Snakes Methods Analysis Based on Laplacian Operator

A function equivalent to traditional power function in Snakes method is used to develop the level set format of Snakes. This format exhibits vivid geometrical and physical characteristics. First, the velocity depends on the graph itself and theoretically it can approach to zero, and as a result, we have sufficient reason to assume that the Snakes curves will stop on the edge. Second, the moving direction of the curve depending on the graph itself testifies why we need not specify the direction at the beginning. Theories in this paper will be helpful in extending the direction self-adaptation of level set methods.