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- W2000682967 abstract "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." @default.
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- W2000682967 date "2010-07-01" @default.
- W2000682967 modified "2023-10-18" @default.
- W2000682967 title "Fuzzy Geodesics and Consistent Sparse Correspondences For: eformable Shapes" @default.
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- W2000682967 doi "https://doi.org/10.1111/j.1467-8659.2010.01762.x" @default.
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