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Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierTechnion - Israel Institute of Technology [Haifa]
dc.contributor.authorGILBOA, Guy
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
dc.date.accessioned2024-04-04T03:09:45Z
dc.date.available2024-04-04T03:09:45Z
dc.date.issued2018
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193632
dc.description.abstractEnNonlinear 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.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.title.enTheoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals
dc.typeArticle de revue
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.description.sponsorshipEuropeNonlocal Methods for Arbitrary Data Sources
bordeaux.journalSIAM Journal on Imaging Sciences
bordeaux.page1416–1440
bordeaux.volume11
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01563922
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01563922v1
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