Publication Type |
pre-print |
School or College |
College of Engineering |
Department |
Computing, School of |
Creator |
Cohen, Elaine |
Other Author |
Yoo, Sang Wook; Seong, Joon-Kyung; Sung, Min-Hyuk; Shin, Sung Yong |
Title |
A triangulation-invariant method for anisotropic geodesic map computation on surface meshes |
Date |
2012-01-01 |
Description |
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. |
Type |
Text |
Publisher |
Institute of Electrical and Electronics Engineers (IEEE) |
Volume |
18 |
Issue |
10 |
First Page |
1664 |
Last Page |
1677 |
Dissertation Institution |
University of Utah |
Language |
eng |
Bibliographic Citation |
Yoo, S. W., Seong, J.-K., Sung, M.-H., Shin, S. Y., & Cohen, E. (2012). A triangulation-invariant method for anisotropic geodesic map computation on surface meshes. IEEE Transactions on Visualization and Computer Graphics, 18(10), no. 6143939, 1664-77. |
Rights Management |
(c) 2012 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. |
Format Medium |
application/pdf |
Format Extent |
4,097,873 bytes |
Identifier |
uspace,17745 |
ARK |
ark:/87278/s66w9vtv |
Setname |
ir_uspace |
ID |
708103 |
Reference URL |
https://collections.lib.utah.edu/ark:/87278/s66w9vtv |