A Computational Approach to Edge Detection
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The present manuscript aims to address and possibly solve three classical problems of edge detection: i - the detection of all step edges from a fine to a coarse scale; ii - the detection of thin bars, i.e. of roof edges; iii - the detection of corners and trihedral junctions. The proposed solution of these problems combines an extensive spatial filtering, inspired by the receptive field properties of neurons in the visual area V1, with classical methods of Computer Vision (Morrone & Burr 1988; Lindeberg 1998; Kovesi 1999) and newly developed algorithms. Step edges are computed by extracting local maxima from the energy summed over a large bank of odd filters of different scale and direction. Thin roof edges are computed by considering maxima of the energy summed over narrow odd and even filters along the direction of maximal response. Junctions are precisely detected by an appropriate combination of the output of directional filters. Detected roof edges are cleaned by using a regularization procedure and are combined with step edges and junctions in a Mumford-Shah type functional with self adaptive parameters, providing a nearly ideal edge detection and segmentation.