Annihilation-driven localised image edge models

We propose a novel edge detection algorithm with sub-pixel accuracy based on annihilation of signals with finite rate of innovation [1, 2]. 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.