Learning Edge-Specific Kernel Functions for Pairwise Graph Matching

In this paper we consider the pairwise graph matching problem of finding correspondences between two point sets using unary and pairwise potentials, which analyze local descriptor similarity and geometric compatibility. Recently, it was shown that it is possible to learn optimal parameters for the features used in the potentials, which significantly improves results in supervised and unsupervised settings. It was demonstrated that even linear assignments (not considering geometry) with well learned potentials may improve over state-of-the-art quadratic assignment solutions. In this paper we extend this idea by directly learning edge-specific kernels for pairs of nodes. We define the pairwise kernel functions based on a statistical shape model that is learned from labeled training data. Assuming that the setting of graph matching is a priori known, the learned kernel functions allow to significantly improve results in comparison to general graph matching. We further demonstrate the applicability of game theory based evolutionary dynamics as effective and easy to implement approximation of the underlying graph matching optimization problem. Experiments on automatically aligning a set of faces and feature-point based localization of category instances demonstrate the value of the proposed method.