The Coherent Circle Hough Transform T.J. Atherton and D.J. Kerbyson Department of Computer Science, University of Warwick, Coventry, UK. Abstract We introduce a novel formulation of the Circle Hough Transform that we call the Coherent Circle Hough Transform. The technique uses phase to code for radii of circles. The usual simplifications of the Circle Hough Transform (CHT) are used in which lines pointing away from edge points are plotted rather than circles. Intersections of these "spokes" accumulate edge magnitude, or edge "energy", near the centres of circles. We introduce the use of a complex accumulator space and allow each spoke to vary in phase along its length. The spokes are in phase near the centre of circles and out of phase elsewhere. The spokes generated by noise are in random phase and destructively interfere. We present results for an isolated circle with additive white Gaussian noise for both the conventional Energy CHT and the new Coherent CHT. The results demonstrate that the technique reduces the mean and variance of the background level in the accumulator array, that the peak to background level improves, and that the peak width is reduced improving localisation of circle centres. 1 Introduction The extension we describe here is novel and builds on earlier work on the Circle Hough Transform (CHT) by many others (Duda 1972, Kimme 1975, Sklansky 1978, Ballard 1982, Davies 1988, Yuen 1989, Leavers 1992), and on work by the authors on fast implementations of the closely related "Spoke Filter" (Minor 1981, Atherton 1990). The use of phase is now accepted as important in other areas, notably stereo (eg Langley 1990, Wilson 1992), and motion (eg Langley 1992). The notion of coherent integration, using phase, is widely accepted, eg in radar, as a superior technique (in terms of noise behaviour) to non-coherent integration, using energy or magnitude alone (eg. Woodward 1964, Levanon 1988). The technique we outline here has the advantages of more robust behaviour under additive noise, and sharper peaks in the accumulator array (Davies 1992), when compared with traditional energy based CHT's. 2 The Circle Hough Transform 2.1 The Origins of the Circle Hough Transform The CHT (Duda 1972, Kimme 1975, Sklansky 1978, Ballard 1982, Davies 1988, Yuen 1990) aims to find circular patterns of a given radius R within images. The Hough Transform achieves this detection by a technique that is related to matched filtering of the image. Hough Transforms have a number of desirable features: • they are integrative in nature • quantifiable behaviour under noise • can detect partially obscured or low contrast objects • their computational complexity is known BMVC 1993 doi:10.5244/C.7.27