DONOSER ET AL.: EDGE-SPECIFIC KERNELS FOR GRAPH MATCHING 1 Learning Edge-Specific Kernel Functions For Pairwise Graph Matching Michael Donoser 1 donoser@icg.tugraz.at Martin Urschler 2 martin.urschler@cfi.lbg.ac.at Horst Bischof 1 bischof@icg.tugraz.at 1 Institute for Computer Graphics and Vision Graz University of Technology, Austria 2 Ludwig Boltzmann Institute for Clinical Forensic Imaging Graz, Austria Abstract In this paper we consider the pairwise graph matching problem of finding correspon- dences between two point sets using unary and pairwise potentials, which analyze local descriptor similarity and geometric compatibility. Recently, it was shown that it is possi- ble 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 func- tions 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 opti- mization problem. Experiments on automatically aligning a set of faces and feature-point based localization of category instances demonstrate the value of the proposed method. 1 Introduction Graphs are frequently used as underlying representation for various computer vision tasks like object localization [18], action recognition [10] or 3D reconstruction [23]. In all these applications, nodes in general represent local features in the image and edges correspond to spatial relations between them. The goal of graph matching is to find correspondences between the nodes of two provided graphs, analyzing local descriptor similarity (unary po- tentials) and spatial relations between the nodes e. g. pairwise relations [15] or sometimes higher-order relations, for example analyzing triangles [14]. Graph matching has become widely used in several applications including tracking [13], shape matching [3] or object detection [18]. Various approaches for efficiently solving this NP-hard problem in an approximated manner are available, as e. g. spectral techniques [9], probabilistic methods [24] or the graduated assignment method [11]. Surprisingly, only few papers focused on the important graph potentials themselves, which have a tremendous c  2011. The copyright of this document resides with its authors. It may be distributed unchanged freely in print or electronic forms.