caa a22 4500 467914877 CHVBK 20180406152859.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s11263-005-3678-x doi (NATIONALLICENCE)springer-10.1007/s11263-005-3678-x 3D Structure Recovery and Unwarping of Surfaces Applicable to Planes [Elektronische Daten] [Nail Gumerov, Ali Zandifar, Ramani Duraiswami, Larry Davis] 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. Springer Science + Business Media, Inc., 2006 3D structure recovery nationallicence unwarping nationallicence applicable surface nationallicence differential geometry nationallicence single view nationallicence Gumerov Nail Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut Zandifar Ali Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut Duraiswami Ramani Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut Davis Larry Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut International Journal of Computer Vision Kluwer Academic Publishers 66/3(2006-03-01), 261-281 0920-5691 66:3<261 2006 66 11263 https://doi.org/10.1007/s11263-005-3678-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-005-3678-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gumerov Nail Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 700 1- Zandifar Ali Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 700 1- Duraiswami Ramani Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 700 1- Davis Larry Perceptual Interfaces and Reality Lab, University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 66/3(2006-03-01), 261-281 0920-5691 66:3<261 2006 66 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer