Modèle de Mumford-Shah pour la détection de structures fines en image

Abstract : This thesis is a contribution to the fine tubular structures detection problem in a 2-D or 3-D image. We are specifically interested in the case of angiographic images. The vessels are surrounded by noise and then the question is to segment precisely the blood network. The theoretical framework of our work is the calculus of variations and we focus on the Mumford-Shah energy. Initially, this model is adapted to the detection of volumetric structures extended in all directions of the image. The aim of this study is to build an energy that favors sets which are extended in one direction, which is the case of fine tubes. We then introduce a new unknown, a Riemannian metric, which captures the geometric structure at each point of the image and we give a new formulation of the Mumford-Shah energy adapted to this metric. The complete analysis of this model is done: we prove that the associated minimizing problem is well posed and we introduce an approximation by gamma-convergence more suitable for digital implementation. Finally, we propose numerical experimentations adapted to this approximation.
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Submitted on : Thursday, November 19, 2015 - 4:57:40 PM
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David Vicente. Modèle de Mumford-Shah pour la détection de structures fines en image. Optimisation et contrôle [math.OC]. Universite d'Orleans, 2015. Français. ⟨tel-01231219⟩

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