A statistical analysis of the Delogne-Kåsa method for fitting circles

Digital Signal Processing: A Review Journal

Volumn 16, Issue 5, 2006, Pages 498-522

  Zelniker, Emanuel E ^a   Clarkson, I Vaughan L ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Circle fitting; Cram r Rao lower bound; Least squares; Maximum likelihood estimation; Moore Penrose inverse; Random matrices; Wishart distribution

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; GAUSSIAN NOISE (ELECTRONIC); MAXIMUM LIKELIHOOD ESTIMATION; MEASUREMENT ERRORS; MICROWAVE CIRCULATORS; STATISTICAL METHODS;

CIRCLE FITTING; CRAMÉR-RAO LOWER BOUND; LEAST SQUARES; MOORE PENROSE INVERSE; RANDOM MATRICES; WISHART DISTRIBUTIONS;

DIGITAL SIGNAL PROCESSING;

EID: 33747883515     PISSN: 10512004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dsp.2005.04.001     Document Type: Article

References (28)

1. Thom A. A statistical examination of the megalithic sites in Britain. J. Roy. Statist. Soc. Ser. A 118 (1955) 275-295
2. Robinson S.M. Fitting spheres by the method of least squares. Comm. ACM 4 (1961) 491
3. Crawford J.F. A non-iterative method for fitting circular arcs to measured points. Nucl. Instrum. Methods Phys. Res. 211 (1983) 223-225
4. Karimäki V. Effective circle fitting for particle trajectories. Nucl. Instrum. Methods Phys. Res. A 305 (1991) 187-191
5. Kåsa I. A circle fitting procedure and its error analysis. IEEE Trans. Instrum. Meas. 25 (1976) 8-14
6. Landau U.M. Estimation of a circular arc center and its radius. Comput. Vision Graph. Image Process. 38 (1986) 317-326
7. Chan N.N. On circular functional relationships. J. Roy. Statist. Soc. Ser. B 27 (1965) 45-56
8. Berman M., and Culpin D. The statistical behaviour of some least squares estimators of the centre and radius of a circle. J. Roy. Statist. Soc. Ser. B 48 (1986) 183-196
9. N. Chernov, C. Lesort, Least squares fitting of circles and lines, J. Math. Imaging Vision, in press
10. P. Delogne, Computer optimization of Deschamps' method and error cancellation in reflectometry, in: Proc. IMEKO-Symp. Microwave Measurements, Budapest, Hungary, 1972, pp. 117-123
11. Thomas S.M., and Chan Y.T. A simple approach to the estimation of circular arc center and its radius. Comput. Vision Graph. Image Process. 45 (1989) 362-370
12. Coope I.D. Circle fitting by linear and non-linear least squares. J. Optim. Theory Appl. 76 (1993) 381-388
13. Moura L., and Kitney R. A direct method for least-squares circle fitting. Comput. Phys. Comm. 64 (1991) 57-63
14. Umback D., and Jones K.N. A few methods for fitting circles to data. IEEE Trans. Instrum. Meas. 52 (2003) 1881-1885
15. Corral C.A., and Lindquist C.S. On implementing Kåsa's circle fit procedure. IEEE Trans. Instrum. Meas. 47 (1998) 789-795
16. Chan Y.T., and Thomas S.M. Cramér-Rao lower bound for estimation of a circular arc center and its radius. Graph. Models Image Process. 57 (1995) 527-532
17. Kanatani K. Cramér-Rao lower bounds for curve fitting. Graph. Models Image Process. 60 (1998) 93-99
18. Späth H. Least-square fitting by cirles. Computing 57 (1996) 179-185
19. Van Trees H.L. Detection, Estimation and Modulation Theory, Part 1 (1968), Wiley, New York
20. Ouellette D.V. Schur complements and statistics. Linear Algebra Appl. 36 (1981) 187-295
21. E.E. Zelniker, I.V.L. Clarkson, A statistical analysis of least squares circle-centre estimation, in: IEEE Int. Symp. Signal Process. Inform. Tech., Darmstadt, Germany, 2003
22. Golub G.H., and Van Loan C.F. Matrix Computations (1996), The Johns Hopkins Univ. Press, Baltimore, MD
23. Muirhead R.J. Aspects of Multivariate Statistical Theory (1982), Wiley, New York
24. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals Series and Products (2000), Academic Press, San Diego
25. Kanatani K. Statistical Optimization for Geometric Computation: Theory and Practice (1996), Elsevier Science, Amsterdam
26. N. Chernov, C. Lesort, Statistical efficiency of curve fitting algorithms, http://arxiv.org/abs/cs.CV/0301015, last date accessed: 27 April 2004
27. Rife D.C., and Boorstyn R.R. Single-tone parameter estimation from discrete-time observations. IEEE Trans. Inform. Theory 20 5 (1974) 591-598
28. Davis P.J. Circulant Matrices (1979), Wiley