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

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 nxn where n=8(q) and q?N, the computational complexity of the ASD2 algorithm is O(n(8/3)) when summing over O(n(2)) digital straight line segments.