A Triangulation-Invariant Method for Anisotropic Geodesic Map Computation on Surface Meshes

Cited 4 time in webofscience Cited 0 time in scopus
  • Hit : 298
  • Download : 0
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.
Publisher
IEEE COMPUTER SOC
Issue Date
2012-10
Language
English
Article Type
Article
Keywords

HAMILTON-JACOBI EQUATIONS; GLOBALLY OPTIMAL TRAJECTORIES; EFFICIENT ALGORITHMS; EIKONAL EQUATION; MANIFOLDS; FRONTS

Citation

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, v.18, no.10, pp.1664 - 1677

ISSN
1077-2626
DOI
10.1109/TVCG.2012.29
URI
http://hdl.handle.net/10203/103008
Appears in Collection
CS-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 4 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0