This work is intended to provide a multifractal approach to the problem of edge detection in images. We show that an alternative description of images, based on the multifractal characterization of the signal, can be used instead of the classical approach that involves smoothing of the discrete data in order to compute derivatives. We focus on the study of edge detection using measures defined as functions of the grey level values in the neighborhood of a given pixel. Each measure is studied through the way it reacts to different types of edges and noise added to the image. Finally, we mention how the use of the multifractal spectrum (A, f(A)) may lead to a global approach to the problems of edge detection and region extraction.