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    Persistence Barcodes for Shapes

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    127-138.pdf (476.3Kb)
    Date
    2004
    Author
    Carlssony, Gunnar
    Zomorodian, Afra
    Collins, Anne
    Guibas, Leonidas
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    Abstract
    In this paper, we initiate a study of shape description and classification via the application of persistent homology to two tangential constructions on geometric objects. Our techniques combine the differentiating power of geometry with the classifying power of topology. The homology of our first construction, the tangent complex, can distinguish between topologically identical shapes with different "sharp" features, such as corners. To capture "soft" curvature-dependent features, we define a second complex, the filtered tangent complex, obtained by parametrizing a family of increasing subcomplexes of the tangent complex. Applying persistent homology, we obtain a shape descriptor, called a barcode, that is a finite union of intervals. We define a metric over the space of such intervals, arriving at a continuous invariant that reflects the geometric properties of shapes. We illustrate the power of our methods through a number of detailed studies of parametrized families of mathematical shapes.
    BibTeX
    @inproceedings {10.2312:SGP:SGP04:127-138,
    booktitle = {Symposium on Geometry Processing},
    editor = {Roberto Scopigno and Denis Zorin},
    title = {{Persistence Barcodes for Shapes}},
    author = {Carlssony, Gunnar and Zomorodian, Afra and Collins, Anne and Guibas, Leonidas},
    year = {2004},
    publisher = {The Eurographics Association},
    ISSN = {1727-8384},
    ISBN = {3-905673-13-4},
    DOI = {10.2312/SGP/SGP04/127-138}
    }
    URI
    http://dx.doi.org/10.2312/SGP/SGP04/127-138
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    Eurographics Association copyright © 2013 - 2023 
    Send Feedback | Contact - Imprint | Data Privacy Policy | Disable Google Analytics
    Theme by @mire NV
    System hosted at  Graz University of Technology.
    TUGFhA