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

Title
A Triangulation-Invariant Method for Anisotropic Geodesic Map Computation on Surface Meshes
Authors
유상욱성준경성민혁신성용Elaine Cohen
Keywords
Curve; Geometric algorithms; Object representations; surface mesh; Geodesic; anisotropy; Hamilton-Jacobi-Bellman; curvature minimization; curvature variation
Issue Date
2012-10
Publisher
IEEE transactions on visualization and computer graphics
Citation
VOL 18, NO 10, 1664-1677
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 curvaturebased 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 iso-contour 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.
URI
http://pubs.kist.re.kr/handle/201004/44662
ISSN
10772626
Appears in Collections:
KIST Publication > Article
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE