A Metric on Shape Space with Explicit Geodesics

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dc.creatorMichor, Peter W.
dc.creatorMumford, David
dc.creatorShah, Jayant
dc.creatorYounes, Laurent
dc.date2007-06-28
dc.date2008-05-05
dc.date.accessioned2026-07-07T09:36:32Z
dc.date.available2026-07-07T09:36:32Z
dc.descriptionThis paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being associated to specific qualifications of the space of curves (closed-open, modulo rotation etc...) Using these isometries, we are able to explicitely describe the geodesics, first in the parametric case, then by modding out the paremetrization and considering horizontal vectors. We also compute the sectional curvature for these spaces, and show, in particular, that the space of closed curves modulo rotation and change of parameter has positive curvature. Experimental results that explicitly compute minimizing geodesics between two closed curves are finally provided
dc.description31 pages, some typos corrected
dc.identifierhttps://arxiv.org/abs/0706.4299
dc.identifierhttp://arxiv.org/abs/0706.4299
dc.identifierRend. Lincei Mat. Appl. 9 (2008) 25-57
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160157
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject58B20, 58D15, 58E12
dc.titleA Metric on Shape Space with Explicit Geodesics
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