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In Defense of Orthonormality Constraints for Nonrigid Structure from Motion

2009

Conference Paper

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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.

Author(s): Akhter, Ijaz and Sheikh, Yaser and Khan, Sohaib
Book Title: Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on
Pages: 2447-2453
Year: 2009

Department(s): Perceiving Systems
Bibtex Type: Conference Paper (inproceedings)
Paper Type: Conference

Organization: IEEE

Links: pdf

BibTex

@inproceedings{akhter2009defense,
  title = {In Defense of Orthonormality Constraints for Nonrigid Structure from Motion},
  author = {Akhter, Ijaz and Sheikh, Yaser and Khan, Sohaib},
  booktitle = {Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on},
  pages = {2447-2453},
  organization = {IEEE},
  year = {2009}
}