Méthodes proximales convexes pour la minimisation des Phi-divergences : applications à la stéréo vision

Doctoral thesis English OPEN
El Gheche, Mireille;
(2014)
  • Publisher: HAL CCSD
  • Subject: Divergence | Optimisation | Proximal algorithms | Optimization | Disparity | Disparité | Convexe | [MATH]Mathematics [math] | Convex | Multi-Views | Multi-Vues | Algorithmes proximaux

Convex optimization aims at searching for the minimum of a convex function over a convex set. While the theory of convex optimization has been largely explored for about a century, several related developments have stimulated a new interest in the topic. The first one i... View more
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    2 Convex optimization background 9 2.1 inverse problems . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Data delity and prior information . . . . . . . . . . . 12 2.2 Algorithms in convex optimization . . . . . . . . . . . . . . . 15 2.2.0.1 Primal algorithms . . . . . . . . . . . . . . . 18 2.2.0.2 Primal-dual algorithms . . . . . . . . . . . . 20 2.3 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3 A parallel proximal splitting method for disparity estimation from multicomponent images under illumination variation 27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 Related work . . . . . . . . . . . . . . . . . . . . . . . 32 3.1.2 Chapter outline . . . . . . . . . . . . . . . . . . . . . . 34 3.2 Stereo matching model . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Problem formulation . . . . . . . . . . . . . . . . . . . 35 3.2.2 Introducing prior information . . . . . . . . . . . . . . 37 3.2.2.1 Constraints on the disparity . . . . . . . . . 38 3.2.2.2 Constraints on the illumination eld . . . . . 39 3.2.2.3 Resulting constraints applied to vector w . . 40 3.3 Proximal approaches for convex optimization . . . . . . . . . 40

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