We propose a novel edge detection algorithm with sub-pixel accuracy based on annihilation of signals with finite rate of innovation. We show that the Fourier domain annihilation equations can be interpreted as spatial domain multiplications. From this new perspective, we obtain an accurate estimation of the edge model by assuming a simple parametric form within each localised block. Further, we build a locally adaptive global mask function (i.e, our edge model) for the whole image. The mask function is then used as an edge- preserving constraint in further processing. Numerical experiments on both edge localisations and image up-sampling show the effectiveness of the proposed approach, which out- performs state-of-the-art method.