Analysis of Properties of Dyadic Patterns for the Fast Hough Transform

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.