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hal.structure.identifierEcole Nationale de l'Aviation Civile [ENAC]
dc.contributor.authorBRIGANT, Alice Le
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorARNAUDON, Marc
hal.structure.identifierThales Air Systems
dc.contributor.authorBARBARESCO, Frédéric
dc.date.accessioned2024-04-04T02:56:24Z
dc.date.available2024-04-04T02:56:24Z
dc.date.issued2016-04-03
dc.identifier.issn0302-9743
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192461
dc.description.abstractEnThis paper focuses on the study of open curves in a manifold M, and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [11] to define a reparameterization invariant metric on the space of immersions M' = Imm([0,1], M) by pullback of a metric on the tangent bundle TM' derived from the Sasaki metric. We observe that such a natural choice of Riemannian metric on TM' induces a first-order Sobolev metric on M' with an extra term involving the origins, and leads to a distance which takes into account the distance between the origins and the distance between the SRV representations of the curves. The geodesic equations for this metric are given, as well as an idea of how to compute the exponential map for observed trajectories in applications. This provides a generalized theoretical SRV framework for curves lying in a general manifold M .
dc.language.isoen
dc.publisherSpringer
dc.title.enReparameterization invariant metric on the space of curves
dc.typeArticle de revue
dc.identifier.doi10.1007/978-3-319-25040-3_16
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1507.06503
bordeaux.journalLecture Notes in Computer Science
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02488009
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02488009v1
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