A large class of segmentation processes is based on edge detection, often performed by gradient computation. This is reliable when one can approximate the signal by a differentiable function, which is not the case for singularities such as corners or junctions. Besides, one has to use different filters to detect step-edge or line singularity model. We present a method to detect those singularities based on multifractal theory. This approach presents several advantages: it allows to do all the computations directly on the discrete signal, without any underlying regularity hypothesis; we obtain a set of low level tools able to detect any kind of singularity; this method is reliable on natural images, as shown by a complete study of noise effect and examples on natural scenes.