Bilinear spatiotemporal basis models
ACM Transactions on Graphics (TOG)
A unified view on deformable shape factorizations
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Learning spatially-smooth mappings in non-rigid structure from motion
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
3D rotation invariant decomposition of motion signals
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Application of heterogenous motion models towards structure recovery from motion
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
Multilinear Factorizations for Multi-Camera Rigid Structure from Motion Problems
International Journal of Computer Vision
Decomposition and dictionary learning for 3D trajectories
Signal Processing
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Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes. These bases are object dependent and therefore have to be estimated anew for each video sequence. In contrast, we propose a dual approach to describe the evolving 3D structure in trajectory space by a linear combination of basis trajectories. We describe the dual relationship between the two approaches, showing that they both have equal power for representing 3D structure. We further show that the temporal smoothness in 3D trajectories alone can be used for recovering nonrigid structure from a moving camera. The principal advantage of expressing deforming 3D structure in trajectory space is that we can define an object independent basis. This results in a significant reduction in unknowns and corresponding stability in estimation. We propose the use of the Discrete Cosine Transform (DCT) as the object independent basis and empirically demonstrate that it approaches Principal Component Analysis (PCA) for natural motions. We report the performance of the proposed method, quantitatively using motion capture data, and qualitatively on several video sequences exhibiting nonrigid motions, including piecewise rigid motion, partially nonrigid motion (such as a facial expressions), and highly nonrigid motion (such as a person walking or dancing).