  Given a rectilinear grid $G$, in which cells are either assigned a single
color, out of $k$ possible colors, or remain white, can we color white grid
cells of $G$ to minimize the total number of corners of the resulting colored
rectilinear polygons in $G$? We show how this problem relates to hypergraph
visualization, prove that it is NP-hard even for $k=2$, and present an exact
dynamic programming algorithm. Together with a set of simple kernelization
rules, this leads to an FPT-algorithm in the number of colored cells of the
input. We additionally provide an XP-algorithm in the solution size, and a
polynomial $\mathcal{O}(OPT)$-approximation algorithm.
