AUJOL, Jean-François; GILBOA, Guy; PAPADAKIS, Nicolas

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AUJOL, Jean-François
Institut de Mathématiques de Bordeaux [IMB]

GILBOA, Guy
Technion - Israel Institute of Technology [Haifa]

PAPADAKIS, Nicolas
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

SIAM Journal on Imaging Sciences. 2018, vol. 11, n° 2, p. 1416–1440

Society for Industrial and Applied Mathematics

Résumé en anglais

Nonlinear eigenfunctions, induced by subgradients of one-homogeneous functionals (such as the 1-Laplacian), have shown to be instrumental in segmentation, clustering and image decomposition. We present a class of flows for finding such eigenfunctions, generalizing a method recently suggested by Nossek and Gilboa. We analyze the flows on grids and graphs in the time-continuous and time-discrete settings. For a specific type of flow within this class, we prove convergence of the numerical iterations procedure and prove existence and uniqueness of the time-continuous case. Several toy examples are provided for illustrating the theoretical results, showing how such flows can be used on images and graphs.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193632

Projet Européen

Nonlocal Methods for Arbitrary Data Sources

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251