We have presented a new external force model for active contours, which we have called the gradient vector flow (GVF) field. The active contour algorithm implemented using this field is called the GVF snake. This external field allows for a much more flexible initialization of the snake -- both from inside and outside the shape and crossing its boundaries -- and causes the snake to converge to concave boundary regions. This new external force and its active contour algorithm apply to both binary and gray-scale imagery and to two-dimensions, three-dimensions, and even higher dimensional data.
The GVF field was shown to have potential applications in shape analysis, as well. The magnitude of the field was shown to have information related to a shape's medial axis, and to the scale space concept of medialness in the theory of cores. Also, the flow pattern of free points (not attached to active contours) was shown to indicate information about the presence of edges and corners. In particular, corners were demonstrated to be points of equilibria in the flow pattern. GVF streamlines also revealed an improved capture range and concave region flow pattern.
Further investigations into the nature and uses of GVF are warranted. In particular, a precise description of the ``capture range'' of the GVF field would help in snake initialization procedures. Also, a better understanding of the relationships between the magnitude of GVF and medial axis properties of shapes could reveal new shape representations and new analysis techniques. Also, making a connection between the parametric snake model used in this paper and the geometric snake models of Caselles et al.  and Malladi et al.  might provide a solution to the ``topology problem'' while simultaneously using GVF external fields.