Enforcing topological constraints in random field image segmentation

We introduce TopoCut: a new way to integrate knowledge about topological properties (TPs) into random ï¬ eldimage segmentation model. Instead of including TPs asadditional constraints during minimization of the energyfunction, we devise an efï¬ cient algorithm for modifyingthe unary potentials such that the resulting segmentationis guaranteed with the desired properties. Our method ismore ï¬'exible in the sense that it handles more topologyconstraints than previous methods, which were only ableto enforce pairwise or global connectivity. In particular,our method is very fast, making it for the ï¬ rst time possibleto enforce global topological properties in practical imagesegmentation tasks.