We approach recognition in the framework of deformable shape matching, relying on a new algorithm for finding correspondences between feature points. This algorithm sets up correspondence as an integer quadratic programming problem, where the cost function has terms based on similarity of corresponding geometric blur point descriptors as well as the geometric distortion between pairs of corresponding feature points. The algorithm handles outliers, and thus enables matching of exemplars to query images in the presence of occlusion and clutter. Given the correspondences, we estimate an aligning transform, typically a regularized thin plate spline, resulting in a dense correspondence between the two shapes. Object recognition is handled in a nearest neighbor framework where the distance between exemplar and query is the matching cost between corresponding points. We show results on two datasets. One is the Caltech 101 dataset (Li, Fergus and Perona), a challenging dataset with large intraclass variation. Our approach yields a 45% correct classification rate in addition to localization. We also show results for localizing frontal and profile faces that are comparable to special purpose approaches tuned to faces.