NDLI: Constrained Diffeomorphic Shape Evolution

Content Provider	Springer Nature Link
Author	Younes, Laurent
Copyright Year	2011
Abstract	We design optimal control strategies in spaces of diffeomorphisms and shape spaces in which the Eulerian velocities of the evolving deformations are constrained to belong to a suitably chosen finite-dimensional space, which is also following the motion. This results in a setting that provides a great flexibility in the definition of Riemannian metrics, extending previous approaches in which shape spaces are built as homogeneous spaces under the action of the diffeomorphism group equipped with a right-invariant metric. We provide specific instances of this general setting, and describe in detail the resulting numerical algorithms, with experimental illustrations in the case of plane curves.
Ending Page	325
Page Count	31
Starting Page	295
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	3
Volume Number	12
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-12-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Groups of diffeomorphisms and homeomorphisms as manifolds Shape analysis Economics general Linear and Multilinear Algebras, Matrix Theory Subriemannian geometry Groups of diffeomorphisms Applications of optimal control and differential games Optimal control Numerical Analysis Computer Science Optimization of shapes other than minimal surfaces Math Applications in Computer Science Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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