GRSA: Generalized Range Swap Algorithm for the Efficient Optimization of MRFs

Markov Random Field (MRF) is an important tool and has been widely used in many vision tasks. Thus, the optimization of MRFs is a problem of fundamental importance. Recently, Veskler and Kumar et. al propose the range move algorithms, which are one of the most successful solvers to this problem. However, two problems have limited the applicability of previous range move algorithms: 1) They are limited in the types of energies they can handle (i.e. only truncated convex functions); 2) These algorithms tend to be very slow compared to other graph-cut based algorithms (e.g. a-expansion and ab-swap). In this paper, we propose a generalized range swap algorithm (GRSA) for efficient optimization of MRFs. To address the first problem, we extend the GRSA to arbitrary semimetric energies by restricting the chosen labels in each move so that the energy is submodular on the chosen subset. Furthermore, to feasibly choose the labels satisfying the submodular condition, we provide a sufficient condition of the submodularity. For the second problem, unlike previous range move algorithms which execute the set of all possible range moves, we dynamically obtain the iterative moves by solving a set cover problem, which greatly reduces the number of moves during the optimization. Experiments show that the GRSA offers a great speedup over previous range swap algorithms, while it obtains competitive solutions.