We propose a novel approach to point matching under large viewpoint and illumination changes that is suitable for accurate object pose estimation at a much lower computational cost than state-of-the-art methods. Most of these methods rely either on using ad hoc local descriptors or on estimating local affine deformations. By contrast, we treat wide baseline matching of keypoints as a classification problem, in which each class corresponds to the set of all possible views of such a point. Given one or more images of a target object, we train the system by synthesizing a large number of views of individual keypoints and by using statistical classification tools to produce a compact description of this view set. At run-time, we rely on this description to decide to which class, if any, an observed feature belongs. This formulation allows us to use a classification method to reduce matching error rates, and to move some of the computational burden from matching to training, which can be p...