Toward Global Minimum through Combined Local Minima

There are many local and greedy algorithms for energy minimization over Markov Random Field (MRF) such as iterated condition mode (ICM) and various gradient descent methods. Local minima solutions can be obtained with simple implementations and usually require smaller computational time than global algorithms. Also, methods such as ICM can be readily implemented in a various difficult problems that may involve larger than pairwise clique MRFs. However, their short comings are evident in comparison to newer methods such as graph cut and belief propagation. The local minimum depends largely on the initial state, which is the fundamental problem of its kind. In this paper, disadvantages of local minima techniques are addressed by proposing ways to combine multiple local solutions. First, multiple ICM solutions are obtained using different initial states. The solutions are combined with random partitioning based greedy algorithm called Combined Local Minima (CLM). There are numerous MRF problems that cannot be efficiently implemented with graph cut and belief propagation, and so by introducing ways to effectively combine local solutions, we present a method to dramatically improve many of the pre-existing local minima algorithms. The proposed approach is shown to be effective on pairwise stereo MRF compared with graph cut and sequential tree re-weighted belief propagation (TRW-S). Additionally, we tested our algorithm against belief propagation (BP) over randomly generated 30×30 MRF with 2×2 clique potentials, and we experimentally illustrate CLM’s advantage over message passing algorithms in computation complexity and performance.