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    A Condition Number for Non-Rigid Shape Matching

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    Type
    Article
    Authors
    Ovsjanikov, Maks
    Huang, Qi-Xing
    Guibas, Leonidas
    Date
    2011-08-04
    Online Publication Date
    2011-08-04
    Print Publication Date
    2011-08
    Permanent link to this record
    http://hdl.handle.net/10754/597242
    
    Metadata
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    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.
    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.
    Publisher
    Wiley
    Journal
    Computer Graphics Forum
    DOI
    10.1111/j.1467-8659.2011.02024.x
    ae974a485f413a2113503eed53cd6c53
    10.1111/j.1467-8659.2011.02024.x
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