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Algorithmes rapides d'optimisation convexe. Applications à la reconstruction d'images et à la détection de changements.

Pierre Weiss 1
1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : This PhD contains contributions in numerical analysis and in computer vision. In the first part, we focus on the fast resolution, using first order methods, of convex optimization problems. Those problems appear naturally in many image processing tasks like image reconstruction, compressed sensing or texture+cartoon decompositions. They are generally non differentiable or ill-conditioned. We show that they can be solved very efficiently using fine properties of the functions to be minimized. We analyze in a systematic way their convergence rate using recent results due to Y. Nesterov. To our knowledge, the proposed methods correspond to the state of the art of the first order methods. In the second part, we focus on the problem of change detection between two remotely sensed images taken from the same location at two different times. One of the main difficulty to solve this problem is the differences in the illumination conditions between the two shots. This leads us to study the level line illumination invariance. We completely characterize the 3D scenes which produce invariant level lines. We show that they correspond quite well to urban scenes. Then we propose a variational framework and a simple change detection algorithm which gives satisfying results both on synthetic OpenGL scenes and real Quickbird images.
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Submitted on : Wednesday, December 31, 2008 - 5:21:50 AM
Last modification on : Wednesday, October 14, 2020 - 4:24:05 AM
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Pierre Weiss. Algorithmes rapides d'optimisation convexe. Applications à la reconstruction d'images et à la détection de changements.. Mathématiques [math]. Université Nice Sophia Antipolis, 2008. Français. ⟨tel-00349452⟩

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