Fuzzy Geodesics and Consistent Sparse Correspondences For Deformable Shapes

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dc.contributor.authorJian Sunen_US
dc.contributor.authorXiaobai Chenen_US
dc.contributor.authorThomas A. Funkhouseren_US
dc.date.accessioned2015-02-23T17:15:31Z
dc.date.available2015-02-23T17:15:31Z
dc.date.issued2010en_US
dc.description.abstractA geodesic is a parameterized curve on a Riemannian manifold governed by a second order partial differential equation. Geodesics are notoriously unstable: small perturbations of the underlying manifold may lead to dramatic changes of the course of a geodesic. Such instability makes it difficult to use geodesics in many applications, in particular in the world of discrete geometry. In this paper, we consider a geodesic as the indicator function of the set of the points on the geodesic. From this perspective, we present a new concept called fuzzy geodesics and show that fuzzy geodesics are stable with respect to the Gromov-Hausdorff distance. Based on fuzzy geodesics, we propose a new object called the intersection configuration for a set of points on a shape and demonstrate its effectiveness in the application of finding consistent correspondences between sparse sets of points on shapes differing by extreme deformations.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume29en_US
dc.identifier.doi10.1111/j.1467-8659.2010.01762.xen_US
dc.identifier.pages1535-1544en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1535-1544en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1535-1544
dc.titleFuzzy Geodesics and Consistent Sparse Correspondences For Deformable Shapesen_US
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SGP10: Eurographics Symposium on Geometry Processing