Second order elastic metrics on the shape space of curves

Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

232 Downloads (Pure)

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.
Original languageEnglish
Title of host publicationProceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV) 2015
EditorsH. Drira, S. Kurtek, P. Turaga
PublisherBMVA Press
Publication date2015
Pages1-11
ISBN (Print)1-901725-56-1
Publication statusPublished - 2015
Event1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV) 2015 - Swansea, United Kingdom
Duration: 10 Sep 2015 → …
Conference number: 1
http://bmvc2015.swan.ac.uk/?p=2681

Workshop

Workshop1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories (DIFF-CV) 2015
Number1
CountryUnited Kingdom
CitySwansea
Period10/09/2015 → …
OtherPart of the 26th British Machine Vision Conference (BMVC 2015)
Internet address

Fingerprint

Dive into the research topics of 'Second order elastic metrics on the shape space of curves'. Together they form a unique fingerprint.

Cite this