  A line pattern in a free group $F$ is defined by a malnormal collection of
cyclic subgroups. Otal defined a decomposition space $\mathcal{D}$ associated
to a line pattern. We provide an algorithm that computes a presentation for the
\v{C}ech cohomology of $\mathcal{D}$, thought of as a $F$-module. This answers
a relative version of a question of Epstein about boundaries of hyperbolic
groups.
