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Publications about Probability density function
Result of the query in the list of publications :
2 Conference articles |
1 - 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 - Riemannian Analysis of Probability Density Functions with Applications in Vision.
S. Joshi and A. Srivastava and I. H. Jermyn. In Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Minneapolis, USA, June 2007.
Keywords : Probability density function, Metric, Geodesic, Reparameterization.
@INPROCEEDINGS{Joshi07,
|
| author |
= |
{Joshi, S. and Srivastava, A. and Jermyn, I. H.}, |
| title |
= |
{Riemannian Analysis of Probability Density Functions with Applications in Vision}, |
| year |
= |
{2007}, |
| month |
= |
{June}, |
| booktitle |
= |
{Proc. IEEE Computer Vision and Pattern Recognition (CVPR)}, |
| address |
= |
{Minneapolis, USA}, |
| url |
= |
{http://dx.doi.org/10.1109/CVPR.2007.383188 }, |
| pdf |
= |
{ftp://ftp-sop.inria.fr/ariana/Articles/2007_Joshi07.pdf}, |
| keyword |
= |
{Probability density function, Metric, Geodesic, Reparameterization} |
| } |
Abstract :
Applications in computer vision involve statistically analyzing an important class of constrained, non- negative functions, including probability density functions (in texture analysis), dynamic time-warping functions (in activity analysis), and re-parametrization or non-rigid registration functions (in shape analysis of curves). For this one needs to impose a Riemannian structure on the spaces formed by these functions. We propose a em spherical version of the Fisher-Rao metric that provides closed form expressions for geodesics and distances, and allows an efficient computation of statistics. We compare this metric with some previously used metrics and present an application in planar shape classification. |
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2 Technical and Research Reports |
1 - 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. |
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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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