Stochastic image models and texture synthesis

Abstract : This thesis is a study of stochastic image models with applications to texture synthesis. Most of the stochastic texture models under investigation are germ-grain models. In the first part of the thesis, texture synthesis algorithms relying on the shot noise model are developed. In the discrete framework, two different random processes, namely the asymptotic discrete spot noise and the random phase noise, are theoretically and experimentally studied. A fast texture synthesis algorithm relying on these random processes is then elaborated. Numerous results demonstrate that the algorithm is able to reproduce a class of real-world textures which we call micro-textures. In the continuous framework, the Gaussian convergence of shot noise models is further studied and new bounds for the rate of this convergence are established. Finally, a new algorithm for procedural texture synthesis from example relying on the recent Gabor noise model is presented. This new algorithm permits to automatically compute procedural models for real-world micro-textures. The second part of the thesis is devoted to the introduction and study of the transparent dead leaves (TDL) process, a new germ-grain model obtained by superimposing semi-transparent objects. The main result of this part shows that, when varying the transparency of the objects, the TDL process provides a family of models varying from the dead leaves model to a Gaussian random field. In the third part of the thesis, general results on random fields with bounded variation are established with an emphasis on the computation of the mean total variation of random fields. As particular cases of interest, these general results permit the computation of the mean perimeter of random sets and of the mean total variation of classical germ-grain models.
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Theses
General Mathematics [math.GM]. École normale supérieure de Cachan - ENS Cachan, 2010. English. <NNT : 2010DENS0046>


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Bruno Galerne. Stochastic image models and texture synthesis. General Mathematics [math.GM]. École normale supérieure de Cachan - ENS Cachan, 2010. English. <NNT : 2010DENS0046>. <tel-00595283>

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