Algorithms from statistical physics for generative models of images
A general framework for defining generative models of images is Markov random fields (MRFs), with shift-invariant (homogeneous) MRFs being an important special case for modeling textures and generic images. Given a dataset of natural images and a set of filters from which filter histogram statistics are obtained, a shift-invariant MRF can be defined (as in [Neural Comput. 9 (1997) 1627]) as a distribution of images whose mean filter histogram values match the empirical values obtained from the data set. Certain parameters in the MRF model, called potentials, must be determined in order for the model to match the empirical statistics. Standard methods for calculating the potentials are computationally very demanding, such as Generalized Iterative Scaling (GIS), an iterative procedure that converges to the correct potential values. We define a fast approximation, called BKGIS, which uses the Bethe-Kikuchi approximation from statistical physics to speed up the GIS procedure. Results are demonstrated on a model using two filters, and we show synthetic images that have been sampled from the model. Finally, we show a connection between GIS and our previous work on the g-factor.
markov random field histogram statistics generalized iterative scaling minimax entropy learning