  The Gradient Vector Flow (GVF) is a vector diffusion approach based on
Partial Differential Equations (PDEs). This method has been applied together
with snake models for boundary extraction medical images segmentation. The key
idea is to use a diffusion-reaction PDE to generate a new external force field
that makes snake models less sensitivity to initialization as well as improves
the snake's ability to move into boundary concavities. In this paper, we
firstly review basic results about convergence and numerical analysis of usual
GVF schemes. We point out that GVF presents numerical problems due to
discontinuities image intensity. This point is considered from a practical
viewpoint from which the GVF parameters must follow a relationship in order to
improve numerical convergence. Besides, we present an analytical analysis of
the GVF dependency from the parameters values. Also, we observe that the method
can be used for multiply connected domains by just imposing the suitable
boundary condition. In the experimental results we verify these theoretical
points and demonstrate the utility of GVF on a segmentation approach that we
have developed based on snakes.
