High-Order Markov Random Fields for Low-Level Vision

I will introduce several low-level vision tasks, such as image reconstruction and optical flow estimation, and show how they can be approached in a unified way as Bayesian inference problems. One key component of these Bayesian approaches is modeling the prior distribution. In image reconstruction applications, for example in image denoising, this amounts to modeling the prior probability of observing a particular image among all possible images. I will review Markov random fields (MRFs) and show how they can be used to formulate image priors. Past MRF approaches have mostly relied on simple random field structures that only model interactions between neighboring pixels, which is not powerful enough to capture the rich statistics of natural images. In my talk I will introduce a new high-order Markov random field model, termed Fields of Experts (FoE), that better captures the structure of natural images by modeling interactions among larger neighborhoods of pixels. The parameters of this model are learned from a database of natural images using contrastive divergence learning. I will demonstrate the capabilities of the FoE model on various image reconstruction applications. Furthermore, I will show that the Fields-of-Experts model is applicable to a wide range of other low-level vision problems and discuss its application to modeling and estimating optical flow.