The authors extend the alternative Hough transform method for the detection of multiple circles proposed by the authors (1990) to the detection of multiple concentric circles contained in an image. The parameters of a circle are determined by the groups of three edge points on the circle. The extension of the proposed rules to search for the three edge points ensures that every member of a group will be on the same circle, either on the inner circle or on the outer one, instead of some of them lying on the inner circle and some of them lying on the outer one. The application of the proposed method to a noisy gray-scale image containing washers shows that the clusters representing circle centers in the parameter space are much more compact than those obtained by the original Hough method for circle detection without involving postprocessing operations.<>

A novel approach for circle detection based on the Hough transform is presented. It avoids the use of trigonometric functions in the transform equations. Instead of using traditional circle parameterization, which involves gradient direction information, this method uses three edge points to accumulate evidence for circle centers. The method can be extended to the detection of multiple circles where the gradient direction information is only used as a guide to select candidate edge points. A set of rules is proposed for the selection of triple edge points to define circle parameters which can guarantee that the points selected will not be on different circles. The responses for different circles produced in the parameter space using the proposed method are shown to be more compact around the true centers of the circles, thus, removing the need for postprocessing in the parameter space. The application of this method not only reduces the processing time, but also avoids the detection inaccuracy caused by the edge gradient direction errors

The time and storage requirements for the general Hough transform rise exponentially with increases in the resolution of the image and the parameter space. A recent attempt at decreasing these requirements is the adaptive Hough transform, AHT1. But when used to detect images containing more than one shape, the AHT is inaccurate in the determination of the ‘best peak’ locations in the parameter space, and is also vulnerable to clusters of noise. Because all the features in the image space are mapped into the parameter space, the algorithm is computationally intensive. This paper shows how a ‘labelling’ method can be combined with the AHT to solve those problems. Its parallel implementation allows for successful detection of multiple circles, such as those found in many practical industrial applications.