Fast estimation of slopes of linear and quasi-linear structures in noisy background, using Fourier methods

We present a fast algorithm for slope detection on gray scale images, based on 2D Fourier transform and standard filters; this may be used for line or edge detection. Our approach is based on the calculation of “energy” per direction of the image, thus obtaining the “energy spectrum on slope  ” (θ)(θ). This exhibits local maxima at the points where θθ equals the slopes of linear or quasi-linear segments within the image, yet it is not affected by their position within it. The process thus outlined has certain advantages as regards its efficiency of linear structure detection, compared to the Radon and Hough transforms. It was motivated by the study of astrophysical images (solar dynamic radio spectra) which necessitated the introduction of a method for fast extraction of “drifting structures”, since they appear as linear or quasi-linear segments on these spectra.