), Markov random field, copula. Copyright : SPIE @INPROCEEDINGS{moserSPIE2010a, author = {Moser, G. and Krylov, V. and Serpico, S.B. and Zerubia, J.}, title = {High resolution SAR-image classification by Markov random fields and finite mixtures}, year = {2010}, month = {January}, booktitle = {Proc. of SPIE (IS&T/SPIE Electronic Imaging 2010)}, volume = {7533}, pages = {753308}, address = {San Jose, USA}, url = {http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=776565}, pdf = {http://hal.archives-ouvertes.fr/inria-00442348/en/}, keyword = {SAR image classification, Dictionary, amplitude probability density, Stochastic EM (SEM), Markov random field, copula} } Abstract : In this paper we develop a novel classification approach for high and very high resolution polarimetric synthetic aperture radar (SAR) amplitude images. This approach combines the Markov random field model to Bayesian image classification and a finite mixture technique for probability density function estimation. The finite mixture modeling is done via a recently proposed dictionary-based stochastic expectation maximization approach for SAR amplitude probability density function estimation. For modeling the joint distribution from marginals corresponding to single polarimetric channels we employ copulas. The accuracy of the developed semiautomatic supervised algorithm is validated in the application of wet soil classification on several high resolution SAR images acquired by TerraSAR-X and COSMO-SkyMed.

3 - 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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4 Technical and Research Reports

1 - Estimation des paramètres de modèles de processus ponctuels marqués pour l'extraction d'objets en imagerie spatiale et aérienne haute résolution . S. Ben Hadj and F. Chatelain and X. Descombes and J. Zerubia. Rapport de recherche 7350, INRIA, July 2010. Keywords : Marked point process, RJMCMC, Simulated Annealing, Stochastic EM (SEM), pseudo-vraisemblance, Object extraction. @TECHREPORT{RR-7350, author = {Ben Hadj, S. and Chatelain, F. and Descombes, X. and Zerubia, J.}, title = {Estimation des paramètres de modèles de processus ponctuels marqués pour l'extraction d'objets en imagerie spatiale et aérienne haute résolution }, year = {2010}, month = {July}, institution = {INRIA}, type = {Rapport de recherche}, number = {7350}, url = {http://hal.archives-ouvertes.fr/inria-00508431/fr/}, keyword = {Marked point process, RJMCMC, Simulated Annealing, Stochastic EM (SEM), pseudo-vraisemblance, Object extraction} }

2 - High resolution SAR-image classification. V. Krylov and J. Zerubia. Research Report 7108, INRIA, November 2009. Keywords : SAR image classification, Dictionary, amplitude probability density, Stochastic EM (SEM), Markov random field, copula. Copyright : INRIA/ARIANA, 2009 @TECHREPORT{RR-7108, author = {Krylov, V. and Zerubia, J.}, title = {High resolution SAR-image classification}, year = {2009}, month = {November}, institution = {INRIA}, type = {Research Report}, number = {7108}, url = {http://hal.archives-ouvertes.fr/inria-00433036/en/}, pdf = {http://hal.archives-ouvertes.fr/docs/00/44/81/40/PDF/RR-7108.pdf}, keyword = {SAR image classification, Dictionary, amplitude probability density, Stochastic EM (SEM), Markov random field, copula} } Résumé : Dans ce rapport, nous proposons une nouvelle approche pour la classification des images de type Radar à Synthèse d’Ouverture (RSO) haute résolution. Cette approche combine la méthode des champs Markoviens (MRF) pour la classification bayésienne et un modèle de mélange fini pour l’estimation des densités de probabilité. Ce modèle de mélange fini est realisé grace à une approche fondée sur une espérance-maximisation stochastique, à partir d'un dictionnaire, pour l’estimation des densités de probabilité d’amplitude. Cette approche semi-automatique est étendue au cas important des images RSO avec plusieurs polarisations, en utilisant des copulas pour modéliser les distributions jointes. Des résultats expérimentaux, sur plusieurs images RSO réelles (Dual-Pol TerraSAR-X et Single-Pol COSMO-SkyMed), pour la classification de zones humides, sont présentés pour montrer l’efficacité de l’algorithme proposé. Abstract : In this report we propose a novel classification algorithm for high and very high resolution synthetic aperture radar (SAR) amplitude images that combines the Markov random field approach to Bayesian image classification and a finite mixture technique for probability density function estimation. The finite mixture modeling is done by dictionary-based stochastic expectation maximization amplitude histogram estimation approach. The developed semiautomatic algorithm is extended to an important case of multi-polarized SAR by modeling the joint distributions of channels via copulas. The accuracy of the proposed algorithm is validated for the application of wet soil classification on several high resolution SAR images acquired by TerraSAR-X and COSMO-SkyMed.

