We investigate the problem of estimating the 3D shape of an object, given aset of 2D landmarks in a single image. To alleviate the reconstructionambiguity, a widely-used approach is to confine the unknown 3D shape within ashape space built upon existing shapes. While this approach has proven to besuccessful in various applications, a challenging issue remains, i.e., thejoint estimation of shape parameters and camera-pose parameters requires tosolve a nonconvex optimization problem. The existing methods often adopt analternating minimization scheme to locally update the parameters, andconsequently the solution is sensitive to initialization. In this paper, wepropose a convex formulation to address this problem and develop an efficientalgorithm to solve the proposed convex program. We demonstrate the exactrecovery property of the proposed method, its merits compared to alternativemethods, and the applicability in human pose and car shape estimation.
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