CVPR 2009 – In Defense of Orthonormality Constraints for Nonrigid Structure from Motion

Ijaz Akhter, Yaser Sheikh, Sohaib Khan
IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2009
(Oral, 4.1% acceptance rate)

Abstract

In factorization approaches to nonrigid structure from motion, the 3D shape of a deforming object is usually modeled as a linear combination of a small number of basis shapes. The original approach to simultaneously estimate the shape basis and nonrigid structure exploited orthonormality constraints for metric rectification. Recently, it has been asserted that structure recovery through orthonormality constraints alone is inherently ambiguous and cannot result in a unique solution. This assertion has been accepted as conventional wisdom and is the justification of many remedial heuristics in literature. Our key contribution is to prove that orthonormality constraints are in fact sufficient to recover the 3D structure from image observations alone. We characterize the true nature of the ambiguity in using orthonormality constraints for the shape basis and show that it has no impact on structure reconstruction. We conclude from our experimentation that the primary challenge in using shape basis for nonrigid structure from motion is the difficulty in the optimization problem rather than the ambiguity in orthonormality constraints.

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Text Reference:

Ijaz Akhter, Yaser Sheikh, Sohaib Khan,
"In Defense of Orthonormality Constraints for Nonrigid Structure from Motion",
in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,
CVPR 2009, Miami, Florida, 20-25 June 2009

Bibtex Reference:

@inproceedings{akhter2009defense,
  title={In defense of orthonormality constraints for nonrigid structure from motion},
  author={Akhter, I. and Sheikh, Y. and Khan, S.},
  booktitle={Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on},
  pages={1534--1541},
  year={2009},
  organization={IEEE}
}