An image processing method is presented that enables an efficient and robust separation of straight line-like structures from an isotropic background texture. The algorithm is based on a transform sequence mapping both image components onto two nearly disjoint and parameter invariant areas in the resulting transform domain. Applying a linear notch filter to the transformed image enables us to ascertain for each component of the discrete Fourier spectrum of the image, whether it contributes more to the line-like structures or more to the background. Based on this decision, the spectrum is split into two complementary and disjoint spectra, the inverse Fourier transforms of which are taken as estimates for both image components. In practical applications, the algorithm behaves robustly with respect to its parameters as well as to the assumptions made about the images.