  We study the following problem in computer vision from the perspective of
algebraic geometry: Using $m$ pinhole cameras we take $m$ pictures of a line in
$\mathbb P^3$. This produces $m$ lines in $\mathbb P^2$ and the question is
which $m$-tuples of lines can arise that way. We are interested in polynomial
equations and therefore study the complex Zariski closure of all such tuples of
lines. The resulting algebraic variety is a subvariety of $(\mathbb P^2)^m$ and
is called line multiview variety. In this article, we study its ideal. We show
that for generic cameras the ideal is generated by $3\times 3$-minors of a
specific matrix. We also compute Gr\"obner bases and discuss to what extent our
results carry over to the non-generic case.
