Before revision:  Our method is based on a primal-dual optimization formulation where the primal problem has a natural network flow interpretation, and the dual problem has a cut-based interpretation using the \ell_2-norm penalty for general submodular cut-costs.
After revision:  Our method is based on a primal-dual optimization formulation where the primal problem has a natural network flow interpretation, and the dual problem has a cut-based interpretation using the \ell_2-norm penalty on associated cut-costs.