Publications of S.B. Serpico

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• 5 Articles
• 9 Conference articles
• 5 Technical and Research Reports

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5 Articles

1 - Classification of Very High Resolution SAR Images of Urban Areas Using Copulas and Texture in a Hierarchical Markov Random Field Model. A. Voisin and V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. IEEE Geoscience and Remote Sensing Letters, 2012. Note : to appear in 2013 Keywords : Hierarchical Markov random fields (MRFs) , Supervised classification, synthetic aperture radar (SAR), Textural features, urban areas, wavelets. @ARTICLE{Voisin13, 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 Using Copulas and Texture in a Hierarchical Markov Random Field Model}, year = {2012}, journal = {IEEE Geoscience and Remote Sensing Letters}, note = {to appear in 2013}, url = {http://dx.doi.org/10.1109/LGRS.2012.2193869}, keyword = {Hierarchical Markov random fields (MRFs) , Supervised classification, synthetic aperture radar (SAR), Textural features, urban areas, wavelets} }

2 - Supervised High Resolution Dual Polarization SAR Image Classification by Finite Mixtures and Copulas. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. IEEE Journal of Selected Topics in Signal Processing, 5(3): pages 554-566, June 2011. Keywords : Polarimetric synthetic aperture radar, Supervised classification, probability density function (pdf), dictionary-based pdf estimation, Markov random field, copula. Copyright : IEEE @ARTICLE{krylovJSTSP2011, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Supervised High Resolution Dual Polarization SAR Image Classification by Finite Mixtures and Copulas}, year = {2011}, month = {June}, journal = { IEEE Journal of Selected Topics in Signal Processing}, volume = {5}, number = {3}, pages = {554-566}, url = {http://dx.doi.org/10.1109/JSTSP.2010.2103925}, pdf = {http://hal.archives-ouvertes.fr/inria-00562326/en/}, keyword = {Polarimetric synthetic aperture radar, Supervised classification, probability density function (pdf), dictionary-based pdf estimation, Markov random field, copula} } Abstract : In this paper a novel supervised classification approach is proposed for high resolution dual polarization (dualpol) amplitude satellite synthetic aperture radar (SAR) images. A novel probability density function (pdf) model of the dual-pol SAR data is developed that combines finite mixture modeling for marginal probability density functions estimation and copulas for multivariate distribution modeling. The finite mixture modeling is performed via a recently proposed SAR-specific dictionarybased stochastic expectation maximization approach to SAR amplitude pdf estimation. For modeling the joint distribution of dual-pol data the statistical concept of copulas is employed, and a novel copula-selection dictionary-based method is proposed. In order to take into account the contextual information, the developed joint pdf model is combined with a Markov random field approach for Bayesian image classification. The accuracy of the developed dual-pol supervised classification approach is validated and compared with benchmark approaches on two high resolution dual-pol TerraSAR-X scenes, acquired during an epidemiological study. A corresponding single-channel version of the classification algorithm is also developed and validated on a single polarization COSMO-SkyMed scene.

3 - 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.

4 - SAR amplitude probability density function estimation based on a generalized Gaussian model. G. Moser and J. Zerubia and S.B. Serpico. IEEE Trans. on Image Processing, 15(6): pages 1429-1442, June 2006. Keywords : SAR Images, Generalised Gaussians, Mellin transform. Copyright : IEEE @ARTICLE{moser_ieeeip05, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {SAR amplitude probability density function estimation based on a generalized Gaussian model}, year = {2006}, month = {June}, journal = {IEEE Trans. on Image Processing}, volume = {15}, number = {6}, pages = {1429-1442}, url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1632197}, pdf = {http://hal.archives-ouvertes.fr/inria-00561372/en/}, keyword = {SAR Images, Generalised Gaussians, Mellin transform} } Abstract : In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “method-of-log-cumulants” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.

