Multiview structure from motion in trajectory space

Most nonrigid objects exhibit temporal regularities in their deformations. Recently it was proposed that these regularities can be parameterized by assuming that the nonrigid structure lies in a small dimensional trajectory space. In this paper, we propose a factorization approach for 3D reconstruction from multiple static cameras under the compact trajectory subspace representation. Proposed factorization is analogous to rank-3 factorization of rigid structure from motion problem, in transformed space. The benefit of our approach is that the 3D trajectory basis can be directly learned from the image observations. This also allows us to impute missing observations and denoise tracking errors without explicit estimation of the 3D structure. In contrast to standard triangulation based methods which require points to be visible in at least two cameras, our approach can reconstruct points, which remain occluded even in all the cameras for quite a long time. This makes our solution especially suitable for occlusion handling in motion capture systems. We demonstrate robustness of our method on challenging real and synthetic scenarios.