A NOTE ON THE LEAST-SQUARES FITTING OF ELLIPSES

被引：156
作者：
ROSIN, PL [1 ]
机构：
[1] CURTIN UNIV TECHNOL,SCH COMP SCI,COGNIT SYST GRP,PERTH,WA 6001,AUSTRALIA
来源：
PATTERN RECOGNITION LETTERS | 1993年 / 14卷 / 10期
关键词：
ELLIPSE; LEAST SQUARES FITTING; NORMALIZATION; CURVATURE BIAS; SINGULARITY; TRANSFORMATIONAL INVARIANCE;
D O I：
10.1016/0167-8655(93)90062-I
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The characteristics of two normalisations for the general conic equation are investigated for use in least squares fitting: either setting F = 1 or A + C = 1. The normalisations vary in three main areas: curvature bias, singularities, transformational invariance. It is shown that setting F = 1 is the more appropriate for ellipse fitting since it is less heavily curvature biased. Setting A + C = 1 produces more eccentric conics, resulting either in over-elongated ellipses or hyperbolae. Although the F = 1 normalisation is less well suited than the A + C = 1 normalisation with respect to singularities and transformational invariance both these problems are solved by normalising the data, shifting it so that it is centred on the origin before fitting, and then re-expressing the fit in the original frame of reference.
引用
收藏
页码：799 / 808
页数：10
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