Circle, ellipse and parabola parametrisation using integral transforms

The standard Hough transform can be adapted to parametrise circles. The authors propose an approach which produces results significantly faster than by standard methods, whilst utilising the maximum amount of information in the image. Their circular disc detection algorithm uses two transforms to find the 3 parameters needed to define a circle. The first transforms into a parameter space locating disc centres, using a two-dimensional transform; the second, a one-dimensional transform, determines disc radius for each of the previously determined centres. This algorithm has been extensively tested with extremely good results. Ellipse detection, requiring 5 parameters, is considerably harder. However, the circular disc algorithms can act as a preprocessor giving very accurate values for ellipse location and orientation, along with estimates of the semi-major and minor axis.