Two-way ambiguity in 2D projective reconstruction from three uncalibrated 1D images

We show that there is, in general, a two-way ambiguity for 2D projective re construction from three uncalibrated 1D views, independent of the number of point correspondences. The two distinct projective reconstructions are exa ctly related by a quadratic transformation with the three camera centers as fundamental points. Unique 2D reconstruction is possible only when the thr ee camera centers are aligned. By Carlsson duality, there is a dual two-way ambiguity for 2D projective reconstruction from six point correspondences, independent of the number of 1D views. The theoretical results are demonst rated on numerical examples.