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It is well known that edges have a wide variety of intensity profiles. Current edge detecion strategies are generally based on one or at most a very few intensity profiles. Some strategies require the use of a detector 'tuned' to the profile of the edge under consideration, thereby implementing a matched filter. Since the edge profile is unknown a priori, many detectors are used at each pixel. The problem is then to decide which detector output is to be believed. This is the response combination problem . Ifthe profile changes along the edge, these strategies either detect more than one edge, displaced from the actual edge location, or break the edge into segments, losing connectivity information. The problem with these edge detection approaches is that they invariably incorporate a profiledependent edge model, either implicitly or explicitly. Further, they make little use of the 2dimensional information inherent in the image. The proposed algorithm addresses both of these issues. Our edge model is based on three assumptions: 1) edge detection and edge localization are two distinct operations, 2) large magnitudes of second directional derivatives of intensity exist in the close neighbourhood of valid edges, and 3) the variation in orientation of edge elements (edgels) in the close neighbourhood of edges is very low since the directions which maximize the second directional derivatives at all pixels in a small neighbourhood of the edge are similar. Research in human visual psychophysics and constraints on the dynamic intensity range of practical imaging systems support assumptions 1 and 2. Assumption 3 is based on the spatial coherence of three-dimensional objects, and the corresponding spatial coherence of their images. Thus, in the proposed algorithm, edge detection is the task of locating narrow regions or edge ribbons containing edgels having sufficiently similar orientations at which the magnitude of the second directional derivative of intensity is maximized. The consistency of edgel orientation is shown to be a measure of the local signal to noise ratio. Edge localization is performed by cornputing the centroid of the distribution of second directional derivative magnitudes over segments of the edge ribbon which span its width, and for which edge! orientation is sufficiently similar. Use of the centroid for edge localization permits sub-pixel resolution. Psychophysical evidence supports this localization paradigm.
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