Constrained Diffeomorphic Shape Evolution |
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Authors: | Laurent Younes |
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Affiliation: | 1.Center for Imaging Science and Department of Applied Mathematics and Statistics,Johns Hopkins University,Baltimore,USA |
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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. |
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