Weighted distance maps computation on parametric three-dimensional manifolds

Authors:
Alexander M. Bronstein;Michael M. Bronstein;Ron Kimmel
Affiliations:
Department of Computer Science, Technion - Israel Institute of Technology, Haifa 32000, Israel;Department of Computer Science, Technion - Israel Institute of Technology, Haifa 32000, Israel;Department of Computer Science, Technion - Israel Institute of Technology, Haifa 32000, Israel
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

We propose an efficient computational solver for eikonal equations on parametric three-dimensional manifolds. Our approach is based on the fast marching method for solving the eikonal equation in O(nlogn) steps on n grid points by numerically simulating wavefront propagation. The obtuse angle splitting problem is reformulated as a set of small integer linear programs, that can be solved in O(n). Numerical simulations demonstrate the accuracy of the proposed algorithm.