Reconstruction tridimensionnelle multi-vues de papier Multiple-View Threedimensional Paper Sheet Reconstruction

and key words Smoothly bent paper-like surfaces are developable. They are however difficult to minimally parameterize since the number of meaningful parameters is intrinsically dependent on the actual deformation. Previous generative models are either incomplete, i.e. limited to subsets of developable surfaces, or depend on huge parameter sets. Our first contribution is a generative model governed by a quasi-minimal set of intuitive parameters, namely rules and angles. More precisely, a flat mesh is bent along guiding rules, while a number of extra rules controls the level of smoothness. The generated surface is guaranteed to be developable. The second contribution is an automatic multi-camera 3D reconstruction algorithm. First of all, the cameras and a sparse structure are reconstructed from the images using Structure-from-Motion method. A 2D parametrization of the reconstructed points is computed by dimensionality reduction. This parameterization is used to initialize the proposed model since it easily allows us to estimate the surface curvature. The initial model parameters are eventually tuned through model-based bundle-adjustment. Paper, 3D reconstruction, developable surfaces. traitement du signal 2008_volume 25_numero 3 167

[1]  Johannes Wallner,et al.  Approximation algorithms for developable surfaces , 1999, Comput. Aided Geom. Des..

[2]  Jean Duchon,et al.  Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces , 1976 .

[3]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[4]  T. Banchoff,et al.  Differential Geometry of Curves and Surfaces , 2010 .

[5]  Martin Peternell,et al.  Developable surface fitting to point clouds , 2004, Comput. Aided Geom. Des..

[6]  H. Pottmann,et al.  Approximation by ruled surfaces , 1999 .

[7]  Helmut Pottmann,et al.  Approximation of developable surfaces with cone spline surfaces , 1998, Comput. Aided Des..

[8]  Andrew W. Fitzgibbon,et al.  Bundle Adjustment - A Modern Synthesis , 1999, Workshop on Vision Algorithms.

[9]  Pascal Fua,et al.  Physically Valid Shape Parameterization for Monocular 3-D Deformable Surface Tracking , 2005, BMVC.

[10]  Larry S. Davis,et al.  Structure of Applicable Surfaces from Single Views , 2004, ECCV.

[11]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[12]  Meng Sun,et al.  A Technique for Constructing Developable Surfaces , 1996, Graphics Interface.

[13]  Maurizio Pilu.  Undoing paper curl distortion using applicable surfaces , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[14]  Tosiyasu L. Kunii,et al.  Bending and creasing virtual paper , 1994, IEEE Computer Graphics and Applications.

[15]  Jeanny Hérault,et al.  Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets , 1997, IEEE Trans. Neural Networks.

[16]  Andrew Zisserman,et al.  Multiple View Geometry , 1999 .

[17]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[18]  Maurizio Pilu,et al.  Undoing page curl distortion using applicable surfaces , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[19]  David S. Doermann,et al.  Flattening curved documents in images , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).