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dc.contributor.advisorCelledoni, Elenanb_NO
dc.contributor.authorFonn, Eivindnb_NO
dc.date.accessioned2014-12-19T13:58:05Z
dc.date.available2014-12-19T13:58:05Z
dc.date.created2010-09-04nb_NO
dc.date.issued2009nb_NO
dc.identifier348795nb_NO
dc.identifierntnudaim:4541nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/258493
dc.description.abstractShape analysis and recognition is a field ripe with creative solutions and innovative algorithms. We give a quick introduction to several different approaches, before basing our work on a representation introduced by Klassen et. al., considering shapes as equivalence classes of closed curves in the plane under reparametrization, and invariant under translation, rotation and scaling. We extend this to a definition for nonclosed curves, and prove a number of results, mostly concerning under which conditions on these curves the set of shapes become manifolds. We then motivate the study of geodesics on these manifolds as a means to compute a shape metric, and present two methods for computing such geodesics: the shooting method from Klassen et. al. and the ``direct'' method, new to this paper. Some numerical experiments are performed, which indicate that the direct method performs better for realistically chosen parameters, albeit not asymptotically.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for matematiske fagnb_NO
dc.subjectntnudaimno_NO
dc.subjectSIF3 fysikk og matematikkno_NO
dc.subjectIndustriell matematikkno_NO
dc.titleComputing Metrics on Riemannian Shape Manifolds: Geometric shape analysis made practicalnb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber40nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fagnb_NO


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