One of the most effective image processing techniques is the use of convolutional neural networks, where we combine intensity values at grid points in the vicinity of each point. To speed up computations, researchers have developed a dilated version of this technique, in which only some points are processed. It turns out that the most efficient case is when we select points from a sub-grid. In this paper, we explain this empirical efficiency proving that the sub-grid is indeed optimal – in some reasonable sense. To be more precise, we prove that all reasonable optimality criteria, the optimal subset of the original grid is either a sub-grid, or a sub-grid-like set.