Efficient parallel message computation for MAP inference

First order Markov Random Fields (MRFs) have become a predominant tool in Computer Vision over the past decade. Such a success was mostly due to the development of efficient optimization algorithms both in terms of speed as well as in terms of optimality properties. Message passing algorithms are among the most popular methods due to their good performance for a wide range of pairwise potential functions (PPFs). Their main bottleneck is computational complexity. In this paper, we revisit message computation as a distance transformation using a more formal setting than [8] to generalize it to arbitrary PPFs. The method is based on [20] yielding accurate results for a specific class of PPFs and in most other cases a close approximation. The proposed algorithm is parallel and thus enables us to fully take advantage of the computational power of parallel processing architectures. The proposed scheme coupled with an efficient belief propagation algorithm [8] and implemented on a massively parallel coprocessor provides results as accurate as state of the art inference methods, though is in general one order of magnitude faster in terms of speed.