Single Image Pop-Up from Discriminatively Learned Parts

We introduce a new approach for estimating a fine grained 3D shape and continuous pose of an object from a single image. Given a training set of view exemplars, we learn and select appearance-based discriminative parts which are mapped onto the 3D model through a facility location optimization. The training set of 3D models is summarized into a set of basis shapes from which we can generalize by linear combination. Given a test image, we detect hypotheses for each part. The main challenge is to select from these hypotheses and compute the 3D pose and shape coefficients at the same time. To achieve this, we optimize a function that considers simultaneously the appearance matching of the parts as well as the geometric reprojection error. We apply the alternating direction method of multipliers (ADMM) to minimize the resulting convex function. Our main and novel contribution is the simultaneous solution for part localization and detailed 3D geometry estimation by maximizing both appearance and geometric compatibility with convex relaxation.