双同心椭圆弧的几何拟合方法

提出一种带有同心条件的双椭圆弧拟合方法。该方法利用椭圆几何定义得到的残差来衡量误差,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8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、长短轴比率较接近1.1、样本噪声较小的时候,算法较稳定、准确。该方法也可以扩展处理多个同心椭圆弧的拟合问题。

Fitting of double concentric elliptic arcs based ellipse's geometry definition

A fitting method is presented for the double concentric elliptic arcs.In the method，the fitting error is evaluated by the residual error reduced from the ellipse’s geometry definition，and the least-square equations are deduced，which 8 geometric parameters can be solved by iteration method from.Experiments’ result shows that the fitting method will be accurate and stable when the radian is larger，the rate between long axis and short axis is closer to 1.1，and the double elliptic arcs have the lower noise.In addition，the method can be simply extended to solve the fitting problem of several concentric fragmental ellipses.