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Apprentissage statistique, variétés de formes et applications à la segmentation d'images

Abstract : Image segmentation with shape priors has received a lot of attention over the past few years. Most existing work focuses on a linearized shape space with small deformation modes around a mean shape, which is only relevant when considering similar shapes. In this thesis, we introduce a new framework that can handle more general shape priors. We model a category of shapes as a finite dimensional manifold, the shape prior manifold, which we analyze from the shape samples using dimensionality reduction techniques such as diffusion maps. An embedding function is then learned from the manifold. Unfortunately, this model does not provide an explicit projection operator onto the underlying shape manifold, and therefore, our work tackles this problem. Our solution is threefold. First, we propose different solutions to the out-of-sample problem and define three attracting forces directed towards the manifold. These forces can be used as projection operators onto the manifold: 1. Projection towards the closest point 2. Projection with the same embedding 3. Projection at constant embedding Next, we introduce a shape prior term for the active contours/regions framework through a non-linear energy term designed to attract shapes towards the manifold. Finally, we describe a variational framework for manifold denoising. Results with real objects such as car silhouettes or anatomical structures show the potential of our method.
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Contributor : Ecole Des Ponts Paristech <>
Submitted on : Friday, July 18, 2008 - 8:00:00 AM
Last modification on : Wednesday, March 23, 2011 - 10:43:53 AM
Long-term archiving on: : Friday, September 10, 2010 - 12:39:21 PM


  • HAL Id : pastel-00004040, version 1



Patrick Etyngier. Apprentissage statistique, variétés de formes et applications à la segmentation d'images. Mathématiques [math]. Ecole des Ponts ParisTech, 2008. Français. ⟨pastel-00004040⟩



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