Estimating Markov Random Field Potentials for Natural Images

Markov Random Field (MRF) models with potentials learned from the data have recently received attention for learning the low-level structure of natural images. A MRF provides a principled model for whole images, unlike ICA, which can in practice be estimated for small patches only. However, learning the filters in an MRF paradigm has been problematic in the past since it required computationally expensive Monte Carlo methods. Here, we show how MRF potentials can be estimated using Score Matching (SM). With this estimation method we can learn filters of size 12×12 pixels, considerably larger than traditional ”hand-crafted” MRF potentials. We analyze the tuning properties of the filters in comparison to ICA filters, and show that the optimal MRF potentials are similar to the filters from an overcomplete ICA model.