Uncalibrated 1D projective camera and 3D affine reconstruction of lines

We describe a linear algorithm to recover 3D affine shape/motion from line correspondences over three views with uncalibrated affine cameras. The key idea is the introduction of a one-dimensional projective camera. This converts the 3D affine reconstruction of "lines" into 2D projective reconstruction of "points". Using the full tensorial representation of three uncalibrated 1D views, we prove that the 3D affine reconstruction of lines from minimal data is unique up to a re-ordering of the views. 3D affine line reconstruction can be performed by properly rescaling image coordinates instead of using projection matrices. The algorithm is validated on both simulated and real image sequences.