  Despite the availability of many Markov Random Field (MRF) optimization
algorithms, their widespread usage is currently limited due to imperfect MRF
modelling arising from hand-crafted model parameters and the selection of
inferior inference algorithm. In addition to differentiability, the two main
aspects that enable learning these model parameters are the forward and
backward propagation time of the MRF optimization algorithm and its inference
capabilities. In this work, we introduce two fast and differentiable message
passing algorithms, namely, Iterative Semi-Global Matching Revised (ISGMR) and
Parallel Tree-Reweighted Message Passing (TRWP) which are greatly sped up on a
GPU by exploiting massive parallelism. Specifically, ISGMR is an iterative and
revised version of the standard SGM for general pairwise MRFs with improved
optimization effectiveness, and TRWP is a highly parallel version of Sequential
TRW (TRWS) for faster optimization. Our experiments on the standard stereo and
denoising benchmarks demonstrated that ISGMR and TRWP achieve much lower
energies than SGM and Mean-Field (MF), and TRWP is two orders of magnitude
faster than TRWS without losing effectiveness in optimization. We further
demonstrated the effectiveness of our algorithms on end-to-end learning for
semantic segmentation. Notably, our CUDA implementations are at least $7$ and
$700$ times faster than PyTorch GPU implementations for forward and backward
propagation respectively, enabling efficient end-to-end learning with message
passing.
