Tightening MRF Relaxations with Planar Subproblems

TL;DR

This paper introduces a novel technique for tightening lower bounds in planar MRFs by adding cycle consistency constraints through subproblems, leading to faster convergence and improved performance on hard potentials.

Contribution

The authors propose a new dual-decomposition based method that enforces cycle consistency in planar MRFs, enhancing lower-bound computation efficiency.

Findings

Method converges quickly with few subproblems.

Outperforms existing methods on certain hard potentials.

Effective in tightening bounds for planar MRFs.

Abstract

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.