3 - 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.

4 - Dictionary-based Stochastic Expectation-Maximization for SAR amplitude probability density function estimation. G. Moser and J. Zerubia and S.B. Serpico. Research Report 5154, INRIA, France, March 2004. Keywords : Synthetic Aperture Radar (SAR), Stochastic EM (SEM), Finite mixing model. @TECHREPORT{5154, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {Dictionary-based Stochastic Expectation-Maximization for SAR amplitude probability density function estimation}, year = {2004}, month = {March}, institution = {INRIA}, type = {Research Report}, number = {5154}, address = {France}, url = {https://hal.inria.fr/inria-00071429}, pdf = {https://hal.inria.fr/file/index/docid/71429/filename/RR-5154.pdf}, ps = {https://hal.inria.fr/docs/00/07/14/29/PS/RR-5154.ps}, keyword = {Synthetic Aperture Radar (SAR), Stochastic EM (SEM), Finite mixing model} } Résumé : En télédetection, un problème vital est le besoin de développer des modèles précis pour représenter les statistiques des intensités des images. Dans ce rapport de recherche, nous traitons le problème de l'estimation de la densité de probabilité de l'amplitude d'une image de type Radar à Synthèse d'Ouverture (RSO). Plusieurs modèles théoriques ou heuristiques, ultilisés pour représenter l'amplitude d'un signal du type RSO, ont été proposés dans la littérature et ce sont révelés être efficaces pour différentes types de classes dans le contexte des cartes d'occupation des sols, rendant ainsi difficile le choix d'une seule densité de probabilité paramétrique. Dans ce rapport de recherche, un algorithme d'estimation innovant est proposé, se fondant sur un modèle de mélange fini pour la densité de probabilité de l'amplitude, les diverses composantes du mélange appartenant à un dictionnaire specifique. La mèthode proposée dans ce rapport intégre, de fa on automatique, les procédures de sélection d'un modèle optimal pour chaque composante, d'estimation de paramètres et d'optimisation du nombre de composantes, en combinant un algorithme EM stochastique et la méthode des logs-cumulants pour l'estimation de la densité de probabilité paramètrique. Des resultats expérimentaux sur plusieurs images RSO réelles sont présentés, montrant ainsi que la mèthode proposée est suffisamment précise pour modéliser les statistiques du signal d'amplitude radar de type RSO. 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 the pixel intensities. In the current research report, we address the problem of parametric probability density function (PDF) estimation in the context of Synthetic Aperture Radar (SAR) amplitude data analysis. Specifically, several theoretical and heuristic models for the PDFs of SAR data have been proposed in the literature, and have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal SAR parametric PDF a hard task. In thia report, an innovative estimation algorithm is proposed, which addresses this problem by adopting a finite mixture model (FMM) for the amplitude PDF, with mixture components belonging to a given dictionary of SAR-specific PDFs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components, by combining the Stochastic Expectation Maximization (SEM) iterative methodology and the recently proposed «method-of-log-cumulants» (MoLC) for parametric PDF estimation for non-negative random variables. Experimental results on several real SAR images are presented, showing the proposed method is accurately modelling the statistics of SAR amplitude data.

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