Sparse Non-Local CRF

CRF is a classical computer vision model which is also useful for deep learning. There are two common CRF types: sparse and dense. Sparse CRF connects only the nearby pixels, while dense CRF has global connectivity. Therefore dense CRF is a more general model, but it is much harder to optimize compared to sparse CRF. In fact, only a certain form of dense CRF is optimized in practice, and even then approximately. We propose a new sparse non-local CRF: it has a sparse number of connections, but it has both local and non-local ones. Like sparse CRF, the total number of connections is small, and our model is easy to optimize exactly. Like dense CRF, our model is more general than sparse CRF due to non-local connections. We show that our sparse non-local CRF can model properties similar to that of the popular Gaussian edge dense CRF. Besides efficiency, another advantage is that our edge weights are less restricted compared to Gaussian edge dense CRF. We design models that take advantage of this flexibility. We also discuss connection of our model to other CRF models. Finally, to prove the usefulness of our model, we evaluate it on the classical application of segmentation from a bounding box and for deep learning based salient object segmentation. We improve state of the art for both applications.