Efficient parallel optimization for potts energy with hierarchical fusion

Potts energy frequently occurs in computer vision applications. We present an efficient parallel method for optimizing Potts energy based on the extension of hierarchical fusion algorithm. Unlike previous parallel graph-cut based optimization algorithms, our approach has optimality bounds even after a single iteration over all labels, i.e. after solving only k-1 max-flow problems, where k is the number of labels. This is perhaps the minimum number of max-flow problems one has to solve to obtain a solution with optimality guarantees. Our approximation factor is O(log₂k). Although this is not as good as the factor of 2 approximation of the well known expansion algorithm, we achieve very good results in practice. In particular, we found that the results of our algorithm after one iteration are always better than the results after one iteration of the expansion algorithm. We demonstrate experimentally the computational advantages of our parallel implementation on the problem of stereo correspondence, achieving a factor of 1.5 to 2.6 speedup compared to the serial implementation. These results were obtained with a small number of processors. The expected speedups with a larger number of processors are greater.