The segmentation of structure from 2D and 3D images is an important rst step in analyzing medical data. For example, it is necessary to segment the brain in an MR image, before it can be rendered in 3D for visualization purposes. Segmentation

and split. Although this topological constraint may be reasonable in the segmentation of the liver, it would certainly be undesirable when segmenting blood vessels in an MR image. An algorithm to overcome these diculties was rst introduced by