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Vision 3D multi-images : contribution à l'obtention de solutions globales par optimisation polynomiale et théorie des moments

Florian Bugarin 1, 2
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The overall objective of this thesis is to apply a polynomial optimization method, based on moments theory, on some vision problems. These problems are often nonconvex and they are classically solved using local optimization methods. Without additional hypothesis, these techniques don't converge to the global minimum and need to provide an initial estimate close to the exact solution. Global optimization methods overcome this drawback. Moreover, the polynomial optimization based on moments theory could take into account particular constraints. In this thesis, we extend this method to the problems of minimizing a sum of many rational functions. In addition, under particular assumptions of "sparsity", we show that it is possible to deal with a large number of variables while maintaining reasonable computation times. Finally, we apply these methods to particular computer vision problems: minimization of projective distortions due to image rectification process, Fundamental matrix estimation, and multi-view 3D reconstruction with and without radial distortions.
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https://tel.archives-ouvertes.fr/tel-00771425
Contributor : Florian Bugarin <>
Submitted on : Tuesday, January 8, 2013 - 4:59:25 PM
Last modification on : Thursday, February 27, 2020 - 1:12:56 AM
Document(s) archivé(s) le : Saturday, April 1, 2017 - 2:06:27 AM

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  • HAL Id : tel-00771425, version 1

Citation

Florian Bugarin. Vision 3D multi-images : contribution à l'obtention de solutions globales par optimisation polynomiale et théorie des moments. Optimisation et contrôle [math.OC]. Institut National Polytechnique de Toulouse - INPT, 2012. Français. ⟨tel-00771425⟩

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