Analysis of properties of dyadic patterns for the fast Hough transform

We obtain an estimate for the maximum deviation from a geometric straight line to a discrete (dyadic) pattern approximating this line which is used for computing the fast Hough transform (discrete Radon transform) for a square image with side $n=2^p$, $p\in\mathbb{N}$. For $p$ even, the maximum deviation amounts to ${p}/{6}$. An important role in the proof is played by analysis of subtle properties of a simple combinatorial object, an array of cyclic shifts of an arbitrary binary number.