CIRCLE FITTING BY LINEAR AND NONLINEAR LEAST-SQUARES

被引:146
作者
COOPE, ID
机构
[1] Department of Mathematics, University of Canterbury, Christchurch
关键词
CURVE FITTING; CIRCLE FITTING; TOTAL LEAST SQUARES; NONLINEAR LEAST SQUARES;
D O I
10.1007/BF00939613
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
The problem of determining the circle of best fit to a set of points in the plane (or the obvious generalization to n-dimensions) is easily formulated as a nonlinear total least-squares problem which may be solved using a Gauss-Newton minimization algorithm. This straight-forward approach is shown to be inefficient and extremely sensitive to the presence of outliers. An alternative formulation allows the problem to be reduced to a linear least squares problem which is trivially solved. The recommended approach is shown to have the added advantage of being much less sensitive to outliers than the nonlinear least squares approach.
引用
收藏
页码:381 / 388
页数:8
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