Edge detection and ridge detection with automatic scale selection

When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image ope rators are applied. This article presents a systematic methodology for addr essing this problem. A mechanism is presented for automatic selection of sc ale levels when detecting one-dimensional image features, such as edges and ridges. A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An impor tant consequence of this definition is that it allows the scale levels to v ary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from t he third-order derivative in the gradient direction. For a certain way of n ormalizing these differential descriptors, by expressing them in terms of s o-called gamma-normalized derivatives, an immediate consequence of this def inition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at tine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge . Since the scale-space edge is defined from the intersection of two zero-cro ssing surfaces in scale-space, the edges will by definition form closed cur ves. This simplifies selection of salient edges, and a novel significance m easure is proposed, by integrating the edge strength along the edge. Moreov er, the scale information associated with each edge provides useful clues t o the physical nature of the edge. With just slight modifications, similar ideas can be used for formulating r idge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge. It is shown how the methodology can be implemented in terms of straightforw ard visual front-end operations, and the validity of the approach is suppor ted by theoretical analysis as well as experiments on real-world and synthe tic data.