Factorial Markov Random Fields

In this paper we propose an extension to the standard Markov Random Field (MRF) model in order to handle layers. Our extension, which we call a Factorial MRF (FMRF), is analogous to the extension from Hidden Markov Models (HMM’s) to Factorial HMM’s. We present an efficient EM-based algorithm for inference on Factorial MRF’s. Our algorithm makes use of the fact that layers are a priori independent, and that layers only interact through the observable image. The algorithm iterates between wide inference, i.e., inference within each layer for the entire set of pixels, and deep inference, i.e., inference through the layers for each single pixel. The efficiency of our method is partly due to the use of graph cuts for binary segmentation, which is part of the wide inference step. We show experimental results for both real and synthetic images.