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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.