A novel application of the Hough transform (HT) neighborhood approach to collinear segment detection was proposed in [1]. It, however, suffered from one major weakness in that it could not provide an effective solution to the case of segment intersection. This paper analyzes a vital prerequisite step, disturbance elimination in the Hough space, and shows why, this method alone, is incapable of distinguishing the true segment endpoints. To address the problem, a unique HT butterfly separation method is proposed in this correspondence, as an essential complement to the above publication.

In this paper, we extend our previously proposed line detection method to line segmentation using a so-called unite-and-divide (UND) approach. The methodology includes two phases, namely the union of spectra in the frequency domain, and the division of the sinogram in Radon space. In the union phase, given an image, its sinogram is obtained by parallel 2D multilayer Fourier transforms, Cartesian-to-polar mapping and 1D inverse Fourier transform. In the division phase, the edges of butterfly wings in the neighborhood of every sinogram peak are firstly specified, with each neighborhood area corresponding to a window in image space. By applying the separated sinogram of each such windowed image, we can extract the line segments. The division Phase identifies the edges of butterfly wings in the neighborhood of every sinogram peak such that each neighborhood area corresponds to a window in image space. Line segments are extracted by applying the separated sinogram of each windowed image. Our experiments are conducted on benchmark images and the results reveal that the UND method yields higher accuracy, has lower computational cost and is more robust to noise, compared to existing state-of-the-art methods.