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Multifractal analysis for multivariate data with application to remote sensing / Sébastien Combrexelle (2016)  

Public Titre : Multifractal analysis for multivariate data with application to remote sensing Type de document : Thèse/HDR Auteurs : Sébastien Combrexelle, Auteur ; Jean-Yves Tourneret, Directeur de thèse ; Steve Mclaughlin, Directeur de thèse Editeur : Toulouse : Université de Toulouse Année de publication : 2016 Importance : 211 p. Format : 21 x 30 cm Note générale : bibliographie Thèse en vue de l'obtention du Doctorat de l'Université de Toulouse, Spécialité Signal, Image, Acoustique et Optimisation Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement d'image optique [Termes IGN] analyse fractale [Termes IGN] analyse multivariée [Termes IGN] approche hiérarchique [Termes IGN] estimation bayesienne [Termes IGN] image hyperspectrale [Termes IGN] modèle statistique [Termes IGN] télédétection [Termes IGN] texture d'image [Termes IGN] transformation en ondelettes Résumé : (auteur) Texture characterization is a central element in many image processing applications. Texture analysis can be embedded in the mathematical framework of multifractal analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, the wavelet coefficients or wavelet leaders. Although successfully applied in various contexts, multifractal analysis suffers at present from two major limitations. First, the accurate estimation of multifractal parameters for image texture remains a challenge, notably for small image sizes. Second, multifractal analysis has so far been limited to the analysis of a single image, while the data available in applications are increasingly multivariate. The main goal of this thesis is to develop practical contributions to overcome these limitations. The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. This yields robust and accurate estimation procedures, effective both for small and large images. The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. This is achieved via the design of suitable priors relating the dynamical properties of the multifractal parameters of the different components composing the dataset. Different priors are investigated and compared in this thesis by means of numerical simulations conducted on synthetic multivariate multifractal images. This work is further completed by the investigation of the potential benefits of multifractal analysis and the proposed Bayesian methodology for remote sensing via the example of hyperspectral imaging. Note de contenu : Introduction 1- Multifractal analysis 2- Statistical model and univariate Bayesian estimation 3- Bayesian multifractal analysis of multivariate images Numéro de notice : 25811 Affiliation des auteurs : non IGN Thématique : IMAGERIE/MATHEMATIQUE Nature : Thèse étrangère Note de thèse : Thèse de Doctorat : Spécialité : Signal, Image, Acoustique et Optimisation : Toulouse : 2016 Organisme de stage : Institut de Recherche en Informatique de Toulouse (I.R.I.T.) En ligne : http://www.theses.fr/2016INPT0078 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95074