LAUSR

Estimating 3D shape of an object from 2D observations in a monocular image is fundamentally an inverse problem due to the ambiguity of the projection from 3D to 2D and becomes more challenging when there are undesirable outliers in the observations. In this paper, we develop a robust model to estimate 3D shape from 2D landmarks with an unknown camera pose. The 3D shape of the object is assumed as a linear combination of a group of prior shape bases. At the same time, we explicitly model the outliers as sparse noises to handle severely contaminated observations. The objective function is nonconvex and nonsmooth constrained on Stiefel manifold, where the coupling of underdetermined shape representation coefficients and camera pose makes it more difficult to solve. We first propose a numerical algorithm based on alternating direction method of multipliers for the no-outlier case. We set the orthogonality constraints into the smooth subproblem, which admits a closed-form solution, and the other subproblems are all well known and can be easily solved. We then extend this algorithm to the proposed robust model. The proposed algorithms can achieve convergence rapidly. The experimental results on both synthetic data and real data show that the proposed method outperforms the other methods.