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Integer Linear Programming (ILP) formulations of Markov random fields (MRFs)models with global connectivity priors were investigated previously in computervision, e.g., \cite{globalinter,globalconn}. In these works, only LinearPrograming (LP) relaxations \cite{globalinter,globalconn} or simplifiedversions \cite{graphcutbase} of the problem were solved. This paperinvestigates the ILP of multi-label MRF with exact connectivity priors via abranch-and-cut method, which provably finds globally optimal solutions. Themethod enforces connectivity priors iteratively by a cutting plane method, andprovides feasible solutions with a guarantee on sub-optimality even if weterminate it earlier. The proposed ILP can be applied as a post-processingmethod on top of any existing multi-label segmentation approach. As it providesglobally optimal solution, it can be used off-line to generate ground-truthlabeling, which serves as quality check for any fast on-line algorithm.Furthermore, it can be used to generate ground-truth proposals for weaklysupervised segmentation. We demonstrate the power and usefulness of our modelby several experiments on the BSDS500 and PASCAL image dataset, as well as onmedical images with trained probability maps.

An ILP Solver for Multi-label MRFs with Connectivity Constraints