Non-Rigid Structure-From-Motion on Degenerate Deformations With Low-Rank Shape Deformation Model

Non-rigid structure-from-motion (NRSfM) is the process of recovering time-varying 3D structures and poses of a deformable object from an uncalibrated monocular video sequence. Currently, most NRSfM algorithms utilize a non- degenerate assumption for non-rigid object deformations whereby the 3D structures of a non-rigid object can be assumed to be a linear combination of basis shapes with full rank three. Unfortunately, this assumption will produce extra degrees-of-freedom when the non-rigid object has some degenerate deformations with shape bases of rank less than three. These extra degrees-of-freedom will yield spurious shape deformations due to non-negligible noise in real applications, which will cause substantial reconstruction errors. To solve this problem, we propose a low-rank shape deformation model to represent 3D structures of degenerate deformations. When modeling degenerate deformations, the proposed model exploits the rank-deficient nature of degenerate deformations in addition to the low-rank property of non-rigid objects´ trajectories, thus providing a more accurate and compact representation compared with existing models. Based on this model, we formulate the NRSfM problem as two coherent optimization problems. These problems are solved with iterative non-linear optimization algorithms. Experiments on synthetic and motion capture data are conducted. The results exhibit the significant advantages of our approach over state-of-the-art NRSfM algorithms for the 3D recovery of non-rigid objects with degenerate deformations.