A Triple-Stage Robust Ellipse Fitting Algorithm Based on Outlier Removal

Ellipse fitting is a fundamental yet critical task in computer vision, and the development of robust and accurate algorithms is crucial for various applications. In this study, we propose a triple-stage robust ellipse fitting algorithm to address the challenges posed by noise and outliers in the input data. Specifically, to overcome the sensitivity of existing methods to outliers, we introduce an adaptive outlier removal (AOR) algorithm. This algorithm dynamically removes outliers based on the probability density of all data points, eliminating the need for manual parameter adjustment and enhancing robustness to outliers. Furthermore, we tackle the issue of multiple ellipses in the input data by projecting the filtered points into the polar coordinate system. The points are then divided into equal intervals based on the polar angle, facilitating linear clustering to identify the point sets belonging to candidate ellipses, which helps to avoid erroneous fits and improve accuracy. Finally, to avoid solving the geometric distance between the point and the quadratic curve, a simplified ellipse fitting objective function and its corresponding optimization scheme are developed, in which the ellipse parameters are iteratively solved. To verify the universality and accuracy of the algorithm, we tested it on both synthetic data and real-world images from various scenarios with state-of-the-art approaches. Additionally, experiments have been carried out on a physical spacecraft pose measurement platform. The experimental results demonstrate that the algorithm exhibits excellent performance in terms of fitting accuracy and robustness, with a position estimation error of less than 2 mm and an attitude estimation error of less than 0.1°.