When is it possible to project two sets of labeled points lying in a pair of projective planes to the same points on a projective line? Here one answer: such projections exist if and only if the two 2D point sets are themselves images of a common point set in 3D projective space. Furthermore, when the two sets of points are in general position, it is possible to give a complete description of the loci of pairs of projection centers. I will describe the roles of classical invariant theory, Cremona transformations, and geometric computer vision in this description.