基于最小二乘法的椭圆拟合改进算法

Optimal ellipse fitting method based on least-square principle

基于最小二乘法研究了一种改进的椭圆拟合算法.最小二乘椭圆拟合算法,由于包含误差较大样本点在内的所有样本点都参与运算,所以会对椭圆拟合的最后结果产生偏差.针对这种情况,采用随机理论的思想,先随机选取6个点拟合椭圆,然后计算与此椭圆匹配的所有样本点个数.重复此过程一定次数,采用投票机制,匹配样本点多的椭圆即为最优椭圆,构造了一种快速准确剔除误差较大样本点的改进椭圆拟合算法,并在实际图像应用中验证了算法能够有效地处理包含有较大比例误差点的样本空间,拟合出具有高精度的椭圆,并且算法的速度能够满足实时性的要求.

The fragmental ellipse fitting algorithm based on least square was studied. The ellipse-constraint algebraic fitting always provides an elliptical solution, but the bias is inevitably added to result because the algorithm involves all the sample data including some much biased data. Based on this situation, the random theory was introduced. First, an ellipse was fitted by six points which were selected randomly. Then the number of points which match the ellipse was calculated. Repeating the process some times, according to the voting mechanism, the best ellipse is the ellipse whose matching point number is largest. A rapid algorithm with the ability to abandon the biased sample data was presented. The application of algorithm in a real-time image processing system demonstrates that this algorithm can efficiently fit an ellipse to experimental data including a significant percentage of gross errors and the rapidity of the algorithm can meet the requirement of real-time system.