<p>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.</p>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:ntnu-9868 |
| Date | January 2009 |
| Creators | Fonn, Eivind |
| Publisher | Norwegian University of Science and Technology, Department of Mathematical Sciences, Institutt for matematiske fag |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, text |
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