A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model's energy between two points. Initialization is made easier and the curve cannot be trapped at a local minimum by spurious edges. We modify 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 in a Riemannian metric, or as a path of minimal cost. We then make use of a new efficient numerical method to find the shortest path which is the global minimum of the energy among all paths joining the two end points. The method is extended to closed contours, given only one point on the objects' boundary by using a topology--based saddle search routine. We show examples of our method applied to real aerial and medical images.