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 reconstruction from three uncalibrated 1D views, independent of the number of point correspondences. The two distinct projective reconstructions are exactly related by a quadratic transformation with the three camera centers as fundamental points. Unique 2D reconstruction is possible only when the three camera centers are aligned. By Carlsson duality (1995), 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 demonstrated on numerical examples.