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As richer models for stereo vision are constructed, there is a growing interest in learning model parameters. To estimate parameters in Markov Random Field (MRF) based stereo formulations, one usually needs to perform approximate probabilistic inference. Message passing algorithms based on variational methods and belief propagation are widely used for approximate inference in MRFs. Conditional Random Fields (CRFs) are discriminative versions of traditional MRFs and have recently been applied to the problem of stereo vision. However, CRF parameter training typically requires expensive inference steps for each iteration of optimization. Inference is particularly slow when there are many discrete disparity levels, due to high state space cardinality. We present a novel CRF for stereo matching with an explicit occlusion model and propose sparse message passing to dramatically accelerate the approximate inference needed for parameter optimization. We show that sparse variational message passing iteratively minimizes the KL divergence between the approximation and model distributions by optimizing a lower bound on the partition function. Our experimental results show reductions in inference time of one order of magnitude with no loss in approximation quality. Learning using sparse variational message passing improves results over prior work using graph cuts.

Efficiently Learning Random Fields for Stereo Vision with Sparse Message Passing