The Euler-Poincare theory of Metamorphosis

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dc.creatorHolm, Darryl D.
dc.creatorTrouve, Alain
dc.creatorYounes, Laurent
dc.date2008-06-04
dc.date.accessioned2026-07-07T09:44:18Z
dc.date.available2026-07-07T09:44:18Z
dc.descriptionIn the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show that the metamorphosis equations contain the equations for a perfect complex fluid \cite{Ho2002}. This result connects the ideas underlying the process of metamorphosis in image matching to the physical concept of order parameter in the theory of complex fluids. After developing the general theory, we reinterpret various examples, including point set, image and density metamorphosis. We finally discuss the issue of matching measures with metamorphosis, for which we provide existence theorems for the initial and boundary value problems.
dc.identifierhttps://arxiv.org/abs/0806.0870
dc.identifierhttp://arxiv.org/abs/0806.0870
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162826
dc.subjectComputer Vision and Pattern Recognition
dc.subjectChaotic Dynamics
dc.titleThe Euler-Poincare theory of Metamorphosis
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