Learning Edge-Specific Kernel Functions For Pairwise Graph Matching

Motivation Graph matching has become widely used in several computer vision applications including tracking, shape matching or object detection. Many different approaches are available for solving the NPhard problem in an approximated manner, e. g. based on spectral techniques, probabilistic methods or graduated assignments. Surprisingly, only few papers focused on the important graph potentials themselves, which have a tremendous influence on the quality of the obtainable results. For example, it was shown in [1] that solving a linear assignment problem using well chosen potentials even improves over related state-ofthe-art quadratic assignment solutions. One important challenge of using powerful potentials in graph matching is their right parametrization, which is mostly done manually. Only a few papers focused on the problem of choosing the right parameters. Caetano et al. [1] showed how to learn optimal parameters for the features used in the potentials from manually labeled reference data sets and Leordeanu et al. [2] extended this idea to an unsupervised setting. Both approaches strongly agree on the fact that learning the parameters is important for improving the matching performance. In this paper we follow the idea of learning optimal parameters for the task of graph matching, but instead of learning fixed parameters for the features used as done in [1, 2], we directly learn edge-specific kernel functions for each node pair, assuming that the setting of graph matching is a-priori known. Such a-priori knowledge is indeed available in several important computer vision applications like automated face alignment, model fitting and object localization.