A hidden property of the gradient vector flow diffusion process

Snakes, or active contours, are one of the major paradigms in image segmentation. With the gradient vector flow (GVF) as external force, they have a larger capture range and the ability to progress into concave boundaries. However, when we have to deal with highly non-convex shapes, the GVF field forms an area where the forces point in opposite directions and the snake stops. GVF is built as a diffusion process of the gradient vectors of an edge map derived from the image. In this paper, we will view the diffusion process as a mechanism having the gradient vectors of the edge map as the input and the resulting GVF as the output. We will show how a modified input will result in a GVF able to drive the snake in such a highly non-convex boundary. This ability is revealed as a generalized property of the GVF diffusion process.