Modern computer vision (CV) is often based on convolutional neural networks (CNNs) that excel at hierarchical feature extraction. The previous generation of CV approaches was often based on conditional random fields (CRFs) that excel at modeling flexible higher order interactions. As their benefits are complementary they are often combined. However, these approaches generally use mean-field approximations and thus, arguably, did not directly optimize the real problem. Here we revisit dual-decomposition-based approaches to CRF optimization, an alternative to the mean-field approximation. These algorithms can efficiently and exactly solve sub-problems and directly optimize a convex upper bound of the real problem, providing optimality certificates on the way. Our approach uses a novel fixed-point iteration algorithm which enjoys dual-monotonicity, dual-differentiability and high parallelism. The whole system, CRF and CNN can thus be efficiently trained using back-propagation. We demonstrate the effectiveness of our system on semantic image segmentation, showing consistent improvement over baseline models.
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