  Let $\Omega \subset \mathbb{R}^2$ and let $\mathcal{L} \subset \Omega$ be a
one-dimensional set with finite length $L =|\mathcal{L}|$. We are interested in
minimizers of an energy functional that measures the size of a set projected
onto itself in all directions: we are thus asking for sets that see themselves
as little as possible (suitably interpreted). Obvious minimizers of the
functional are subsets of a straight line but this is only possible for $L \leq
\mbox{diam}(\Omega)$. The problem has an equivalent formulation: the expected
number of intersections between a random line and $\mathcal{L}$ depends only on
the length of $\mathcal{L}$ (Crofton's formula). We are interested in sets
$\mathcal{L}$ that minimize the variance of the expected number of
intersections. We solve the problem for convex $\Omega$ and slightly less than
half of all values of $L$: there, a minimizing set is the union of copies of
the boundary and a line segment.
