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Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric

Vialard, François-Xavier (2018), Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric. https://basepub.dauphine.fr/handle/123456789/17942

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01682108
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
10
Metadata
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Author(s)
Vialard, François-Xavier
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a Sobolev space of higher-order than the order of the metric in order to gain compactness. It provides the theoretical guarantee of existence of minimizers which is compulsory for numerical simulations.
Subjects / Keywords
Riemannian splines; diffeomorphism groups; right-invariant metric