Efficient joint object matching via linear programming

Joint object matching, also known as multi-image namely, the problem of finding consistent partial maps among all pairs objects within a collection, is crucial task in many areas computer vision. This subsumes bipartite graph matching and partitioning special cases NP-hard, general. We develop scalable linear programming (LP) relaxations with theoretical performance guarantees for joint matching. start by proposing new characterization maps; this turn enables us to formulate an integer (ILP) problem. To construct strong LP relaxations, we study facial structure convex hull feasible region ILP, which refer polytope. present exponential family facet-defining inequalities that can be separated strongly polynomial time, hence obtaining polytope both tight cheap compute. analyze proposed focus on permutation group synchronization, important case show under random corruption model input maps, simple relaxation, is, containing only very small fraction inequalities, recovers ground truth high probability if level below 40%. Finally, via preliminary computational synthetic data, outperform popular SDP relaxation terms recovery tightness.