Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach

We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable shape model and a sparse representation is often used to capture complex shape variability. But the model inference is still a challenge due to the nonconvexity in optimization resulted from joint estimation of shape and viewpoint. In contrast to prior work that relies on a alternating scheme with solutions depending on initialization, we propose a convex approach to addressing this challenge and develop an efficient algorithm to solve the proposed convex program. Moreover, we propose a robust model to handle gross errors in the 2D correspondences. We demonstrate the exact recovery property of the proposed method, the advantage compared to the nonconvex baseline methods and the applicability to recover 3D human poses and car models from single images.