Estimating Markov Random Field Potentials for Natural Images
Urs Köster, Jussi T. Lindgren and Aapo Hyvärinen
In: ICA 2009, 15-18 Mar 2009, Paraty RJ / Brazil.
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.