3-D curve reconstruction from uncalibrated cameras

There has been considerable work recently on the problem of reconstruction of 3D points sets from two images, taken by uncalibrated cameras. However, the point correspondence has to be given. In this paper we deal with reconstruction of curves rather than points. While we need the correspondence between curves, this is an easier problem because curves are far fewer and more distinctive than points. We derive a simple and general reconstruction method, based on an invariant coordinate system. We then apply it to non-coplanar conics and to combinations of a 3D conic with points. 3D cubics are also discussed. Unlike previous work we do not need to know the epipolar geometry; we recover it from the images.