  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.
