Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals for Segmentation and Clustering

Abstract : 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-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 examples are provided showing how such flows can be used on images and graphs.
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Pré-publication, Document de travail
2017
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Contributeur : Nicolas Papadakis <>
Soumis le : mardi 18 juillet 2017 - 11:55:59
Dernière modification le : mercredi 19 juillet 2017 - 01:06:39

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Jean-François Aujol, Guy Gilboa, Nicolas Papadakis. Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals for Segmentation and Clustering. 2017. 〈hal-01563922〉

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