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PATCH REDUNDANCY IN IMAGES: A STATISTICAL TESTING FRAMEWORK AND SOME APPLICATIONS

hal.structure.identifierCentre de Mathématiques et de Leurs Applications [CMLA]
dc.contributor.authorDE BORTOLI, Valentin
hal.structure.identifierCentre de Mathématiques et de Leurs Applications [CMLA]
dc.contributor.authorDESOLNEUX, Agnès
hal.structure.identifierInstitut Denis Poisson [IDP]
dc.contributor.authorGALERNE, Bruno
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLECLAIRE, Arthur
dc.date.accessioned2024-04-04T03:01:14Z
dc.date.available2024-04-04T03:01:14Z
dc.date.issued2019
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192883
dc.description.abstractEnIn this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally and thus we give some examples of functions (auto-similarity and template similarity) which, given one or two images, computes a similarity measurement between patches. Two patches are said to be similar if the similarity measurement is small enough. To derive a criterion for taking a decision on the similarity between two patches we present an a contrario model. Namely, two patches are said to be similar if the associated similarity measurement is unlikely to happen in a background model. Choosing Gaussian random fields as background models we derive non-asymptotic expressions for the probability distribution function of similarity measurements. We introduce a fast algorithm in order to assess redundancy in natural images and present applications in denoising, periodicity analysis and texture ranking.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enpatch
dc.subject.enredundancy
dc.subject.enstatistical framework
dc.subject.ena contrario method
dc.subject.enimage denoising
dc.subject.entexture
dc.subject.enperiodicity analysis
dc.title.enPATCH REDUNDANCY IN IMAGES: A STATISTICAL TESTING FRAMEWORK AND SOME APPLICATIONS
dc.typeArticle de revue
dc.identifier.doi10.1137/18M1228219
dc.subject.halStatistiques [stat]
dc.subject.halInformatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV]
dc.subject.halInformatique [cs]/Traitement des images
bordeaux.journalSIAM Journal on Imaging Sciences
bordeaux.page893-926
bordeaux.volume12
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-01931733
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01931733v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Imaging%20Sciences&rft.date=2019&rft.volume=12&rft.issue=2&rft.spage=893-926&rft.epage=893-926&rft.au=DE%20BORTOLI,%20Valentin&DESOLNEUX,%20Agn%C3%A8s&GALERNE,%20Bruno&LECLAIRE,%20Arthur&rft.genre=article


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