Computing approximate geodesics and minimal surfaces using watershed and graph cuts

Geodesics and minimal surfaces are widely used for medical im- age segmentation. At least two dierent approaches are used to compute such segmentations. First, geodesic active contours use dierential geometry to compute optimal contours minimizing a given Riemannian metric. Second, Boykov and Kolmogorov have proposed a method based on integral geometry to compute similar contours using a graph representation of the image and combinato- rial optimization. In this paper we present a technique to compute approximate geodesics and minimal surfaces using a low-level seg- mentation and graph-cuts optimization. Our approach speeds-up the computation of minimal surfaces when a low-level segmentation is available.