We introduce a new approach for estimating the 3D pose and the 3D shape 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 from the training set through a facil- ity location optimization. The training set of 3D models is summarized into a sparse set of shapes from which we can generalize by linear combination. Given a test picture, 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 minimizes simultaneously the geometric reprojection error as well as the appearance matching of the parts. We apply the alternating direction method of multipliers (ADMM) to minimize the resulting convex function. We evaluate our approach on the Fine Grained 3D Car dataset with superior performance in shape and pose errors. Our main and novel contribution is the simultaneous solution for part localization, 3D pose and shape by maximizing both geometric and appearance compatibility.
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