基于几何对称性的椭圆拟合算法

Ellipse Fitting Algorithm Based on Geometric Symmetry

针对椭圆视觉检测精度不易控制、检测效率低的问题,该文提出一种基于椭圆几何对称性的椭圆检测算法。通过与椭圆边界相切的两根平行切线,提取椭圆边界中关于中心点对称的两个切点,通过两个切点的坐标可以得到椭圆中心点的坐标,由椭圆的几何性质可知两切点间最大的距离即为长轴长,两切点间最小的距离即为短轴长。采用二分法迭代逼近椭圆的长短半轴,通过计算长轴处两切点连接的直线与水平轴的夹角即可拟合出椭圆方程。经实验验证,该文提出的算法精度高、计算量小、拟合精度可调,在保证拟合精度的同时,提升了椭圆检测效率。

Aiming at the problems that ellipse vision detection accuracy is difficult to control and detection efficiency is low,this paper proposes an ellipse detection algorithm based on ellipse geometric symmetry.Two parallel tangent lines that are tangent to the boundary of the ellipse are used to extract two tangent points that are symmetrical about the center point in the boundary of the ellipse.The coordinates of the center point of the ellipse can be obtained by the coordinates of the two tangent points.The longest distance between the points is the long axis length,and the shortest distance between the two tangent points is the short axis length.The long and short semi-axes of the ellipse are approximated by the dichotomy method.The angle can be fitted to the ellipse equation.The experimental verification shows that the algorithm proposed in this paper has high accuracy,small calculation amount and adjustable fitting accuracy.While ensuring the fitting accuracy,it improves the ellipse detection efficiency.