  In this paper, we introduce a generalized asymmetric fronts propagation model
based on the geodesic distance maps and the Eikonal partial differential
equations. One of the key ingredients for the computation of the geodesic
distance map is the geodesic metric, which can govern the action of the
geodesic distance level set propagation. We consider a Finsler metric with the
Randers form, through which the asymmetry and anisotropy enhancements can be
taken into account to prevent the fronts leaking problem during the fronts
propagation. These enhancements can be derived from the image edge-dependent
vector field such as the gradient vector flow. The numerical implementations
are carried out by the Finsler variant of the fast marching method, leading to
very efficient interactive segmentation schemes. We apply the proposed Finsler
fronts propagation model to image segmentation applications. Specifically, the
foreground and background segmentation is implemented by the Voronoi index map.
In addition, for the application of tubularity segmentation, we exploit the
level set lines of the geodesic distance map associated to the proposed Finsler
metric providing that a thresholding value is given.
