基于最小方差迭代圆拟合的立木胸径提取算法研究

A Iterative Circle Fitting Algorithm for Tree Diameter at Breast Height Based on Minimum Variance

为了提高基于二维激光数据的立木胸径提取算法的精度与稳定性,提出了一种基于最小方差的迭代圆拟合算法。该算法参照最小二乘法得到拟合圆的初始圆心坐标后,以降低半径向量的方差为目的,设定迭代步长,迭代后得到最终圆心坐标,圆心坐标与每个扫描数据点之间的平均距离为拟合半径。运用该算法对实际直径为680mm的立木激光数据进行胸径提取,并与常用的最小二乘圆拟合算法,Nlinfit算法,Taubin算法,Pratt算法进行比较表明,基于最小方差的迭代圆拟合算法得到的拟合圆的直径为728.944 18mm,其精度高于其他4种常用算法,且拟合圆直径的标准差为1.926 01,在5种算法拟合的过程中稳定性最好。

An iterative circle fitting algorithm based on minimum variance was proposed to improve the accuracy and stability of DBH extraction algorithm.The initial coordinate of circle center was obtained by referring to least square method.To reduce the variance of the radius vector,iteration step-size was set and iterated to establish the coordinate of circle center.The average distance between circle center coordinate and each scan data point was defined as fitting radius.Based on the algorithm,the diameter at breast height of a standing tree with an actual diameter of 680 mm was extracted;the radius of the fitting circle was729.944 18 mm.The result was compared with other four algorithms,such as least square circle fitting,Nlinfit,Taubin,and Pratt,the accuracy of the algorithm presented in this paper was the highest and most stable with the standard deviation of iteration diameter of 1.926 01,and the stability was best among the five algorithms.