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Décompositions multi-échelles de données définies sur des graphes

Moncef Hidane 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : signals defined on general weighted graphs. This manuscript discusses three approaches that we have developed. The first approach is based on a variational and iterative process. It generalizes the structure-texture decomposition, originally proposed for images. Two versions are proposed: one is based on a quadratic prior while the other is based on a total variation prior. The study of the convergence is performed and the choice of parameters discussed in each case. We describe the application of the decompositions we get to the enhancement of details in images and 3D models. The second approach provides a multiresolution analysis of the space of signals on a given graph. This construction is based on the organization of the graph as a hierarchy of partitions. We have developed an adaptive algorithm for the construction of such hierarchies. Finally, in the third approach, we adapt the lifting scheme to signals on graphs. This adaptation raises a number of practical problems. We focused on the one hand on the subsampling step for which we adopted a greedy approach, and on the other hand on the iteration of the transform on induced subgraphs.
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  • HAL Id : tel-01081399, version 1

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Moncef Hidane. Décompositions multi-échelles de données définies sur des graphes. Traitement des images [eess.IV]. Université de Caen, 2013. Français. ⟨tel-01081399⟩

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