Circle detection using Hough transform filters

A novel formulation of the circle Hough transform (CHT) is introduced which enables the detection of circles of different radii to be made using a single parameter space. We formulate the CHT as one or more convolution operations. Comparisons are made between conventional CHT techniques, formulated as filters, and a novel complex vector CHT. This technique exploits both edge orientation and distance from an edge point coded as complex phase. We present results that show that the novel phase and orientation CHT has a positional accuracy of ~±2 pixels at good signal to noise ratios (SNR) down to ~-16 dB. Using orientation alone, the positional accuracy is poorer falling to ~±10 pixels but at SNR levels of ~-25 dB