  We present an algebraic study of line correspondences for pinhole cameras, in
contrast to the thoroughly studied point correspondences. We define the line
multiview variety as the Zariski closure of the image of the map projecting
lines in 3-space to tuples of image lines in 2-space. We prove that in the case
of generic camera matrices the line multiview variety is a determinantal
variety and we provide a complete set-theoretic description for any camera
arrangement. We investigate basic properties of this variety such as dimension,
smoothness, and multidegree. Finally, we give experimental results for the
Euclidean distance degree and robustness under noise for the triangulation of
lines.
