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dc.contributor.authorGay-Balmaz, François
dc.contributor.authorHolm, Darryl
dc.contributor.authorMeier, David
dc.contributor.authorRatiu, Tudor
dc.contributor.authorVialard, François-Xavier
dc.date.accessioned2011-10-05T13:46:39Z
dc.date.available2011-10-05T13:46:39Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7126
dc.language.isoenen
dc.subjectcomputational anatomyen
dc.subjectdiffeomorphic templatesen
dc.subject.ddc519en
dc.titleInvariant higher-order variational problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our approach formulates Euler-Poincaré theory in higher-order tangent spaces on Lie groups. In particular, we develop the Euler-Poincaré formalism for higher-order variational problems that are invariant under Lie group transformations. The theory is then applied to higher-order template matching and the corresponding curves on the Lie group of transformations are shown to satisfy higher-order Euler-Poincaré equations. The example of SO(3) for template matching on the sphere is presented explicitly. Various cotangent bundle momentum maps emerge naturally that help organize the formulas. We also present Hamiltonian and Hamilton-Ostrogradsky Lie-Poisson formulations of the higher-order Euler-Poincaré theory for applications on the Hamiltonian side.en
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol309
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages413-458
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00220-011-1313-y
dc.identifier.urlsitehttp://arxiv.org/abs/1012.5060v1en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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