Before revision:  We make use of the Finsler metrics with Randers form, by which the asymmetric and anisotropic measures of the geodesic curve length are taken into account to avoid the shortcuts and leaking problems. This allows the fronts of the geodesic distance map to benefit from the asymmetric information derived from the image edges .
After revision:  We make use of the Finsler metrics with Randers form, by which the asymmetric and anisotropic measures of the geodesic curve length are taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edges .