为了满足姿态测量时对椭圆合作目标的高精度定位要求, 提出了一种基于灰度导数加权的椭圆拟合算法(WGG)。首先, 在进行预处理之后的二值图像上提取初始边缘点, 采用简单的代数拟合方法得到椭圆参数; 其次, 考虑二值化过程中的不确定因素会对提取边界点带来干扰, 根据原始图像中边缘灰度的渐变性, 利用边缘点的灰度导数值对其进行高斯函数拟合; 最后, 求取每一个边缘点的正交相切点, 并构造优化目标函数求取椭圆最优参数。实验结果表明, 对测试图像提取出来的椭圆拟合误差能达到0.013像素以内, 与真实值点的平均误差为0.017像素, 真实图像中椭圆的平均拟合误差为0.0086像素。对于不同的外界环境该方法都能获得更精确的亚像素边缘和椭圆中心, 具有很高的精确性和鲁棒性。

In order to meet the need of high precision positioning of elliptical cooperative objects during attitude measurement, an ellipse fitting method based on the weighted gray gradient (WGG) was proposed. Firstly, the initial edge points on the pretreatment binary image can be obtained, and the parameters of the ellipse can be computed by the algebraic fitting. Secondly, the effect of many uncertain factors on extraction of the initial edge points should be considered. According to the gradual intensity change of the image, the gradient of gray value can be computed based on Gaussian Function. Lastly, after getting the orthogonal contact point of the edge points, the final optimization object function for the optimal ellipse parameters can be constructed. And then the optimal parameters can be computed. The results show that, the fitting precision of the ellipses in test image is about 0.011 pixel, and the point average error of the true value is 0.017 pixel. In real images, the fitting precision of the ellipses is about 0.0086 pixel. And in different environment, this method can get more accurate sub-pixel edge points and the ellipse center with favorable accuracy and robustness.