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Issue No.10 - Oct. (2012 vol.18)

pp: 1664-1677

Sang Wook Yoo , Korea Advanced Institute of Science and Technology, Daejeon

Joon-Kyung Seong , Soongsil University, Seoul

Min-Hyuk Sung , Korea Institute of Science and Technology, Seoul

Sung Yong Shin , Korea Advanced Institute of Science and Technology, Daejeon

Elaine Cohen , University of Utah, Salt Lake City

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.29

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.

INDEX TERMS

Measurement, Equations, Surface treatment, Approximation algorithms, Least squares approximation, shape analysis., Geodesic, anisotropy, surface mesh, Hamilton-Jacobi-Bellman, curvature minimization, curvature variation minimization

CITATION

Sang Wook Yoo, Joon-Kyung Seong, Min-Hyuk Sung, Sung Yong Shin, Elaine Cohen, "A Triangulation-Invariant Method for Anisotropic Geodesic Map Computation on Surface Meshes",

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