Contributions Méthodologiques Et Appliquéesà La Méthode Des Modèles Déformables Methodological and Applied Contributions to the Deformable Models Framework

Deformable models constitute a flexible framework to address various shape reconstruction problems in image processing. They have been initially proposed for the purpose of image segmentation, but they have also proven successful in many other contexts in computer vision and in medical imaging, including region tracking, stereovision, shape from shading and shape from unstructured point sets. The key elements of this framework are the design of an energy functional, the choice of a minimization procedure and of a geometric representation. In this thesis, we tackle these three elements, with the objective of increasing the applicability and efficiency of deformable models. With regard to the geometric representation, we overcome the loss of the point correspondence and the inability to control topology changes with the level set method. We propose two associated applications in the field of medical imaging: the generation of unfolded area preserving representations of the cerebral cortex, and the segmentation of several head tissues from anatomical magnetic resonance images. With regard to the minimization procedure, we show that the robustness to local minima can be improved by substituting a spatially coherent minimizing flow to a traditional gradient descent. Finally, with regard to the design of the energy functional, we propose a novel modeling of multi-view stereovision and scene flow estimation with deformable models, relying on a global image-based matching score.