Power histogram for circle detection on images

• A new and simple circle detector based on the power theorem of circles is proposed.
• Transforms the edge pixel pairs into 1D power space, and detects peaks in power histogram for circle locating.
• Incorporates the inherent geometric properties of circle and generates only a few number of candidate circles for validation.
• A robust peak detection and cross-validation algorithm for enhancing the robustness of the method.
• Experiments on synthetic, hand-sketched and natural images are carried out.

The detection of circles from digital images is very important to shape recognition. In this paper, we propose and analyze a novel method, based on power histograms to detect circles in an image. The key idea is to transform an image into several power histograms that are computed from the pairwise distance products referring to the rays emanated from some reference points on the image. According to the circle power theorem, the edge pixels on a circle share the same circle powers with respect to an arbitrary point on the image. The peaks in the power histograms provide strong evidence for the existence of real circles. A multi-reference cross validation among various peaks can systematically remove randomness and eliminate false detections. Experimental results over several synthetic as well as natural images with varying ranges of complexity validate the efficacy of the proposed method in terms of its accuracy, simplicity, and robustness.