Why Use Sobolev Metrics on the Space of Curves

Abstract

We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of efficient numerical methods for higher order Sobolev type metrics is an extremely desirable goal.

22 pages, many figures

References in corpus (4)

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• Precise Matching of PL Curves in $R^N$ in the Square Root Velocity Framework
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