Abstract: Image matching has been a central research topic in computer vision over the last decades. Typical approaches to correspondence involve matching feature points between images. In this paper, we present a novel problem for establishing correspondences between a sparse set of image features and a previously learned subspace model. We formulate the matching task as an energy minimization, and jointly optimize over all possible feature assignments and parameters of the subspace model. This problem is in general NP-hard. We propose a convex relaxation approximation, and develop two optimization strategies: naïve gradient-descent and quadratic programming. Alternatively, we reformulate the optimization criterion as a sparse eigenvalue problem, and solve it using a recently proposed backward greedy algorithm. Experimental results on facial feature detection show that the quadratic programming solution provides better selection mechanism for relevant features.