5 - 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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9 Conference articles

1 - Change detection with synthetic aperture radar images by Wilcoxon statistic likelihood ratio test. V. Krylov and G. Moser and A. Voisin and S.B. Serpico and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Orlando, United States, October 2012. @INPROCEEDINGS{ICIP12, author = {Krylov, V. and Moser, G. and Voisin, A. and Serpico, S.B. and Zerubia, J.}, title = {Change detection with synthetic aperture radar images by Wilcoxon statistic likelihood ratio test}, year = {2012}, month = {October}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Orlando, United States}, url = {http://hal.inria.fr/hal-00724284}, keyword = {} }

2 - Classification of multi-sensor remote sensing images using an adaptive hierarchical Markovian model. A. Voisin and V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. In EURASIP, Bucarest, Romania, August 2012. @INPROCEEDINGS{EURASIP12, author = {Voisin, A. and Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Classification of multi-sensor remote sensing images using an adaptive hierarchical Markovian model}, year = {2012}, month = {August}, booktitle = {EURASIP}, address = {Bucarest, Romania}, url = {http://hal.inria.fr/hal-00723286}, keyword = {} }

3 - Multichannel hierarchical image classification using multivariate copulas. A. Voisin and V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. In IS&T/SPIE Electronic Imaging – Computational Imaging X, San Francisco, United States, January 2012. @INPROCEEDINGS{SPIE12, author = {Voisin, A. and Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Multichannel hierarchical image classification using multivariate copulas}, year = {2012}, month = {January}, booktitle = {IS&T/SPIE Electronic Imaging – Computational Imaging X}, address = {San Francisco, United States}, url = {http://dx.doi.org/10.1117/12.917298}, keyword = {} }

4 - Classification of very high resolution SAR images of urban areas by dictionary-based mixture models, copulas and Markov random fields using textural features. A. Voisin and G. Moser and V. Krylov and S.B. Serpico and J. Zerubia. In Proc. of SPIE (SPIE Symposium on Remote Sensing 2010), Vol. 7830, Toulouse, France, September 2010. Keywords : SAR Images, Supervised classification, Urban areas, Textural features, Copulas, Markov Random Fields. Copyright : SPIE @INPROCEEDINGS{7830-23, author = {Voisin, A. and Moser, G. and Krylov, V. and Serpico, S.B. and Zerubia, J.}, title = {Classification of very high resolution SAR images of urban areas by dictionary-based mixture models, copulas and Markov random fields using textural features}, year = {2010}, month = {September}, booktitle = {Proc. of SPIE (SPIE Symposium on Remote Sensing 2010)}, volume = {7830}, address = {Toulouse, France}, url = {http://hal.archives-ouvertes.fr/inria-00516333/en}, pdf = {http://hal.archives-ouvertes.fr/docs/00/51/63/33/PDF/Classification_of_VHR_SAR_SPIE_sept2010_Toulouse_Voisin.pdf}, keyword = {SAR Images, Supervised classification, Urban areas, Textural features, Copulas, Markov Random Fields} } Abstract : This paper addresses the problem of the classification of very high resolution SAR amplitude images of urban areas. The proposed supervised method combines a finite mixture technique to estimate class-conditional probability density functions, Bayesian classification, and Markov random fields (MRFs). Textural features, such as those extracted by the grey-level co-occurrency method, are also integrated in the technique, as they allow improving the discrimination of urban areas. Copula theory is applied to estimate bivariate joint class-conditional statistics, merging the marginal distributions of both textural and SAR amplitude features. The resulting joint distribution estimates are plugged into a hidden MRF model, endowed with a modified Metropolis dynamics scheme for energy minimization. Experimental results with COSMO-SkyMed images point out the accuracy of the proposed method, also as compared with previous contextual classifiers.

5 - Multichannel SAR Image Classification by Finite Mixtures, Copula Theory and Markov Random Fields. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. In Proc. of Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2010), Vol. 1305, pages 319-326, Chamonix, France, July 2010. Keywords : multichannel SAR, Classification, probability density function estimation, Markov random field, copula. Copyright : AIP @INPROCEEDINGS{krylovMaxEnt10, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {Multichannel SAR Image Classification by Finite Mixtures, Copula Theory and Markov Random Fields}, year = {2010}, month = {July}, booktitle = {Proc. of Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2010)}, volume = {1305}, pages = {319-326}, address = {Chamonix, France}, url = {http://hal.archives-ouvertes.fr/inria-00495557/en/}, pdf = {http://hal.archives-ouvertes.fr/docs/00/49/55/57/PDF/krylov_MaxEnt2010.pdf}, keyword = {multichannel SAR, Classification, probability density function estimation, Markov random field, copula} } Abstract : The last decades have witnessed an intensive development and a significant increase of interest to remote sensing, and, in particular, to synthetic aperture radar (SAR) imagery. In this paper we develop a supervised classification approach for medium and high resolution multichannel SAR amplitude images. The proposed technique combines finite mixture modeling for probability density function estimation, copulas for multivariate distribution modeling and the Markov random field approach to Bayesian image classification. The finite mixture modeling is done via a recently proposed SAR-specific dictionary-based stochastic expectation maximization approach to class-conditional amplitude probability density function estimation, which is applied separately to all the SAR channels. For modeling the class-conditional joint distributions of multichannel data the statistical concept of copulas is employed, and a dictionary-based copula selection method is proposed. Finally, the Markov random field approach enables to take into account the contextual information and to gain robustness against the inherent noise-like phenomenon of SAR known as speckle. The designed method is an extension and a generalization to multichannel SAR of a recently developed single-channel and Dual-pol SAR image classification technique. The accuracy of the developed multichannel SAR classification approach is validated on several multichannel Quad-pol RADARSAT-2 images and compared to benchmark classification techniques.

