Handle URI:
http://hdl.handle.net/10754/597242
Title:
A Condition Number for Non-Rigid Shape Matching
Authors:
Ovsjanikov, Maks; Huang, Qi-Xing; Guibas, Leonidas
Abstract:
© 2011 The Author(s). Despite the large amount of work devoted in recent years to the problem of non-rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the hardness of the problem of shape matching, and introduce the notion of the shape condition number, which captures the intuition that some shapes are inherently more difficult to match against than others. In particular, we make a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. We analyze two commonly used classes of methods in deformable shape matching, and show that the stability of both types of techniques can be captured by the appropriate notion of a condition number. We also provide a practical way to estimate the shape condition number and show how it can be used to guide the selection of landmark correspondences between shapes. Thus we shed some light on the reasons why general shape matching remains difficult and provide a way to detect and mitigate such difficulties in practice.
Citation:
Ovsjanikov M, Huang Q-X, Guibas L (2011) A Condition Number for Non-Rigid Shape Matching. Computer Graphics Forum 30: 1503–1512. Available: http://dx.doi.org/10.1111/j.1467-8659.2011.02024.x.
Publisher:
Wiley-Blackwell
Journal:
Computer Graphics Forum
Issue Date:
Aug-2011
DOI:
10.1111/j.1467-8659.2011.02024.x
Type:
Article
ISSN:
0167-7055
Sponsors:
This work was supported by NSF grants CCF 1011228, a KAUST-Stanford AEA grant, and a Stanford Graduate Fellowship. We also thank the anonymous reviewers for the valuable comments and suggestions.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorOvsjanikov, Maksen
dc.contributor.authorHuang, Qi-Xingen
dc.contributor.authorGuibas, Leonidasen
dc.date.accessioned2016-02-25T12:28:47Zen
dc.date.available2016-02-25T12:28:47Zen
dc.date.issued2011-08en
dc.identifier.citationOvsjanikov M, Huang Q-X, Guibas L (2011) A Condition Number for Non-Rigid Shape Matching. Computer Graphics Forum 30: 1503–1512. Available: http://dx.doi.org/10.1111/j.1467-8659.2011.02024.x.en
dc.identifier.issn0167-7055en
dc.identifier.doi10.1111/j.1467-8659.2011.02024.xen
dc.identifier.urihttp://hdl.handle.net/10754/597242en
dc.description.abstract© 2011 The Author(s). Despite the large amount of work devoted in recent years to the problem of non-rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the hardness of the problem of shape matching, and introduce the notion of the shape condition number, which captures the intuition that some shapes are inherently more difficult to match against than others. In particular, we make a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. We analyze two commonly used classes of methods in deformable shape matching, and show that the stability of both types of techniques can be captured by the appropriate notion of a condition number. We also provide a practical way to estimate the shape condition number and show how it can be used to guide the selection of landmark correspondences between shapes. Thus we shed some light on the reasons why general shape matching remains difficult and provide a way to detect and mitigate such difficulties in practice.en
dc.description.sponsorshipThis work was supported by NSF grants CCF 1011228, a KAUST-Stanford AEA grant, and a Stanford Graduate Fellowship. We also thank the anonymous reviewers for the valuable comments and suggestions.en
dc.publisherWiley-Blackwellen
dc.titleA Condition Number for Non-Rigid Shape Matchingen
dc.typeArticleen
dc.identifier.journalComputer Graphics Forumen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
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