Regularization Properties for Minimal Geodesics of a Potential Energy

Some new results on our approach 2] of edge integration for shape mod-eling are presented. It enables to nd the global minimum of active contour models' energy between two points. Initialization is made easier and the curve cannot be trapped at a local minimum by spurious edges. We modiied the \snake" energy by including the internal regularization term in the external potential term. Our method is based on the interpretation of the snake as a path of minimal length on a surface or minimal cost. We then make use of level sets propagation to nd the shortest path which is the global minimum of the energy among all paths joining two endpoints. We show that our energy, though only based on a potential integration along the curve, has a regularization eeect like snakes. We show a relation between the maximum curvature along the resulting contour and the potential generated from the image.