Edge Detection and Ridge Detection with Automatic Scale Selection

• Authors: Tony Lindeberg
• Venue: International Journal of Computer Vision
• Year: 1998

When computing descriptors of image data,the type of information that can be extractedmay be strongly dependent on the scalesat which the image operators are applied. This article presents a systematic methodology foraddressing this problem. A mechanism is presented forautomatic selection of scale levelswhen detecting one-dimensional image features,such as edges and ridges.A novel concept of a scale-space edge is introduced, defined asa connected set of points in scale-space at which: (i) the gradientmagnitude assumes a local maximum in the gradient direction, and (ii)a normalized measure of the strength of the edge response is locallymaximal over scales. An important consequence of this definitionis that it allows the scale levels to vary along the edge. Twospecific measures of edge strength are analyzed in detail, thegradient magnitude and a differential expression derived from thethird-order derivative in the gradient direction. For a certainway of normalizing these differential descriptors, by expressing themin terms of so-called γ-normalized derivatives, animmediate consequence of this definition is that the edge detectorwill adapt its scale levels to the local imagestructure. Specifically, sharp edges will be detected at finescales so as to reduce the shape distortions due to scale-spacesmoothing, whereas sufficiently coarse scales will be selected atdiffuse edges, such that an edge model is a valid abstraction of theintensity profile across the edge.Since the scale-space edge is defined from the intersection oftwo zero-crossing surfaces in scale-space,the edges will by definition form closed curves. This simplifies selection of salient edges,and a novel significance measure is proposed,by integrating the edge strength along the edge. Moreover, the scale information associated with each edgeprovides useful clues to the physical nature of the edge.With just slight modifications, similar ideas can be used for formulatingridge detectors with automatic selection,having the characteristic property that the selected scales on a scale-space ridgeinstead reflect the width of the ridge.It is shown how the methodology can be implemented in terms of straightforward visual front-end operations,and the validity of the approach is supported by theoretical analysis aswell as experiments on real-world and synthetic data.