Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/13377
Title: Second order elastic metrics on the shape space of curves
Authors: Bauer, M
Bruveris, M
Harms, P
Møller-Andersen, J
Keywords: math.DG;math.DG;math.NA;58B20 (Primary), 62H25, 62H30 (Secondary)
Issue Date: 2016
Citation: Arxiv, (2016)
Abstract: Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects.
URI: http://bura.brunel.ac.uk/handle/2438/13377
ISSN: http://arxiv.org/abs/1507.08816v1
Appears in Collections:Dept of Mathematics Research Papers

Files in This Item:
File Description SizeFormat 
Fulltext.pdf841.25 kBAdobe PDFView/Open


Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.