Deep graph matching meets mixed-integer linear programming: Relax at your own risk ?
Zhoubo Xu, Puqing Chen, Romain Raveaux, Xin Yang, Huadong Liu
TL;DR
This work tackles the problem of deep graph matching by embedding an exact mixed-integer linear program (MILP) solver inside an end-to-end architecture (DIP-GM). It investigates how solver quality and problem relaxations affect training and matching accuracy, introducing a topology-relaxed MILP variant and a quality-aware stopping criterion. The key findings show that exact solvers can yield strong performance, but well-chosen relaxations (and efficient heuristics) can maintain or even improve accuracy while reducing computation. The study offers practical guidance on when to employ combinatorial vs. continuous solvers in deep graph matching and demonstrates state-of-the-art results on Pascal VOC and SPair-71K datasets. Overall, the paper provides both methodological advances and empirical insights into the integration of combinatorial optimization and deep learning for graph matching.
Abstract
Graph matching is an important problem that has received widespread attention, especially in the field of computer vision. Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no research to explain what role the graph matching algorithm plays in the model. Therefore, we propose an approach integrating a MILP formulation of the graph matching problem. This formulation is solved to optimal and it provides inherent baseline. Meanwhile, similar approaches are derived by releasing the optimal guarantee of the graph matching solver and by introducing a quality level. This quality level controls the quality of the solutions provided by the graph matching solver. In addition, several relaxations of the graph matching problem are put to the test. Our experimental evaluation gives several theoretical insights and guides the direction of deep graph matching methods.