We propose an efficient and adaptive method for MAP-MRF inference that provides increasingly tighter upper and lower bounds on the optimal objective. Similar to Sontag et al. (2008b), our method starts by solving the first-order LOCAL(G) linear programming relaxation. This is followed by an adaptive tightening of the relaxation where we incrementally add higher-order interactions to enforce proper marginalization over groups of variables. Computing the best interaction to add is an NP-hard problem. We show good solutions to this problem can be readily obtained from “local primal-dual gaps ” given the current primal solution and a dual reparameterization vector. This is not only extremely efficient, but in contrast to previous approaches, also allows us to search over prohibitively large sets of candidate interactions to add. We demonstrate the superiority of our approach on MAP-MRF inference problems encountered in computer vision. 1

We describe a new technique for computing lower-bounds on the minimum energy configuration of a planar Markov Random Field (MRF). Our method successively adds large numbers of constraints and enforces consistency over binary projections of the original problem state space. These constraints are represented in terms of subproblems in a dual-decomposition framework that is optimized using subgradient techniques. The complete set of constraints we consider enforces cycle consistency over the original graph. In practice we find that the method converges quickly on most problems with the addition of a few subproblems and outperforms existing methods for some interesting classes of hard potentials. 1