GRMA: Generalized Range Move Algorithms for the Efficient Optimization of MRFs

Markov random fields (MRF) have become an important tool for many vision applications, and the optimization of MRFs is a problem of fundamental importance. Recently, Veksler and Kumar et al. proposed the range move algorithms, which are some of the most successful optimizers. Instead of considering only two labels as in previous move-making algorithms, they explore a large search space over a range of labels in each iteration, and significantly outperform previous move-making algorithms. However, two problems have greatly limited the applicability of range move algorithms: (1) They are limited in the energy functions they can handle (i.e., only truncated convex functions); (2) They tend to be very slow compared to other move-making algorithms (e.g., $$\alpha $$α-expansion and $$\alpha \beta $$αβ-swap). In this paper, we propose two generalized range move algorithms (GRMA) for the efficient optimization of MRFs. To address the first problem, we extend the GRMAs to more general energy functions by restricting the chosen labels in each move so that the energy function is submodular on the chosen subset. Furthermore, we provide a feasible sufficient condition for choosing these subsets of labels. To address the second problem, we dynamically obtain the iterative moves by solving set cover problems. This greatly reduces the number of moves during the optimization. We also propose a fast graph construction method for the GRMAs. Experiments show that the GRMAs offer a great speedup over previous range move algorithms, while yielding competitive solutions.