TPAMI 2011 – Trajectory Space: A Dual Representation for Nonrigid Structure from Motion

| July 1, 2011

Ijaz Akhter, Yaser Sheikh, Sohaib Khan, Takeo Kanade
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 33, No 7, Jul 2011


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 basis 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).


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Text Reference
Ijaz Akhter, Yaser Sheikh, Sohaib Khan, Takeo Kanade
"Trajectory Space: A Dual Representation for Nonrigid Structure from Motion"
IEEE Transactions on Image Processing, Vol. 33, No. 7, pp. 1442 - 1456, July 2011

Bibtex Reference

  title={Trajectory space: A dual representation for nonrigid structure from motion},
  author={Akhter, I. and Sheikh, Y. and Khan, S. and Kanade, T.},
  journal={Pattern Analysis and Machine Intelligence, IEEE Transactions on},


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