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Maximum Persistency in Energy Minimization
"... We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, maxsum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variable ..."
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We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, maxsum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases. We pose the problem of finding the maximum optimal partial assignment identifiable by the new sufficient condition. A polynomial method is proposed which is guaranteed to
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 graphcut based optimization algorithms, our approach has optimality bounds even af ..."
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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 graphcut based optimization algorithms, our approach has optimality bounds even after a single iteration over all labels, i.e. after solving only k1 maxflow problems, where k is the number of labels. This is perhaps the minimum number of maxflow problems one has to solve to obtain a solution with optimality guarantees. Our approximation factor is O(log2 k). 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. 1.