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

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SplinesConferenceArticleNew.pdf (268.4Kb)
Date
2018
Publishing date
01-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01682108
Dewey
Analyse
Sujet
Riemannian splines; diffeomorphism groups; right-invariant metric
URI
https://basepub.dauphine.fr/handle/123456789/17942
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Vialard, François-Xavier
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
10
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.

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