Generalized ordering constraints for multilabel optimization

We propose a novel framework for imposing label ordering constraints in multilabel optimization. In particular, label jumps can be penalized differently depending on the jump direction. In contrast to the recently proposed MRF-based approaches, the proposed method arises from the viewpoint of spatially continuous optimization. It unifies and generalizes previous approaches to label ordering constraints: Firstly, it provides a common solution to three different problems which are otherwise solved by three separate approaches [4, 10, 14]. We provide an exact characterization of the penalization functions expressible with our approach. Secondly, we show that it naturally extends to three and higher dimensions of the image domain. Thirdly, it allows novel applications, such as the convex shape prior. Despite this generality, our model is easily adjustable to various label layouts and is also easy to implement. On a number of experiments we show that it works quite well, producing solutions comparable and superior to those obtained with previous approaches.