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    Soft Maps Between Surfaces

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    v31i5pp1617-1626.pdf (725.4Kb)
    Date
    2012
    Author
    Solomon, Justin ORCID
    Nguyen, Andy
    Butscher, Adrian
    Ben-Chen, Mirela
    Guibas, Leonidas
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    Abstract
    The problem of mapping between two non-isometric surfaces admits ambiguities on both local and global scales. For instance, symmetries can make it possible for multiple maps to be equally acceptable, and stretching, slippage, and compression introduce difficulties deciding exactly where each point should go. Since most algorithms for point-to-point or even sparse mapping struggle to resolve these ambiguities, in this paper we introduce soft maps, a probabilistic relaxation of point-to-point correspondence that explicitly incorporates ambiguities in the mapping process. In addition to explaining a continuous theory of soft maps, we show how they can be represented using probability matrices and computed for given pairs of surfaces through a convex optimization explicitly trading off between continuity, conformity to geometric descriptors, and spread. Given that our correspondences are encoded in matrix form, we also illustrate how low-rank approximation and other linear algebraic tools can be used to analyze, simplify, and represent both individual and collections of soft maps.
    BibTeX
    @article {10.1111:j.1467-8659.2012.03167.x,
    journal = {Computer Graphics Forum},
    title = {{Soft Maps Between Surfaces}},
    author = {Solomon, Justin and Nguyen, Andy and Butscher, Adrian and Ben-Chen, Mirela and Guibas, Leonidas},
    year = {2012},
    publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2012.03167.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2012.03167.x
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    • 31-Issue 5
    • SGP12: Eurographics Symposium on Geometry Processing

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