The g Factor: Relating Distributions on Features to Distributions on Images

We describe the g-factor, which relates probability distributions on image features to distributions on the images themselves. The g-factor depends only on our choice of features and lattice quanti(cid:173) zation and is independent of the training image data. We illustrate the importance of the g-factor by analyzing how the parameters of Markov Random Field (i.e. Gibbs or log-linear) probability models of images are learned from data by maximum likelihood estimation. In particular, we study homogeneous MRF models which learn im(cid:173) age distributions in terms of clique potentials corresponding to fea(cid:173) ture histogram statistics (d.