A Novel Subpixel Circle Detection Method Based on the Blurred Edge Model

Circle detection is a critical issue in computer vision and image processing. Whether in natural images or industrial images, the accuracy of circle detection has a significant impact on advanced vision applications. Conventional methods, such as circle Hough transform, random circle detection, and EDCircles, only reach pixel-level edge accuracy. This article proposes a subpixel circle detection method based on subpixel edges with accuracy of one-tenth of one pixel. All candidate circles are first detected by EDCircles. The circle scoring formula based on polarity, radius, and contour is then proposed to sort the detected circles, and the circle with the highest score is selected as the target. The 2-D subpixel calculation problem is transformed into the 1-D fitting problem, and the subpixel edge region is selected according to the gradient direction of the circular edge. To reduce the error of the step model and the real edge, the blurred edge model is proposed to fit the region. Subsequently, the parameters of the edge model are transformed into subpixel coordinates. To solve the problem that the traditional $L2$ -loss function is not robust to outliers, the Huber loss function is finally applied to the circle fitting, and the gradient descent method is adopted to calculate the circle parameters. Experiments on natural and industrial images show that the proposed method has good performance on robustness and accuracy.