Manifold guided composite of Markov random fields for image modeling

We present a new generative image model, integrating techniques arising from two different domains: manifold modeling and Markov random fields. First, we develop a probabilistic model with a mixture of hyperplanes to approximate the manifold of orientable image patches, and demonstrate that it is more effective than the field of experts in expressing local texture patterns. Next, we develop a construction that yields an MRF for coherent image generation, given a configuration of local patch models, and thereby establish a prior distribution over an MRF space. Taking advantage of the model structure, we derive a variational inference algorithm, and apply it to low-level vision. In contrast to previous methods that rely on a single MRF, the method infers an approximate posterior distribution of MRFs, and recovers the underlying images by combining the predictions in a Bayesian fashion. Experiments quantitatively demonstrate superior performance as compared to state-of-the-art methods on image denoising and inpainting.