Patteru Re~oWmi~m Vol 10. No. 6. pp 607 613, 1983. Prinled in Great Britain (~)31 3203X3 $3(~)+ qx~ Pergamon Press Lid ~ 1983 Pattern Recognition Society THE MAGNITUDE ACCURACY OF THE TEMPLATE EDGE DETECTOR J. KITTLI,P.., J. ]Lt.IN(iWORTH and K. PALIiR Technology Division, SERC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OXII 0QX, U.K. (Received 1 March 1983; received for publication 29 April 1983) Abstract--The magnitude accuracy of the template edge detector is studied under the assumption of a particular model for the image sensing device. It is shown that this computationally simple detector is more accurate than the Sobel detector. The effect of edge displacement on the detector output is then considered. Finally. a method for compensating the edge magnitude fluctuations due to edge displacement is proposed. Edge detection Sobel operator Magnitude accuracy Template detector Edge magnitude absorption I. INTRODUCTION The two main prerequisites of accurate and reliable automatic image analysis and interpretation are a low noise and distortion-free performance of the image forming device and accurate image segmentation. Before image segmentation can even be attempted, it is essential that the image at the output of the sensing device faithfully represents the sensed scene. To achieve a faithful representation of the imaged scene, it is necessary to model the characteristics of the sensing device and its response. The propagation properties of the media between the scene and the sensor in relation to the physical phenomenon used for image forming can also play a role which should not be ignored in modelling. Additional factors include the geometry of the sensing array, the viewing angle, method of illumi- nation and others. Based on the models for each of these various aspects of the image forming process, the data at the output of the sensing device can be appropriately corrected for the respective distortions. The reduction or elimination of noise and image enchancement by filtering, for instance, are also normally considered as integral parts of the problem of representation of the imaged scene. Once an image corrected for the various forms of distortion is acquired, its automatic analysis would proceed with image segmentation. This step results in partitioning the image into homogeneous parts in which picture elements have similar properties. The aim of this process is to separate an object in the scene from the background or from other objects that may be present. There are various approaches to image, segmen- tation depending on the pixel properties that charac- terise image segments. The simplest methods are grey level thresholding or colour slicing, but these are often inadequate in practical applications. Other possibi- lities involve the detection of local features, such as lines and shapes, or the global matching of an image with, for instance, the templates of objects it contains.t 1 ~ Objects may also be discernable from the back- ground or from each other by the presence of rapid image intensity changes which mark object boun- daries. A suitable image transform that enables us to detect these abrupt changes of grey level values is the gradient operation. Various implementations of this differentiation process which take into account other factors, such as object boundary continuity, noise, the inherent grey level discontinuity at the object boun- dary and the boundary directionality, then lead to specific edge detection algorithms, an abundance of which have been proposed in the literature. ~5 ~ The majority of edge detection algorithms fall into the category of local methods. A small window (mask, kernel) centered at a pixel is used to detect any local intensity variation which would be indicative of the presence of an edge at the pixel. As a typical example we can mention the Kirsch operator, ~8~ which is one of the first edge detectors suggested. The Hueckel operator ~9~ on the other hand is representative of regional methods where a step func- tion giving rise to an ideal edge is fitted to the pixel intensities in a region of interest. In global methods, ~1°' edge extraction isviewed as an image filtering problem. Another alternative is to detect edges sequentially using a line following algorithm. ~3~ Also, approaches based on dynamic programming and relaxation meth- ods have been considered for edge detection. ~11"12~ The purpose of this paper is to study the magnitude accuracy of the template edge detector. ~a~"~ This particular edge detector is very important because of its robustness and ease of implementation. The study will be based on the model of image acquisition devices considered by Abdou and Pratt, ~4~ lannino and Shapiro ~5~ and Kittler. ~3~6~ First, in Section 2. the 607