An efficient solution to the eikonal equation on parametric manifolds

Abstract

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.