Higher-order Segmentation via Multicuts

•We propose a novel and general formulation for hyper-graph correlation clustering.•Any permutation invariant function can be included into a multicut problem.•We provide a comparison of LP and ILP cutting plane methods and rounding procedures for the multicut problem.•Many sparse Potts models can be solved to global optimality very efficient by the proposed method.•The C++ implementations used in this manuscript is freely available online.