Gradient Vector Flow Deformable Models

Deformable models are used extensively in image processing, computer vision, and medical imaging applications, particularly to delineate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This chapter presents an external force for deformable models, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional deformable model external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding deformable model is formulated directly from a dynamic force equation rather than a energy minimization formulation. Using several two-dimensional examples and two three-dimensional examples, we show that GVF has a large capture range and is able to move deformable models into boundary concavities.