Multiple-View Threedimensional Paper Sheet Reconstruction
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 developable surfaces 3d reconstruction