  In this work we introduce a fully-connected graph structure in the Deep
Gaussian Conditional Random Field (G-CRF) model. For this we express the
pairwise interactions between pixels as the inner-products of low-dimensional
embeddings, delivered by a new subnetwork of a deep architecture. We
efficiently minimize the resulting energy by solving the resulting low-rank
linear system with conjugate gradients, and derive an analytic expression for
the gradient of our embeddings which allows us to train them end-to-end with
backpropagation.
  We demonstrate the merit of our approach by achieving state of the art
results on three challenging Computer Vision benchmarks, namely semantic
segmentation, human parts segmentation, and saliency estimation. Our
implementation is fully GPU based, built on top of the Caffe library, and will
be made publicly available.
