3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach
  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. 
Xiaowei Zhou, Spyridon Leonardos, Xiaoyan Hu, Kostas Daniilidis
cs.CV