Least Squares Fitting of Circles and Ellipses to Measured Data

BIT Numerical Mathematics

Volumn 39, Issue 1, 1999, Pages 176-191

  Watson, G A ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Conics; Least squares fit; Measured data

Indexed keywords

EID: 0043232750     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022381510996     Document Type: Article

References (21)

1. P. T. Boggs, R. H. Byrd and R. B. Schnabel, A stable, and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. Stat. Comp., 8 (1987), pp. 1052-1078.
2. F. L. Bookstein. Fitting conic sections to scattered data, Computer Graphics and Image Processing. 9 (1979), pp. 56-71.
3. J. P. Boyle and R. L. Dykstra, A method for finding projections onto the intersection of convex sets in Hilbert spaces, in Advances in Order Restricted Statistical Inference, Lecture Notes in Statistics, Springer, New York, 1985, pp. 28-47.
4. B. P. Butler, A. B. Forbes and P. M. Harris, Algorithms for geometric tolerance assessment, NPL Report DITC 228/94, Teddington, UK, 1994.
5. A. B. Forbes, Least-squares best fit geometric elements, in Algorithms for Approximation II, J. C. Mason and M. G. Cox, eds, Chapman and Hall, London, 1990, pp. 311-319.
6. N. Gaffke and R. Mathar, A cyclic projection algorithm via duality, Metrika, 36 (1989), pp. 29-54.
7. W. Gander, G. H. Golub and R. Strebel, Fitting of circles and ellipses: least square solution, BIT, 34 (1994), pp. 556-577.
8. H.-P. Helfrich and D. Zwick. A trust region method for implicit orthogonal distance regression, Numer. Algorithms, 5 (1993), pp. 535-545.
9. F. L. Hulting, Discussion contribution to the paper by M. M. Dowling, P. M. Griffin, K.-L. Tsui and C. Zhou, Statistical issues in geometric feature inspection using coordinate measuring machines, Technometrics 39 (1987), pp. 18-20.
10. I. Kasa, A circle fitting procedure and its error analysis, IEEE Trans. Instr. Measurement, 25 (1976), pp. 8-14.
11. V. Pratt, Direct least-squares fitting of algebraic surfaces, Computer Graphics, 21 (1987), pp. 145-152.
12. P. L. Rosin, A note on the least squares fitting of ellipses, Pattern Recognition Letters, 14 (1993), pp. 799-808.
13. D. M. Sourlier, Three-dimensional Feature-Independent Bestfit in Coordinate Metrology, PhD Dissertation, Swiss Federal Institute of Technology, Zürich, 1995.
14. H. Späth, Orthogonal least squares fitting by conic sections, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Van Huffel, ed., SIAM, Philadelphia, 1997, pp. 259-264.
15. H. Späth, Least squares fitting of ellipses and hyperbolas, Comput. Statist., 12 (1997), pp. 329-341.
16. H. Späth, Least squares fitting by circles, Computing, 57 (1996), pp. 179-185.
17. H. Späth, Orthogonal squared distance fitting with parabolas, in IMAGS-GAMM International Symposium on Numerical Methods and Error Bounds, G. Alefeld and J. Herzberger, eds., Akademie-Verlag, Berlin, 1996, pp. 261-269.
18. R. Strebel, D. Sourlier and W. Gander, A comparison of orthogonal least squares fitting in coordinate metrology, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Van Huffel, ed., SIAM, Philadelphia, 1997, pp. 249-258.
19. J. M. Varah, Least squares data fitting with implicit functions, BIT, 36 (1996), pp. 842-854.
20. G. A. Watson, Fitting conic sections to measured data, Proceedings of the Conference on Approximation Theory, Nashville, USA, January 1998 (to appear).
21. D. S. Zwick, Applications of orthogonal distance, regression in metrology, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Van Huffel, ed., SIAM, Philadelphia, 1997, pp. 265-272..