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Modèles 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 arespecifically interested in the case of angiographic images. The vessels are surrounded by noise and thenthe question is to segment precisely the blood network. The theoretical framework of our work is thecalculus of variations and we focus on the Mumford-Shah energy. Initially, this model is adapted to thedetection of volumetric structures extended in all directions of the image. The aim of this study is to buildan energy that favors sets which are extended in one direction, which is the case of fine tubes. Then, weintroduce a new unknown, a Riemannian metric, which captures the geometric structure at each point ofthe image and we give a new formulation of the Mumford-Shah energy adapted to this metric. Thecomplete analysis of this model is done: we prove that the associated problem of minimization is wellposed and we introduce an approximation by gamma-convergence more suitable for numerics. Eventually,we propose numerical experimentations adapted to this approximation.
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Submitted on : Thursday, September 8, 2016 - 10:10:08 AM
Last modification on : Thursday, March 5, 2020 - 6:49:31 PM
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David Vicente. Modèles de Mumford-Shah pour la détection de structures fines en image. Mathématiques générales [math.GM]. Université d'Orléans, 2015. Français. ⟨NNT : 2015ORLE2055⟩. ⟨tel-01362065⟩



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