How well do filter-based MRFs model natural images?

Markov random fields (MRFs) have found widespread use as models of natural image and scene statistics. Despite progress in modeling image properties beyond gradient statistics with high-order cliques, and learning image models from example data, existing MRFs only exhibit a limited ability of actually capturing natural image statistics. In this paper we investigate this limitation of previous filter-based MRF models, which appears in contradiction to their maximum entropy interpretation. We argue that this is due to inadequacies in the leaning procedure and suggest various modifications to address them. We demonstrate that the proposed learning scheme allows training more suitable potential functions, whose shape approaches that of a Dirac-delta function, as well as models with larger and more filters. Our experiments not only indicate a substantial improvement of the models' ability to capture relevant statistical properties of natural images, but also demonstrate a significant performance increase in a denoising application to levels previously unattained by generative approaches.