Potts model, parametric maxflow and k-submodular functions

Igor Gridchyn and Vladimir Kolmogorov.

In International Conference on Computer Vision (ICCV), December 2013.


The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19,20]. It identifies a part of an optimal solution by running k maxflow computations, where k is the number of labels. The number of "labeled" pixels can be significant in some applications, e.g. 50-93% in our tests for stereo. We show how to reduce the runtime to O(log k) maxflow computations (or one parametric maxflow computation). Furthermore, the output of our algorithm allows to speed-up the subsequent alpha expansion for the unlabeled part, or can be used as it is for time-critical applications.

To derive our technique, we generalize the algorithm of Felzenszwalb et al. [7] for Tree Metrics. We also show a connection to k-submodular functions from combinatorial optimization, and discuss k-submodular relaxations for general energy functions.



arXiv version