  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.
