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dc.contributor.authorMennucci, Andrea C.en_US
dc.contributor.authorYezzi, Anthonyen_US
dc.contributor.authorSundaramoorthi, Ganeshen_US
dc.date.accessioned2013-09-11T20:08:42Z
dc.date.available2013-09-11T20:08:42Z
dc.date.issued2008
dc.identifier.citationA. Mennucci, A. Yezzi, and G. Sundaramoorthi, "Properties of Sobolev-type metrics in the space of curves,” Interfaces and Free Boundaries, 10 (4), 423-445 (Oct/Nov. 2008)en_US
dc.identifier.issn1463-9963
dc.identifier.urihttp://hdl.handle.net/1853/48931
dc.description©2008 European Mathematical Societyen_US
dc.descriptionDOI: 10.4171/IFB/196en_US
dc.description.abstractWe define a manifold M where objects c ϵ M are curves, which we parameterize as c : S¹ → R ⁿ (n ≥2, S¹ is the circle). Given a curve c, we define the tangent space TcM of M at c including in it all deformations h : S¹ → R ⁿ of c. We study geometries on the manifold of curves, provided by Sobolev–type Riemannian metrics H[superscript j]. We initially present some mathematical examples to show how the metrics H[superscript j] simplify or regularize gradient flows used in Computer Vision applications. We then provide some basilar results of Hj metrics; and, for the cases j = 1, 2, we characterize the completion of the space of smooth curves; we call this completion(s) “H¹ and H² Sobolev–type Riemannian Manifolds of Curves”. As a byproduct, we prove that the Fréchet distance of curves (see [MM06b]) coincides with the distance induced by the “Finsler L H [superscript ∞] metric” defined in §2.2 in [YM04b].en_US
dc.language.isoen_USen_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectActive contoursen_US
dc.subjectVisual object trackingen_US
dc.subjectShape analysisen_US
dc.subjectFiltering in the space of curvesen_US
dc.subjectSobolev-type metricsen_US
dc.titleProperties of Sobolev-type metrics in the space of curvesen_US
dc.typeArticleen_US
dc.typePost-printen_US
dc.contributor.corporatenameScuola normale superiore (Italy)en_US
dc.contributor.corporatenameGeorgia Institute of Technology. School of Electrical and Computer Engineeringen_US
dc.contributor.corporatenameGeorgia Institute of Technology. School of Mathematicsen_US
dc.publisher.originalEuropean Mathematical Societyen_US
dc.identifier.doi10.4171/IFB/196


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