Template-based paper reconstruction from a single image is well posed when the rulings are parallel

We deal with the 3D reconstruction of deformed paperlike surfaces given a template and a single perspective image, for which the internal camera parameters are known. The general problem is ill-posed. We show that when the surface rulings are parallel the problem is well-posed. Given a procedure to recover the rulings direction, this particular problem is equivalent to the reconstruction of a 2D curve seen from a set of ID camera pairs given a ID template. Paper can be physically modeled by exploiting local properties. This allows us to formulate the reconstruction problem by non linear variational optimization. We provide experimental results which validate our approach on simulated and real data.

[1]  Vincent Lepetit,et al.  Fast Non-Rigid Surface Detection, Registration and Realistic Augmentation , 2008, International Journal of Computer Vision.

[2]  Matthew Turk,et al.  A Morphable Model For The Synthesis Of 3D Faces , 1999, SIGGRAPH.

[3]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Pierre Gurdjos,et al.  Shape from Contour for the Digitization of Curved Documents , 2007, ACCV.

[5]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Mads Nielsen,et al.  A Variational Algorithm For Motion Compensated Inpainting , 2004, BMVC.

[7]  Larry S. Davis,et al.  3D Structure Recovery and Unwarping of Surfaces Applicable to Planes , 2006, International Journal of Computer Vision.

[8]  Adrien Bartoli,et al.  A Quasi-Minimal Model for Paper-Like Surfaces , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[9]  Vincent Lepetit,et al.  Deformable Surface Tracking Ambiguities , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[10]  Pau Gargallo,et al.  Minimizing the Reprojection Error in Surface Reconstruction from Images , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[11]  H. Pottmann,et al.  Computational Line Geometry , 2001 .

[12]  Timothy K. Shih,et al.  Digital Inpainting - Survey and Multilayer Image Inpainting Algorithms (Keynote Paper) , 2005 .

[13]  Vincent Lepetit,et al.  Real-time nonrigid surface detection , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[14]  Luc Van Gool,et al.  Dense matching of multiple wide-baseline views , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[15]  Jan Erik Solem.  Variational Problems and Level Set Methods in Computer Vision - Theory and Applications , 2006 .