Geometric least squares fitting of circle and ellipse

被引:26
|
作者
Ahn, SJ [1 ]
Rauh, W [1 ]
机构
[1] Fraunhofer Inst Mfg Engn & Automat IPA, D-70569 Stuttgart, Germany
关键词
orthogonal distances fitting; circle fitting; ellipse fitting; orthogonal contacting point; singular value decomposition; nonlinear least squares; Gauss-Newton iteration;
D O I
10.1142/S0218001499000549
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The least squares fitting of geometric features to given points minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. For the geometric fitting of circle and ellipse, robust algorithms are proposed which are based on the coordinate descriptions of the corresponding point on the circle/ellipse for the given point, where the connecting line of the two points is the shortest path from the given point to the circle/ellipse.
引用
收藏
页码:987 / 996
页数:10
相关论文
共 50 条
  • [1] Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola
    Ahn, SJ
    Rauh, W
    Warnecke, HJ
    [J]. PATTERN RECOGNITION, 2001, 34 (12) : 2283 - 2303
  • [2] GEOMETRIC INTERPRETATION AND PRECISION ANALYSIS OF ALGEBRAIC ELLIPSE FITTING USING LEAST SQUARES METHOD
    Kurt, O.
    Arslan, O.
    [J]. ACTA GEODAETICA ET GEOPHYSICA HUNGARICA, 2012, 47 (04): : 430 - 440
  • [3] Geometric interpretation and precision analysis of algebraic ellipse fitting using least squares method
    O. Kurt
    O. Arslan
    [J]. Acta Geodaetica et Geophysica Hungarica, 2012, 47 : 430 - 440
  • [4] ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method
    Prasad, Dilip K.
    Leung, Maylor K. H.
    Quek, Chai
    [J]. PATTERN RECOGNITION, 2013, 46 (05) : 1449 - 1465
  • [5] A DIRECT METHOD FOR LEAST-SQUARES CIRCLE FITTING
    MOURA, L
    KITNEY, R
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 1991, 64 (01) : 57 - 63
  • [6] CIRCLE FITTING BY LINEAR AND NONLINEAR LEAST-SQUARES
    COOPE, ID
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1993, 76 (02) : 381 - 388
  • [7] Phase Offset Estimation using Least Squares Ellipse Fitting technique
    Sarankumar, B.
    Ong, L. T.
    [J]. 2013 7TH INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING AND COMMUNICATION SYSTEMS (ICSPCS), 2013,
  • [8] Geometric matching of circular features by least squares fitting
    Borkowski, J
    Matuszewski, BJ
    Mroczka, J
    Shark, LK
    [J]. PATTERN RECOGNITION LETTERS, 2002, 23 (07) : 885 - 894
  • [9] LEAST SQUARES FITTING OF A GREAT CIRCLE THROUGH POINTS ON A SPHERE
    DEWITTE, L
    [J]. COMMUNICATIONS OF THE ACM, 1960, 3 (11) : 611 - 613
  • [10] Application of least-squares fitting of ellipse and hyperbola for two dimensional data
    Lawiyuniarti, M. P.
    Rahmadiantri, E.
    Alamsyah, I. M.
    Rachmaputri, G.
    [J]. 1ST INTERNATIONAL CONFERENCE OF EDUCATION ON SCIENCES, TECHNOLOGY, ENGINEERING, AND MATHEMATICS (ICE-STEM), 2018, 948