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

doi:10.1088/1361-6420/ab0cb2

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FELD, Tal
Department of Electrical Engineering - Technion [Haïfa] [EE-Technion]

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

GILBOA, Guy
Department of Electrical Engineering - Technion [Haïfa] [EE-Technion]

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Inverse Problems. 2019

IOP Publishing

Resumen en inglés

In this paper we examine the problem of minimizing generalized Rayleigh quotients of the form J(u)/H(u), where both J and H are absolutely one-homogeneous functionals. This can be viewed as minimizing J where the solution is constrained to be on a generalized sphere with H(u) = 1, where H is any norm or semi-norm. The solution admits a nonlinear eigenvalue problem, based on the subgradients of J and H. We examine several flows which minimize the ratio. This is done both by time-continuous flow formulations and by discrete iterations. We focus on a certain flow, which is easier to analyze theoretically, following the theory of Brezis on flows with maximal monotone operators. A comprehensive theory is established, including convergence of the flow. We then turn into a more specific case of minimizing graph total variation on the L1 sphere, which approximates the Cheeger-cut problem. Experimental results show the applicability of such algorithms for clustering and classification of images.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192814

DOI

http://dx.doi.org/10.1088/1361-6420/ab0cb2

Proyecto europeo

Nonlocal Methods for Arbitrary Data Sources

Proyecto ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251