Edge based segmentations are intuitive since edges usually show an object boundary. However in some or many cases, edges are not sharp or are simply not there. Region based segmentations is a solution to this problem. Here is an example using a level set framework.
Beyond being a powerful segmentation technique, Graph Cuts can be used for efficient energy minimization. This page explains the rough idea of the alpha-expansion and the alpha-beta-swap algorithm. Two examples are then ilustrated. One restoring a noisy image, and one recovered the deformation map between two images.