  In this work, we propose a learning-based method to denoise and refine
disparity maps of a given stereo method. The proposed variational network
arises naturally from unrolling the iterates of a proximal gradient method
applied to a variational energy defined in a joint disparity, color, and
confidence image space. Our method allows to learn a robust collaborative
regularizer leveraging the joint statistics of the color image, the confidence
map and the disparity map. Due to the variational structure of our method, the
individual steps can be easily visualized, thus enabling interpretability of
the method. We can therefore provide interesting insights into how our method
refines and denoises disparity maps. The efficiency of our method is
demonstrated by the publicly available stereo benchmarks Middlebury 2014 and
Kitti 2015.
