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dc.contributor.authorChambolle, Antonin
dc.date.accessioned2015-01-22T09:05:40Z
dc.date.available2015-01-22T09:05:40Z
dc.date.issued1995
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14585
dc.language.isoenen
dc.subjecttheory and algorithms for image segmentationen
dc.subjectvariational problemsen
dc.subjectspecial bounded variation functionsen
dc.subjectΓ-convergenceen
dc.subjectHausdorff measuresen
dc.subject.ddc519en
dc.titleImage Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we discuss the links between Mumford and Shah’s variational problem for (signal and) image segmentation, based on an energy functional of a continuous grey-level function, and the numerical algorithms proposed to solve it. These numerical approaches are based on a discrete functional. We recall that, in one dimension, this discrete functional is asymptotically equivalent to the continuous functional. This can be summarized in a $\Gamma $-convergence result. We show that the same result holds in dimension two, provided that the continuous energy is adapted to the anisotropy of the discrete approaches. We display a few experimental results in dimensions one and two.en
dc.relation.isversionofjnlnameSIAM Journal on Applied Mathematics
dc.relation.isversionofjnlvol55en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate1995
dc.relation.isversionofjnlpages827-863en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/S0036139993257132en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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