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dc.contributor.authorMémoli, Facundoen_US
dc.contributor.authorSapiro, Guillermoen_US
dc.contributor.editorRoberto Scopigno and Denis Zorinen_US
dc.date.accessioned2014-01-29T09:19:46Z
dc.date.available2014-01-29T09:19:46Z
dc.date.issued2004en_US
dc.identifier.isbn3-905673-13-4en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttp://dx.doi.org/10.2312/SGP/SGP04/033-042en_US
dc.description.abstractPoint 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.en_US
dc.publisherThe Eurographics Associationen_US
dc.titleComparing Point Cloudsen_US
dc.description.seriesinformationSymposium on Geometry Processingen_US


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