6 - 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.

7 - 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.

8 - SAR amplitude probability density function estimation based on a generalized Gaussian scattering model. G. Moser and J. Zerubia and S.B. Serpico. In Proc. SPIE Symposium on Remote Sensing, Maspalomas, Gran Canaria, Spain, September 2004. @INPROCEEDINGS{moser2004a, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {SAR amplitude probability density function estimation based on a generalized Gaussian scattering model}, year = {2004}, month = {September}, booktitle = {Proc. SPIE Symposium on Remote Sensing}, address = {Maspalomas, Gran Canaria, Spain}, url = {http://dx.doi.org/10.1117/12.567853}, keyword = {} }

9 - Finite mixture models and stochastic EM for SAR amplitude probability density function estimation based on a dictionary of parametric families. G. Moser and J. Zerubia and S.B. Serpico. In Proc. IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Anchorage , USA, September 2004. @INPROCEEDINGS{moser2004b, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {Finite mixture models and stochastic EM for SAR amplitude probability density function estimation based on a dictionary of parametric families}, year = {2004}, month = {September}, booktitle = {Proc. IEEE International Geoscience and Remote Sensing Symposium (IGARSS)}, address = {Anchorage , USA}, url = {http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1368708}, keyword = {} }

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5 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 - On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation. V. Krylov and G. Moser and S.B. Serpico and J. Zerubia. Research Report 7666, INRIA, July 2011. Keywords : Probability density function, Parameter estimation, generalized gamma distribution, K-distribution, Synthetic Aperture Radar (SAR), Classification. Copyright : INRIA/ARIANA @TECHREPORT{RR-7666, author = {Krylov, V. and Moser, G. and Serpico, S.B. and Zerubia, J.}, title = {On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation}, year = {2011}, month = {July}, institution = {INRIA}, type = {Research Report}, number = {7666}, url = {http://hal.archives-ouvertes.fr/inria-00605274/en/}, keyword = {Probability density function, Parameter estimation, generalized gamma distribution, K-distribution, Synthetic Aperture Radar (SAR), Classification} } Résumé : L'estimation de paramètres de fonctions de densité de probabilité est une étape majeure dans le domaine du traitement statistique du signal et des images. Dans ce rapport, nous étudions les propriétés et les limites de l'estimation de paramètres par la méthode des cumulants logarithmiques (MoLC), qui est une alternative à la fois au maximum de vraisemblance (MV) classique et à la méthode des moments. Nous dérivons la condition générale suffisante de consistance forte de l'estimation par la méthode MoLC, qui représente une propriété asymptotique importante de tout estimateur statistique. Grâce à cela, nous démontrons la consistance forte de l'estimation par la méthode MoLC pour une sélection de familles de distributions particulièrement adaptées (mais non restreintes) au traitement d'images acquises par radar à synthèse d'ouverture (RSO). Nous dérivons ensuite les conditions analytiques d'applicabilité de la méthode MoLC à des échantillons générés qui suivent les lois des différentes familles de distribution de notre sélection. Enfin, nous testons la méthode MoLC sur des données synthétiques et réelles afin de comparer les différentes propriétés inhérentes aux différents types d'images, l'applicabilité de la méthode et les effets d'un nombre restreint d'échantillons. Nous avons, en particulier, considéré les distributions gamma généralisée et K. Comme exemple d'application, nous avons réalisé des classifications supervisées d'images médicales à ultrason ainsi que d'images de télédétection acquises par des capteurs RSO. Les résultats obtenus montrent que la méthode MoLC est une bonne alternative à la méthode des moments, bien qu'elle contienne certaines limitations. Elle est particulièrement utile lorsqu'une approche directe par MV n'est pas possible. Abstract : Parameter estimation of probability density functions is one of the major steps in the mainframe of statistical image and signal processing. In this report we explore the properties and limitations of the recently proposed method of logarithmic cumulants (MoLC) parameter estimation approach which is an alternative to the classical maximum likelihood (ML) and method of moments (MoM) approaches. We derive the general sufficient condition of strong consistency of MoLC estimates which represents an important asymptotic property of any statistical estimator. With its help we demonstrate the strong consistency of MoLC estimates for a selection of widely used distribution families originating (but not restricted to) synthetic aperture radar (SAR) image processing. We then derive the analytical conditions of applicability of MoLC to samples generated from several distribution families in our selection. Finally, we conduct various synthetic and real data experiments to assess the comparative properties, applicability and small sample performance of MoLC notably for the generalized gamma and K family of distributions. Supervised image classification experiments are considered for medical ultrasound and remote sensing SAR imagery. The obtained results suggest MoLC to be a feasible yet not universally applicable alternative to MoM that can be considered when the direct ML approach turns out to be unfeasible.

