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The Potts model has many applications. It is equivalent to some min-cut andmax-flow models. Primal-dual algorithms have been used to solve these problems.Due to the special structure of the models, convergence proof is still adifficult problem. In this work, we developed two novel, preconditioned, andover-relaxed alternating direction methods of multipliers (ADMM) withconvergence guarantee for these models. Using the proposed preconditioners orblock preconditioners, we get accelerations with the over-relaxation variantsof preconditioned ADMM. The preconditioned and over-relaxed Douglas-Rachfordsplitting methods are also considered for the Potts model. Our framework canhandle both the two-labeling or multi-labeling problems with appropriate blockpreconditioners based on Eckstein-Bertsekas and Fortin-Glowinski splittingtechniques.

Efficient ADMM and Splitting Methods for Continuous Min-cut and Max-flow Problems