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    Comparing Point Clouds

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    033-042.pdf (237.1Kb)
    Date
    2004
    Author
    Mémoli, Facundo
    Sapiro, Guillermo
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    Abstract
    Point clouds are one of the most primitive and fundamental surface representations. A popular source of point clouds are three dimensional shape acquisition devices such as laser range scanners. Another important field where point clouds are found is in the representation of high-dimensional manifolds by samples. With the increasing popularity and very broad applications of this source of data, it is natural and important to work directly with this representation, without having to go to the intermediate and sometimes impossible and distorting steps of surface reconstruction. A geometric framework for comparing manifolds given by point clouds is presented in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading to isometry invariant and completely geometric comparisons. This theory is embedded in a probabilistic setting as derived from random sampling of manifolds, and then combined with results on matrices of pairwise geodesic distances to lead to a computational implementation of the framework. The theoretical and computational results here presented are complemented with experiments for real three dimensional shapes.
    BibTeX
    @inproceedings {10.2312:SGP:SGP04:033-042,
    booktitle = {Symposium on Geometry Processing},
    editor = {Roberto Scopigno and Denis Zorin},
    title = {{Comparing Point Clouds}},
    author = {Mémoli, Facundo and Sapiro, Guillermo},
    year = {2004},
    publisher = {The Eurographics Association},
    ISSN = {1727-8384},
    ISBN = {3-905673-13-4},
    DOI = {10.2312/SGP/SGP04/033-042}
    }
    URI
    http://dx.doi.org/10.2312/SGP/SGP04/033-042
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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