  We investigate the problem of estimating the 3D shape of an object, given a
set of 2D landmarks in a single image. To alleviate the reconstruction
ambiguity, a widely-used approach is to confine the unknown 3D shape within a
shape space built upon existing shapes. While this approach has proven to be
successful in various applications, a challenging issue remains, i.e., the
joint estimation of shape parameters and camera-pose parameters requires to
solve a nonconvex optimization problem. The existing methods often adopt an
alternating minimization scheme to locally update the parameters, and
consequently the solution is sensitive to initialization. In this paper, we
propose a convex formulation to address this problem and develop an efficient
algorithm to solve the proposed convex program. We demonstrate the exact
recovery property of the proposed method, its merits compared to alternative
methods, and the applicability in human pose and car shape estimation.
