MAP Estimation of Semi-Metric MRFs via Hierarchical Graph Cuts
This work addresses a computational bottleneck in probabilistic graphical models for researchers in computer vision and machine learning, offering a faster and accurate solution for inference tasks.
The paper tackles the problem of computing maximum a posteriori estimates for discrete pairwise random fields with semimetric potentials by proposing a hierarchical move-making strategy that uses efficient graph cuts. The method achieves the guarantees of linear programming relaxation for metric labeling cases and outperforms existing algorithms in experiments on synthetic and real data.
We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making strategy where each move is computed efficiently by solving an st-MINCUT problem. Unlike previous move making approaches, e.g. the widely used a-expansion algorithm, our method obtains the guarantees of the standard linear programming (LP) relaxation for the important special case of metric labeling. Unlike the existing LP relaxation solvers, e.g. interior-point algorithms or tree-reweighted message passing, our method is significantly faster as it uses only the efficient st-MINCUT algorithm in its design. Using both synthetic and real data experiments, we show that our technique outperforms several commonly used algorithms.