Fuzzy geodesics and consistent sparse correspondences for deformable shapes

Jian Sun, Xiaobai Chen, Thomas Allen Funkhouser

Research output: Contribution to journalArticle

16 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1535-1544
Number of pages10
JournalEurographics Symposium on Geometry Processing
Volume29
Issue number5
StatePublished - Dec 28 2010

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Geometry and Topology

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