  Recent works on deep conditional random fields (CRF) have set new records on
many vision tasks involving structured predictions. Here we propose a
fully-connected deep continuous CRF model for both discrete and continuous
labelling problems. We exemplify the usefulness of the proposed model on
multi-class semantic labelling (discrete) and the robust depth estimation
(continuous) problems.
  In our framework, we model both the unary and the pairwise potential
functions as deep convolutional neural networks (CNN), which are jointly
learned in an end-to-end fashion. The proposed method possesses the main
advantage of continuously-valued CRF, which is a closed-form solution for the
Maximum a posteriori (MAP) inference.
  To better adapt to different tasks, instead of using the commonly employed
maximum likelihood CRF parameter learning protocol, we propose task-specific
loss functions for learning the CRF parameters.
  It enables direct optimization of the quality of the MAP estimates during the
course of learning.
  Specifically, we optimize the multi-class classification loss for the
semantic labelling task and the Turkey's biweight loss for the robust depth
estimation problem.
  Experimental results on the semantic labelling and robust depth estimation
tasks demonstrate that the proposed method compare favorably against both
baseline and state-of-the-art methods.
  In particular, we show that although the proposed deep CRF model is
continuously valued, with the equipment of task-specific loss, it achieves
impressive results even on discrete labelling tasks.
