Analysis of Properties of Dyadic Patterns for the Fast Hough Transform

Simon M. Karpenko, Egor I. Ershov

Abstract: 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.