On a Fast Hough/Radon Transform as a Compact Summation Scheme over Digital Straight Line Segments

Abstract

The Hough transform, interpreted as the discretization of the Radon transform, is a widely used tool in image processing and machine vision. The primary way to speed it up is to employ the Brady–Yong algorithm. However, the accuracy of the straight line discretization utilized in this algorithm is limited. In this study, we propose a novel algorithm called ASD2 that offers fast computation of the Hough transform for images of arbitrary sizes. Our approach adopts a computation scheme similar to the Brady–Yong algorithm but incorporates the best possible line discretization for improved accuracy. By employing the Method of Four Russians, we demonstrate that for an image of size n×n where n=8q and q∈N, the computational complexity of the ASD2 algorithm is O(n8/3) when summing over O(n2) digital straight line segments.