Robust 3D Car Shape Estimation from Landmarks in Monocular Image

The reconstruction of 3D object shape from monocular image is inherently an illposed problem. And it suffers significant performance degradation when large errors are present. In this paper, we propose a robust model to estimate 3D shape from 2D landmarks with unknown camera pose. The 3D shape of the object is assumed as a linear combination of predefined shape basis. To handle severely contaminated observations, we explicitly model the outliers as sparse noise. The objective function hence is nonconvex and non-smooth constrained on Stiefel manifold, where the coupling of the unknown shape representation coefficients and camera pose makes it more difficult to solve. We then propose a numerical algorithm based on Alternative Direction Method of Multipliers to optimize it. We set the orthogonality constraints into the smooth sub-problem, which admits a closed-form solution. The proposed algorithm can achieve convergence rapidly. Experimental results both in controlled experiments and on real data show that, the proposed method outperforms the other methods.