We investigate the problem of estimating the 3D structure of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. To alleviate the reconstruction ambiguity, a widely used approach is to assume the unknown structure as a linear combination of predefined basis shapes and the sparse representation is usually adopted to capture complex shape variability. While this approach has proven to be successful in many applications, a challenging issue remains, i.e., the joint estimation of structure and viewpoint requires to solve a nonconvex optimization problem. Previous methods often adopt an alternating minimization scheme to alternately update the structure and viewpoint, and the solution depends on initialization and might be stuck at local optimum. In this paper, we propose a convex approach to addressing this issue 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 model, its merits compared to alternative methods and the applicability to recover 3D human poses and car shapes from real images.
Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach.
X. Zhou, M. Zhu, S. Leonardos, K. Daniilidis.
3D Shape Estimation from 2D Landmarks: A Convex Relaxation Approach.
X. Zhou, S. Leonardos, X. Hu, K. Daniilidis.
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015.
Matlab code — the MATLAB implementation of the algorithms introduced in the journal version of our work and several demonstration examples.