Abstract: In order to detect accurate locations and boundaries of elliptical objects on images，an ellipse fitting method based on non-linear least squares is presented.Based on the boundary points of the object，by minimizing the Euclidean distance between fitting ellipse and boundary points，this method manages to get an ellipse that is defined by 5 parameters：the center coordinate，azimuth，length of semi major axis and semi minor axis，so that this ellipse is optimal in the sense of non-linear least squares.In practice，especially in the application of pupil feature extraction，this method obtains accurate locations and boundaries of pupils by eliminating the interferences caused by reflections，eyelashes and eyelids.Experimental results demonstrate that this method achieve good performance in terms of accuracy and robustness.

Key words: ellipse fitting, non-linear least squares, pupil

摘要： 为了在图像中确定椭圆目标精确的位置和边界，提出了一种基于非线性最小二乘的椭圆拟合方法。该方法在得到目标边界点的基础上，通过最小化拟合椭圆与边界点之间的欧氏距离，确定出由椭圆中心坐标、长半轴和短半轴长度、旋转角度共5个参数定义的椭圆，使得这一椭圆在非线性最小二乘意义下是最优的。在实际应用中，特别是人眼图像的瞳孔提取中，这种方法能够排除反光、睫毛、眼皮等的干扰，得到较为精确的瞳孔位置和边界。仿真实验和实际数据计算的结果表明，提出的方法有良好的准确性和鲁棒性。

关键词: 椭圆拟合, 非线性最小二乘, 瞳孔