Who killed the directed model?

Prior distributions are useful for robust low-level vision, and undirected models (e.g. Markov Random Fields) have become a central tool for this purpose. Though sometimes these priors can be specified by hand, this becomes difficult in large models, which has motivated learning these models from data. However, maximum likelihood learning of undirected models is extremely difficult- essentially all known methods require approximations and/or high computational cost. Conversely, directed models are essentially trivial to learn from data, but have not received much attention for low-level vision. We compare the two formalisms of directed and undirected models, and conclude that there is no a priori reason to believe one better represents low-level vision quantities. We formulate two simple directed priors, for natural images and stereo disparity, to empirically test if the undirected formalism is superior. We find in both cases that a simple directed model can achieve results similar to the best learnt undirected models with significant speedups in training time, suggesting that directed models are an attractive choice for tractable learning.