Abstract

Many recent techniques for low-level vision problems such as image denoising are formulated in terms of Markov random field (MRF) or conditional random field (CRF) models. Nonetheless, the role of the underlying graph struc- ture is still not well understood. On the one hand there are pairwise structures where each node is connected to its local neighbors. These models tend to allow for fast algorithms but do not capture important higher-order statistics of natural scenes. On the other hand there are more powerful models such as Field of Ex- perts (FoE) that consider joint distributions over larger cliques in order to capture image statistics but are computationally challenging. In this paper we consider a graph structure with longer range connections that is designed to both cap- ture important image statistics and be computationally efficient. This structure incorporates long-range connections in a manner that limits the cliques to size 3, thereby capturing important second-order image statistics while still allowing efficient optimization due to the small clique size. We evaluate our approach by testing the models on widely used datasets. The results show that our method is comparable to the current state-of-the-art in terms of PSNR, is better at preserv- ing fine-scale detail and producing natural-looking output, and is more than an order of magnitude faster.