Closed-form approximate CRF training for scalable image segmentation

We present LS-CRF, a new method for training cyclic Conditional Random Fields (CRFs) from large datasets that is inspired by classical closed-form expressions for the maximum likelihood parameters of a generative graphical model with tree topology. Training a CRF with LS-CRF requires only solving a set of independent regression problems, each of which can be solved efficiently in closed form or by an iterative solver. This makes LS-CRF orders of magnitude faster than classical CRF training based on probabilistic inference, and at the same time more flexible and easier to implement than other approximate techniques, such as pseudolikelihood or piecewise training. We apply LS-CRF to the task of semantic image segmentation, showing that it achieves on par accuracy to other training techniques at higher speed, thereby allowing efficient CRF training from very large training sets. For example, training a linearly parameterized pairwise CRF on 150,000 images requires less than one hour on a modern workstation.