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 - SAR Amplitude Probability Density Function Estimation based on a Generalized Gaussian Scattering Model. G. Moser and J. Zerubia and S.B. Serpico. Research Report 5153, INRIA, France, March 2004. Keywords : Synthetic Aperture Radar (SAR), Generalised Gaussians. @TECHREPORT{5153, author = {Moser, G. and Zerubia, J. and Serpico, S.B.}, title = {SAR Amplitude Probability Density Function Estimation based on a Generalized Gaussian Scattering Model}, year = {2004}, month = {March}, institution = {INRIA}, type = {Research Report}, number = {5153}, address = {France}, url = {https://hal.inria.fr/inria-00071430}, pdf = {https://hal.inria.fr/file/index/docid/71430/filename/RR-5153.pdf}, ps = {https://hal.inria.fr/docs/00/07/14/30/PS/RR-5153.ps}, keyword = {Synthetic Aperture Radar (SAR), Generalised Gaussians} } Résumé : En télédetection, un problème important est celui de développer des modèles précis pour representer les statistiques des intensités des pixels. En ce qui concerne les données du type Radar à Synthèse d'Ouverture (RSO), cette modélisation constitue un point capital pour la classification ou le débruitage d'une image, par exemple. Dans ce rapport de recherche, une nouvelle méthode d'estimation paramétrique pour les amplitudes d'images RSO est proposée. Elle tient compte de la nature physique des phénomènes de diffusion qui générent une image RSO en adoptant une modèle de gaussiennes generalisées pour les phénomènes de rétrodiffusion. Une expression, sous forme explicite, de la densité de probabilité de l'amplitude est obtenue et un algorithme spécifique d'estimation des paramètres est proposé afin de pouvoir utiliser le modèle proposé. Une mèthode récente fondée sur les «logs-cumulants» est appliquée, dérivant de l'utilisation d'une transformée de Mellin (à la place de la transformée de Fourier usuelle) dans le calcul des fonctions caractéristiques et de la généralisation des concepts de moment et de cumulant correspondante. Les estimées obtenues par la mèthode des log-cumulants pour le modèle d'amplitude fondé sur des gaussiennes généralisées se révelent être calculables numériquement et également consistantes. Dans ce rapport de recherche, l'approche paramètrique proposée est validée sur diverses images radar RSO (ERS, XSAR, ESAR et des radar aéroportés). Les résultats expérimentaux montrent que la mèthode proposée modèlise mieux la densité de probabilité de l'amplitude que beaucoup de modèles paramétriques proposés précédemment pour les phénomènes de rétrodiffusion. Abstract : In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on Synthetic Aperture Radar (SAR) data, this modelling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In the present report, an innovative parametric estimation methodology for SAR amplitude data is proposed, which takes into account the physical nature of the scattering phenomena generating a SAR image by adopting a generalized Gaussian (GG) model for the backscattering phenomena. A closed form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed «method-of-log-cumulants» (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions, and from the corresponding generalization of the concepts of moment and of cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also proved to be consistent. The proposed parametric approach is validated using several real ERS-1, XSAR, ESAR and airborne SAR images and the experimental results prove that the method models the amplitude probability density function better than several previously proposed parametric models for the backscattering phenomena.

5 - 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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