Minimal distortion morphs generated by time-dependent vector fields |
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Authors: | Oksana Bihun Steven G Harris |
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Institution: | a Department of Mathematics and Computer Science, Concordia College, MN, United States b Department of Mathematics, University of Missouri, Columbia, MO, United States c Department of Mathematics and Computer Science, Saint Louis University, MO, United States |
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Abstract: | A morph between two Riemannian n-manifolds is an isotopy between them together with the set of all intermediate manifolds equipped with Riemannian metrics. We propose measures of the distortion produced by some classes of morphs and diffeomorphisms between two isotopic Riemannian n-manifolds and, with respect to these classes, prove the existence of minimal distortion morphs and diffeomorphisms. In particular, we consider the class of time-dependent vector fields (on an open subset Ω of Rn+1 in which the manifolds are embedded) that generate morphs between two manifolds M and N via an evolution equation, define the bending and the morphing distortion energies for these morphs, and prove the existence of minimizers of the corresponding functionals in the set of time-dependent vector fields that generate morphs between M and N and are L2 functions from 0,1] to the Sobolev space . |
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Keywords: | Minimal distortion Morph Optimization Time-dependent vector field |
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