ELSEVIER Pattern Recognition Letters 16 (1995) 667-677 Pattern Recognition Letters An adaptive approach to scale selection for line and edge detection M. Concetta Morrone a,b,*, Anacleto Navangione a,c, David Burr a,d a Istituto di Neuroflsiologia del CNR, Via S. Zeno 51, Pisa, Italy b Scuola Normale Superiore and University ofPisa, Pisa, Italy c Dipartimento di Fisiologia, Universit~ di Ferrara, Ferrara, Italy d Dipartimento di Psicologia, Universith di Roma, Rome, Italy Received 15 June 1993; revised 15 October 1994 Abstract One of the standard problems of edge- and line-detecting algorithms is to determine the most appropriate size of the convolution-operator for the particular task, maximising the conflicting goals of resolution and sensitivity. Here we suggest a novel approach to scale selection, where the scale size varies dynamically with the convolution output: the stronger the output, the smaller the spatial scale. This principle has been applied to two types of feature-detection algorithms, and shown to perform well for both one- and two-dimensional images. Keywords: Edge detection; Feature detection; Adaptive algorithms; Local energy function; Quadrature filters; Visual receptive field size 1. Introduction The first stage of most techniques of line and edge detection is to convolve the image with linear operators of limited bandwidth, then search for peaks or zero-crossings in the output (Canny, 1986; Marr and Hildreth, 1980). Using operators of limited bandwidth has certain practical advantages, but poses the problem of what scale the operators should be. The larger the scale of a band-limited operator, the more it integrates information over space, improving signal-to-noise levels, and thereby increasing sensi- tivity. However, the price paid for the integration is * Corresponding author. the loss of spatial resolution. In other words, there exists an inherent tradeoff between sensitivity and resolution, and strategies need be devised to 0ptimise this compromise (Canny, 1986). Some models of edge detection analyse the image over several spatial scales, by parallel cotwolution with operators of different sizes. This approach has several advantages (including the fact that ,it simu- lates to some extent human vision), but poses the problem of how the various outputs should be re- combined to yield a single feature map of the image. Several strategies exist (Marr and Hildretla, 1980; Watt and Morgan, 1985; Witkin, 1983; YUille and Poggio, 1985), but all tend to be computationally expensive, both because of the need for parallel convolution, and because of the recombination pro- cedures. 0167-8655/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-8655(95)00017-8