A Projected Gradient Descent Method for CRF Inference allowing End-To-End Training of Arbitrary Pairwise Potentials

Are we using the right potential functions in the Markov- and Conditional- Random Field graphical models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep learning paradigm. However, most state-of-the-art structured prediction methods also include a random field model with a hand-crafted Gaussian potential to model spatial priors, label consistencies and feature-based image conditioning. In this paper, we challenge this view by introducing a new inference and learning framework which can learn arbitrary pairwise CRF potentials. Both standard spatial and high-dimensional bilateral kernels are considered. Our framework is based on the observation that CRF inference can be achieved via projected gradient descent and consequently, can easily be integrated in deep neural networks to allow for end-to-end training. We compare our approach to several other recent frameworks, both from a theoretical and experimental perspective, and conclude that one can improve performance by using learned potentials.