Efficient Learning for Discriminative Segmentation with Supermodular Losses

Several non-modular loss functions have been considered in the context of image segmentation. These loss functions do not necessarily have the same structure as the segmentation inference algorithm, and in general, we may have to resort to generic submodular minimization algorithms for loss augmented inference. Although these come with polynomial time guarantees, they are not practical to apply to image scale data. In this work, we first propose a supermodular loss function that is itself optimizable with graph cuts. It counts the number of incorrect pixels plus the number of pairs of neighboring pixels that both have incorrect labels