Study on Ellipse Detection Method Based on KMPE Loss Function

For point set containing noise and outliers, the existing ellipse detection methods have low detection accuracy. Aiming at this problem, an ellipse detection method based on kernel mean p-power error (KMPE) loss function is proposed. Firstly, the point set to be detected is pre-processed according to the 3$\sigma$ criterion, and the noise points and outliers with large random errors are filtered out. Secondly, KMPE loss function is introduced, and according to distance constraint of each point on the ellipse to its focuses, a robust nonlinear optimization model of ellipse detection based on KMPE is established. Thirdly, success-history based parameter adaptation for differential evolution (SHADE) algorithm is adopted to solve the optimization model, and the initial estimated parameters of the detected ellipse is obtained. And the data points are divided into inliers and outliers according to the initial estimated parameters. Finally, the SHADE algorithm is adopted again to optimize the optimization model with inliers, and the accuracy estimated parameters of the detected ellipse can be obtained. Experimental results show that the proposed method has high accuracy of ellipse detection, and can effectively suppress the influence of noise and outliers on ellipse detection accuracy.