Fuzzy Geodesics and Consistent Sparse Correspondences For Deformable Shapes
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2010
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Abstract
A 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.
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@article{10.1111:j.1467-8659.2010.01762.x,
journal = {Computer Graphics Forum},
title = {{Fuzzy Geodesics and Consistent Sparse Correspondences For Deformable Shapes}},
author = {Jian Sun and Xiaobai Chen and Thomas A. Funkhouser},
year = {2010},
publisher = {},
DOI = {10.1111/j.1467-8659.2010.01762.x}
}