用最小二乘正交距离方法拟合双同心椭圆弧 *

提出一种带有同心条件的双椭圆弧拟合方法。该方法利用给定点到拟合椭圆弧的正交距离来衡量误差,建立关于误差的最小二乘方程 ,进而采用迭代方法求出描述双椭圆弧的八个参数。算法仿真实验研究了椭圆弧度、长短轴比率以及样本噪声对算法的影响 ,研究表明弧度越大、长短轴长度越接近、样本噪声越小 ,算法越稳定 ,参数估计越准确。该方法也可以推广应用于处理多个同心椭圆弧的拟合问题。

Using least-square orthogonal distance method to fit double concentric elliptical arcs

This paper presented a least-square orthogonal distance fitting method for double concentric fragmental ellipses. In the method, used the orthogonal distances between the given points and the fitting ellipse to evaluate the fitting error, and de-duced the least-square equations therefore solved eight geometric parameters from the equations by iteration method. Experi-mental results show that the larger radian, the closer length of two axis and the lower noise of samples will make the algorithm is more accurate and stable. In addition, the method can be easily extended to solve the fitting problem of several concentric elliptical arcs.