We investigate the problem of estimating the 3D shape of an object defined bya set of 3D landmarks, given their 2D correspondences in a single image. Asuccessful approach to alleviating the reconstruction ambiguity is the 3Ddeformable shape model and a sparse representation is often used to capturecomplex shape variability. But the model inference is still a challenge due tothe nonconvexity in optimization resulted from joint estimation of shape andviewpoint. In contrast to prior work that relies on a alternating scheme withsolutions depending on initialization, we propose a convex approach toaddressing this challenge and develop an efficient algorithm to solve theproposed convex program. Moreover, we propose a robust model to handle grosserrors in the 2D correspondences. We demonstrate the exact recovery property ofthe proposed method, the advantage compared to the nonconvex baseline methodsand the applicability to recover 3D human poses and car models from singleimages.
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