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dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorCharpiat, Guillaume
HAL ID: 6593
dc.contributor.authorNardi, Giacomo
dc.contributor.authorVialard, François-Xavier
dc.date.accessioned2017-11-22T12:46:28Z
dc.date.available2017-11-22T12:46:28Z
dc.date.issued2015
dc.identifier.issn1463-9963
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17016
dc.language.isoenen
dc.subjectCurve evolution
dc.subjectFinsler space
dc.subjectgradient flow
dc.subjectshape registration
dc.subject.ddc621.3en
dc.titlePiecewise rigid curve deformation via a Finsler steepest descent
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al. [15], to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima.We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves.
dc.relation.isversionofjnlnameInterfaces and Free Boundaries
dc.relation.isversionofjnlvol18
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages1-44
dc.relation.isversionofdoi10.4171/IFB/355
dc.relation.isversionofjnlpublisherOxford University Press
dc.subject.ddclabelTraitement du signalen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-20T15:08:43Z


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