Fast scale space image decomposition

The removal of high frequencies from an image while retaining edges, is a complicated problem that has many solutions in the literature. Most of these solutions are, however, iterative and computationally expensive. In this paper, we introduce a direct method with three basic steps. In the first, the image is convolved with a Gaussian function of a defined size. In the second the gradients of the blurred image are compared with those of the original and a third gradient that is the minimum of the two at each pixel is composed. Finally, the combined gradient is integrated in the Fourier domain to obtain the result.