LEAST-SQUARES FITTING OF CIRCLES AND ELLIPSES
LEAST-SQUARES FITTING OF CIRCLES AND ELLIPSES
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DOI：
10.1007/bf01934268
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发表时间：
1994-12-01
影响因子：
1.5
通讯作者：
STREBEL, R
中科院分区：
文献类型：
--
作者：
GANDER, W;GOLUB, GH;STREBEL, R
在计算机图形学、坐标气象学、石油工程、统计学等许多应用领域中，圆和椭圆与平面上给定点的拟合是一个问题。在过去，已经给出了在不最小化到给定点的几何距离的情况下，在某种最小二乘意义下拟合圆和椭圆的算法。在这篇文章中，我们给出了几种算法来计算到给定点的距离平方和最小的椭圆。将这些算法与经典的SIMPLE算法和迭代算法进行了比较。圆和椭圆可以用代数表示，即由形式为F(X)=0的方程表示。如果一个点在曲线上，那么它的坐标x是函数F的零。或者，曲线可以用参数形式表示，这很适合于最小化距离的平方和。
Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g., computer graphics, coordinate meteorology, petroleum engineering, statistics. In the past, algorithms have been given which fit circles and ellipses in some least-squares sense without minimizing the geometric distance to the given points. In this paper we present several algorithms which compute the ellipse for which the sum of the squares of the distances to the given points is minimal. These algorithms are compared with classical simple and iterative methods. Circles and ellipses may be represented algebraically, i.e., by an equation of the form F(x) = 0. Ifa point is on the curve, then its coordinates x are a zero of the function F. Alternatively, curves may be represented in parametric form, which is well suited for minimizing the sum of the squares of the distances.