Non-rigid structure from motion with complementary rank-3 spaces

Non-rigid structure from motion (NR-SFM) is a difficult, underconstrained problem in computer vision. This paper proposes a new algorithm that revises the standard matrix factorization approach in NR-SFM. We consider two alternative representations for the linear space spanned by a small number K of 3D basis shapes. As compared to the standard approach using general rank-3K matrix factors, we show that improved results are obtained by explicitly modeling K complementary spaces of rank-3. Our new method is positively compared to the state-of-the-art in NR-SFM, providing improved results on high-frequency deformations of both articulated and simpler deformable shapes. We also present an approach for NR-SFM with occlusion.