Advanced Radon transform using generalized interpolated Fourier method for straight line detection

► The term “Multilayer fractional Fourier transform” is reinterpreted. ► The interpolated Fourier transform is generalized by adopting different scale factors. ► A method for detecting straight lines from a gray scale image is implemented. Straight line detection is common in computer vision. The Radon transform has received much attention for its efficiency and accuracy compared to the Hough transform. In this paper, a generalized interpolated Fourier transform, hereafter called GIFT, is proposed to speed up the Radon transform. Based on the GIFT, a methodology that can detect straight lines from a gray scale image without any pre-processing is implemented. Two contributions can be claimed. First, the recent work by Pan et al. is reinterpreted and implemented in a clearer way so the traditional Fourier transform can be interpolated to achieve an accurate sampling in the frequency domain. Second, the interpolated Fourier transform is further generalized with flexible parameter determination in two dimensions when applied to 2-D images. The experiments demonstrate that our proposed methodology outperforms the standard Radon transform with lower computational load and higher accuracy. The experiments also show that the GIFT line detector can compete against the random sample consensus, which is a robust estimator popularly used in the field of computer vision.