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Publications about Generalised Gaussians
Result of the query in the list of publications :
Article |
1 - 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 |
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{1429-1442}, |
| url |
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{hhttp://dx.doi.org/10.1109/TIP.2006.871124}, |
| pdf |
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{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. |
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2 Technical and Research Reports |
1 - 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 |
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{5153}, |
| address |
= |
{France}, |
| url |
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{http://www.inria.fr/rrrt/rr-5153.html}, |
| pdf |
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{ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5153.pdf}, |
| ps |
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{ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-5153.ps.gz}, |
| 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. |
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2 - Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification.
G. Aubert and L. Blanc-Féraud and R. March. Research Report 4560, Inria, France, September 2002.
Keywords : Generalised Gaussians, Classification, Regularization.
@TECHREPORT{4560,
|
| author |
= |
{Aubert, G. and Blanc-Féraud, L. and March, R.}, |
| title |
= |
{Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification}, |
| year |
= |
{2002}, |
| month |
= |
{September}, |
| institution |
= |
{Inria}, |
| type |
= |
{Research Report}, |
| number |
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{4560}, |
| address |
= |
{France}, |
| url |
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{http://www.inria.fr/rrrt/rr-4560.html}, |
| pdf |
= |
{ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4560.pdf}, |
| ps |
= |
{ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4560.ps.gz}, |
| keyword |
= |
{Generalised Gaussians, Classification, Regularization} |
| } |
Résumé :
Ce rapport contient la justification mathématique du modèle variationnel proposé en traitement d'image pour la classification supervisée. A partir des travaux effectués en mécanique des fluides pour les transitions de phase, nous avons développé un modèle de classification par minimisation d'une suite de fonctionnelles. Le résultat est une image de classes formée de régions homogènes séparées par des contours réguliers. Ce modèle diffère de ceux utilisés en mécanique des fluides car la perturbation utilisée n'est pas quadratique mais correspond à une fonction de régularisation d'image préservant les contours. La gamma-convergence de cette nouvelle suite de fonctionnelles est prouvée. |
Abstract :
The purpose of this report is to show the theoretical soundness of a variation- al method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the gamma-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge preserving regularization term in image processing. |
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