  We study the joint image of lines incident to points, meaning the set of
image tuples obtained from fixed cameras observing a varying 3D point-line
incidence. We prove a formula for the number of complex critical points of the
triangulation problem that aims to compute a 3D point-line incidence from noisy
images. Our formula works for an arbitrary number of images and measures the
intrinsic difficulty of this triangulation. Additionally, we conduct numerical
experiments using homotopy continuation methods, comparing different approaches
of triangulation of such incidences. In our setup, exploiting the incidence
relations gives both a faster point reconstruction and in three views more
accurate.
