基于最小二乘法的椭圆拟合改进算法研究

为了提高数字图像中椭圆检测的不确定度和拟合精度,在最小二乘椭圆拟合算法的基础上进行了改进。该文对所有样本点进行编号并作归一化处理,通过归一化处理来提高算法的稳定性和鲁棒性。结合随机原理的思想,随机选取6点进行椭圆拟合,所选取的6个点中任意两点之间的距离大于一定的阈值,计算与拟合出与椭圆相匹配的所有样本点。重复该过程一定的次数,匹配样本点个数最多的椭圆即为最优的椭圆。对拟合出的椭圆所用的6个样本点进行坐标反归一化处理,计算出最终的椭圆参数。通过对给定图形进行拟合,验证了该改进算法有效性,与原算法相比,检测的不确定度和拟合精度得到了提高。

The study of an improved randomized algorithm for detecting ellipses based on least square approach

In this paper,an improved ellipse detection algorithm based on least square approach was proposed to improve the uncertainty and fitting precision of ellipse detection in digital image.All the sample points were numbered and normalized in this paper,through the normalized processing to improve the stability and robustness of the algorithm.Combining with the principle of random thoughts, and randomly select six points to fit ellipse,also the distance between any two points of the six selected points is greater than a certain threshold, the number of points which match the ellipse was calculated.Repeating the process for a certain number,the most optimal ellipse is the ellipse whose matching point number is largest,make the six sample points which fit the ellipses unnormalized at coordinate and calculate the final ellipse paraments.Through a given graph was fitted which verified the algorithm is effective,and compared with the original algorithm,the uncertainty of testing and the fitting precision is improved.