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