  Dense image matching is a fundamental low-level problem in Computer Vision,
which has received tremendous attention from both discrete and continuous
optimization communities. The goal of this paper is to combine the advantages
of discrete and continuous optimization in a coherent framework. We devise a
model based on energy minimization, to be optimized by both discrete and
continuous algorithms in a consistent way. In the discrete setting, we propose
a novel optimization algorithm that can be massively parallelized. In the
continuous setting we tackle the problem of non-convex regularizers by a
formulation based on differences of convex functions. The resulting hybrid
discrete-continuous algorithm can be efficiently accelerated by modern GPUs and
we demonstrate its real-time performance for the applications of dense stereo
matching and optical flow.
