Circle Detection Using a Gabor Annulus

We present a novel circle detection technique based on the desirable properties of Gabor wavelet filters. Circles are found frequently in nature, as perfect circular structures provide an optimal area-to-perimeter ratio. The ability to accurately detect circles is therefore useful in a range of practical image processing applications. In the case of circular features identified by strong edges, techniques such as the Circular Hough Transform (CHT) can be used to identify the circle’s centre location. However in real applications it is common to encounter circular features where edges are not clear, and some radial pattern may instead identify the feature. Work by Atherton and Kerbyson [1] focussed on assessing the CHT and modifications to the technique. This includes an ‘Annulus’ version of the CHT which uses a single accumulator space for multiple radii, and a Phase Coded Orientation Annulus (PCOA) which incorporates edge orientation. Gabor wavelet filters are used in a large number of image processing tasks, for example in texture analysis [3] and face recognition [2, 4]. Gabor wavelet filters are a method of extracting the spatial location of underlying frequencies within an image. It is this useful property which acts as the basis for our new filter design aimed at extracting circular or symmetrical features within an image, where clear edges may be absent or only partially present. Our proposed filter aims to use the ability of Gabor wavelets to detect image features and patterns at specific scales and orientations in order to detect circular features. The proposed Gabor Annulus technique therefore offsets the traditional Gabor filter by a radius which wraps around the origin, and is defined as follows: