A Convex Approach for Non-rigid Structure from Motion Via Sparse Representation

This paper presents a convex solution for simultaneously recovering 3D non-rigid structures and camera motions from 2D image sequences based on sparse representation. Most existing methods rely on low rank assumption. However, it will lead to poor reconstruction for objects with strong local deformation. Also, when camera motion is unknown, there is no convex solution for non-rigid structure from motion (NRSfM). In order to solve this problem, we estimate non-rigid structures by sparse representation. In this paper, we estimate camera motions through a sparse spectral-norm minimization approach, and then a fast l1-norm minimization algorithm is introduced to reconstruct 3D structures. Both of them are convex, therefore, our method gives a global optimum. Our method can handle objects with strong local deformation and also doesn't need low rank prior. Experimental results show that our method achieves state-of-the-art reconstruction performance on CMU benchmark dataset.