dc.contributor.advisor Celledoni, Elena nb_NO dc.contributor.author Fonn, Eivind nb_NO dc.date.accessioned 2014-12-19T13:58:05Z dc.date.available 2014-12-19T13:58:05Z dc.date.created 2010-09-04 nb_NO dc.date.issued 2009 nb_NO dc.identifier 348795 nb_NO dc.identifier ntnudaim:4541 nb_NO dc.identifier.uri http://hdl.handle.net/11250/258493 dc.description.abstract Shape 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.language eng nb_NO dc.publisher Institutt for matematiske fag nb_NO dc.subject ntnudaim no_NO dc.subject SIF3 fysikk og matematikk no_NO dc.subject Industriell matematikk no_NO dc.title Computing Metrics on Riemannian Shape Manifolds: Geometric shape analysis made practical nb_NO dc.type Master thesis nb_NO dc.source.pagenumber 40 nb_NO dc.contributor.department Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag nb_NO
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