a method is disclosed to automatically segment 3d and higher - dimensional images into two subsets without user intervention , with no topological restriction on the solution , and in such a way that the solution is an optimal in a precisely defined optimization criterion , including an exactly defined degree of smoothness . a minimum - cut algorithm is used on a graph devised so that the optimization criterion translates into the minimization of the graph cut . the minimum cut thus found is interpreted as the segmentation with desired property .