Deep graph matching meets mixed-integer linear programming: Relax at your own risk ?
This work addresses a gap in computer vision for researchers by analyzing the impact of graph matching algorithms in deep learning, though it appears incremental as it builds on existing methods without introducing a new paradigm.
The paper tackles the lack of understanding of graph matching algorithms' role in deep learning models by proposing an approach that integrates a mixed-integer linear programming (MILP) formulation solved to optimality, providing a baseline and testing relaxations. The experimental evaluation yields theoretical insights and guidance for deep graph matching methods.
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.