Apport des statistiques spatiales à l'élaboration de critères d'homogénéité et à l'inférence en analyse de textures. Application à la caractérisation de matériaux.

Abstract : This thesis deals with statistical inference in the context of spatial data, considering a single image from a larger scene. We propose a practical framework to assess the representativeness of the sample image, and to compute the estimation variance of the empirical mean and variance of a textured image. The first chapter is dedicated to explicitly formulate the problem in statistical terms.
In the second part, two parametric methods aiming at computing the estimation variance are proposed, and the relationships between both methods are pointed out. However, parametric methods suffer from difficulty in proposing a realistic model.
The third part presents a non-parametric framework for computing the estimation variance, based on block subsampling. The results from this method are analyzed in the general Wold decomposition scheme for stationary 2-D processes. This analysis allows us to purpose objective homogeneity criteria for textural parameters, which is necessary for statistical inference.
Those criteria are finally applied in an industrial context of image analysis based characterization of composite materials.
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Submitted on : Friday, August 24, 2007 - 11:49:13 AM
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Rémi Blanc. Apport des statistiques spatiales à l'élaboration de critères d'homogénéité et à l'inférence en analyse de textures. Application à la caractérisation de matériaux.. Traitement du signal et de l'image [eess.SP]. Université Sciences et Technologies - Bordeaux I, 2007. Français. ⟨tel-00168074⟩

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