We present an efficient solution to the Eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applications: image enhancement and face recognition.
1
Technion - Israel Institute of Technology, Haifa, Israel
Alon Spira; Ron Kimmel. An efficient solution to the eikonal equation on parametric manifolds. Interfaces and free boundaries, Tome 6 (2004) no. 3, pp. 315-327. doi: 10.4171/ifb/102
@article{10_4171_ifb_102,
author = {Alon Spira and Ron Kimmel},
title = {An efficient solution to the eikonal equation on parametric manifolds},
journal = {Interfaces and free boundaries},
pages = {315--327},
year = {2004},
volume = {6},
number = {3},
doi = {10.4171/ifb/102},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/102/}
}
TY - JOUR
AU - Alon Spira
AU - Ron Kimmel
TI - An efficient solution to the eikonal equation on parametric manifolds
JO - Interfaces and free boundaries
PY - 2004
SP - 315
EP - 327
VL - 6
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/102/
DO - 10.4171/ifb/102
ID - 10_4171_ifb_102
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%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/102/
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