A triangulation-invariant method for anisotropic geodesic map computation on surface meshes

Sang Wook Yoo, Jun Kyung Seong, Min Hyuk Sung, Sung Yong Shin, Elaine Cohen

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper addresses the problem of computing the geodesic distance map from a given set of source vertices to all other vertices on a surface mesh using an anisotropic distance metric. Formulating this problem as an equivalent control theoretic problem with Hamilton-Jacobi-Bellman partial differential equations, we present a framework for computing an anisotropic geodesic map using a curvature-based speed function. An ordered upwind method (OUM)-based solver for these equations is available for unstructured planar meshes. We adopt this OUM-based solver for surface meshes and present a triangulation-invariant method for the solver. Our basic idea is to explore proximity among the vertices on a surface while locally following the characteristic direction at each vertex. We also propose two speed functions based on classical curvature tensors and show that the resulting anisotropic geodesic maps reflect surface geometry well through several experiments, including isocontour generation, offset curve computation, medial axis extraction, and ridge/valley curve extraction. Our approach facilitates surface analysis and processing by defining speed functions in an application-dependent manner.

Original languageEnglish
Article number6143939
Pages (from-to)1664-1677
Number of pages14
JournalIEEE Transactions on Visualization and Computer Graphics
Volume18
Issue number10
DOIs
Publication statusPublished - 2012 Aug 30
Externally publishedYes

Fingerprint

Triangulation
Surface analysis
Partial differential equations
Tensors
Geometry
Processing
Experiments

Keywords

  • anisotropy
  • curvature minimization
  • curvature variation minimization
  • Geodesic
  • Hamilton-Jacobi-Bellman
  • shape analysis
  • surface mesh

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing

Cite this

A triangulation-invariant method for anisotropic geodesic map computation on surface meshes. / Yoo, Sang Wook; Seong, Jun Kyung; Sung, Min Hyuk; Shin, Sung Yong; Cohen, Elaine.

In: IEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 10, 6143939, 30.08.2012, p. 1664-1677.

Research output: Contribution to journalArticle

Yoo, Sang Wook ; Seong, Jun Kyung ; Sung, Min Hyuk ; Shin, Sung Yong ; Cohen, Elaine. / A triangulation-invariant method for anisotropic geodesic map computation on surface meshes. In: IEEE Transactions on Visualization and Computer Graphics. 2012 ; Vol. 18, No. 10. pp. 1664-1677.
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