  Fully connected pairwise Conditional Random Fields (Full-CRF) with Gaussian
edge weights can achieve superior results compared to sparsely connected CRFs.
However, traditional methods for Full-CRFs are too expensive. Previous work
develops efficient approximate optimization based on mean field inference,
which is a local optimization method and can be far from the optimum. We
propose efficient and effective optimization based on graph cuts for Full-CRFs
with quantized edge weights. To quantize edge weights, we partition the image
into superpixels and assume that the weight of an edge between any two pixels
depends only on the superpixels these pixels belong to. Our quantized edge CRF
is an approximation to the Gaussian edge CRF, and gets closer to it as
superpixel size decreases. Being an approximation, our model offers an
intuition about the regularization properties of the Guassian edge Full-CRF.
For efficient inference, we first consider the two-label case and develop an
approximate method based on transforming the original problem into a smaller
domain. Then we handle multi-label CRF by showing how to implement expansion
moves. In both binary and multi-label cases, our solutions have significantly
lower energy compared to that of mean field inference. We also show the
effectiveness of our approach on semantic segmentation task.
