一种基于最小二乘的不完整椭圆拟合算法

Fragmental ellipse fitting based on least square algorithm

研究了一种基于最小二乘的不完整椭圆拟合算法。基于几何距离的拟合算法可达到较高的拟合精度,但迭代过程敏感于初始条件;由于不完整的椭圆样本点及噪声的存在,简单线性拟合方法可能使拟合结果退化为开放的双曲线,引起拟合失败,基于椭圆约束的代数距离拟合方法可保证拟合结果一定是椭圆,从而为迭代提供适当的初值;利用多个待估计椭圆参数之间的相互约束,即使非常短的椭圆弧也可得到稳定的拟合结果。仿真结果与实际图像应用验证了算法的有效性。

The fragmental ellipse fitting algorithm based on least square is studied. Although the geometric fitting of ellipse offers high accuracy, the iteration process makes this fitting algorithm sensitive to the initial parameters. With very scattered data and high noise level, the simple linear fitting often yields unbounded hyperbola, a failed fitting. In contrast, the ellipse-constraint algebraic fitting always provides an elliptical solution and gives a proper initial estimate. Considering the parameter constraints on the position and shape of the ellipse, robust fitting result is obtained even for very short ellipse arc and high noise level. Simulation result and real image fitting are presented to validate the algorithm.