Constrained Diffeomorphic Shape Evolution
Tóm tắt
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.
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