Graph Transduction Learning with Connectivity Constraints with Application to Multiple Foreground Cosegmentation

The proposed approach is based on standard graph transduction, semi-supervised learning (SSL) framework. Its key novelty is the integration of global connectivity constraints into this framework. Although connectivity leads to higher order constraints and their number is an exponential, finding the most violated connectivity constraint can be done efficiently in polynomial time. Moreover, each such constraint can be represented as a linear inequality. Based on this fact, we design a cutting-plane algorithm to solve the integrated problem. It iterates between solving a convex quadratic problem of label propagation with linear inequality constraints, and finding the most violated constraint. We demonstrate the benefits of the proposed approach on a realistic and very challenging problem of co segmentation of multiple foreground objects in photo collections in which the foreground objects are not present in all photos. The obtained results not only demonstrate performance boost induced by the connectivity constraints, but also show a significant improvement over the state-of-the-art methods.