A Fast Hough Transform for the Parametrisation of Straight Lines using Fourier Methods

T he Hough transform is a useful technique in the detection of straight lines and curves in an image. Due to the mathematical similarity of the Hough transform and the forward Radon transform, the Hough transform can be computed using the Radon transform which, in turn, can be evaluated using the central slice theorem. This involves a two-dimensional Fourier transform, an x-y to rmapping and a 1D Fourier transform. This can be implemented in specialized hardware to take advantage of the computational savings of the fast Fourier transform. In this paper, we outline a fast and ecient method for the computation of the Hough transform using Fourier methods. The maxima points generated in the Radon space, corresponding to the parametrisation of straight lines, can be enhanced with a post transform convolutional ®lter. This can be applied as a 1D ®ltering operation on the resampled data whilst in the Fourier space, so further speeding the computation. Additionally, any edge enhancement or smoothing operations on the input function can be combined into the ®lter and applied as a net ®lter function.