Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | AUJOL, Jean-François | |
hal.structure.identifier | Technion - Israel Institute of Technology [Haifa] | |
dc.contributor.author | GILBOA, Guy | |
hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | PAPADAKIS, Nicolas | |
dc.date.accessioned | 2024-04-04T03:09:45Z | |
dc.date.available | 2024-04-04T03:09:45Z | |
dc.date.issued | 2018 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193632 | |
dc.description.abstractEn | 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. | |
dc.language.iso | en | |
dc.publisher | Society for Industrial and Applied Mathematics | |
dc.title.en | Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals | |
dc.type | Article de revue | |
dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
dc.description.sponsorshipEurope | Nonlocal Methods for Arbitrary Data Sources | |
bordeaux.journal | SIAM Journal on Imaging Sciences | |
bordeaux.page | 1416–1440 | |
bordeaux.volume | 11 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 2 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-01563922 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01563922v1 | |
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