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ECCV
2004
Springer

Structure of Applicable Surfaces from Single Views

10 years 9 months ago
Structure of Applicable Surfaces from Single Views
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.
Nail A. Gumerov, Ali Zandifar, Ramani Duraiswami,
Added 15 Oct 2009
Updated 15 Oct 2009
Type Conference
Year 2004
Where ECCV
Authors Nail A. Gumerov, Ali Zandifar, Ramani Duraiswami, Larry S. Davis
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