Steerable Random Fields

In contrast to traditional Markov random field (MRF) models, we develop a steerable random field (SRF) in which the field potentials are defined in terms of filter responses that are steered to the local image structure. In particular, we use the structure tensor to obtain derivative responses that are either aligned with, or orthogonal to, the predominant local image structure, and analyze the statistics of these steered filter responses in natural images. Clique potentials are defined over steered filter responses using a Gaussian scale mixture model and are learned from training data. The SRF model connects random field models with anisotropic regularization and provides a statistical motivation for the latter. We demonstrate that steering the random field to the local image structure improves image denoising and inpainting performance compared with traditional pairwise MRFs.