Graph matching based a probabilistic spectral method

A large number of tasks in computer vision involve finding consistent correspondences between two sets of features. A common solution is graph matching which is widely used in various research areas. In this paper, we consider the graph matching problem as an Integer Quadratic Programming (IQP) formulation. Solution of this problem is NP-hard as it is known to all. Therefore, we focus on an efficient approximation algorithm using a spectral technique. Firstly, we introduce a probabilistic interpretation of the spectral graph matching problem. It is easier to solve than previous spectral methods. Secondly, spectral matching can be interpreted as a maximum likelihood estimate of the assignment probabilities and that the graduated assignment algorithm boils down to an estimate maximize formulation. Finally, we propose a new graph matching algorithm that achieves robust matching results. We experimentally demonstrate the effectiveness of our approach for synthetic graph and real images.