International Journal of Computer Vision

, Volume 66, Issue 3, pp 261–281 | Cite as

3D Structure Recovery and Unwarping of Surfaces Applicable to Planes

  • Nail A. Gumerov
  • Ali Zandifar
  • Ramani Duraiswami
  • Larry S. Davis
Article

Abstract.

The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.

Keywords:

3D structure recovery unwarping applicable surface differential geometry single view 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Nail A. Gumerov
    • 1
  • Ali Zandifar
    • 1
  • Ramani Duraiswami
    • 1
  • Larry S. Davis
    • 1
  1. 1.Perceptual Interfaces and Reality LabUniversity of MarylandCollege ParkUSA

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