Classical geometrical approach to circle fitting - Review and new developments

Journal of Electronic Imaging

Volumn 12, Issue 1, 2003, Pages 179-193

  Rusu, Corneliu ^a,b   Tico, Marius ^c   Kuosmanen, Pauli ^a   Delp, Edward J ^d  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

^c NOKIA RESEARCH CENTER   (United States)

^d PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; CONFORMAL MAPPING; ERROR ANALYSIS; INVERSE PROBLEMS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; ROBUSTNESS (CONTROL SYSTEMS); SCATTERING;

CIRCLE FITTING; MEAN-SQUARE ERROR (MSE);

IMAGE ANALYSIS;

EID: 0037280974     PISSN: 10179909     EISSN: 1560229X     Source Type: Journal    
DOI: 10.1117/1.1525792     Document Type: Article

References (18)

1. V. Pratt, "Direct least-squares fitting of algebraic surfaces," Comput. Graph. 21(4), 145-152 (1987).
2. J. Pegna and C. Guo, "Computational metrology of the circle," in IEEE Proc. Computer Graphics International, pp. 350-363 (1998).
3. G. Vosselman and R. M. Haralick, "Performance analysis of line and circle fitting in digital images," in Proc. Workshop on Performance Characteristics of Vision Algorithms, Cambridge (Apr. 1996).
4. M. Berman and P. I. Somlo, "Efficient procedures for fitting circles and ellipses with application to sliding termination measurements," IEEE Trans. Instrum. Meas. IM-35(1), 31-35 (1986).
5. Z. Zhang, "Parameter estimation techniques: a tutorial with applications to conic fitting," Int. J. Image Vis. Comput. 15(1), 59-76 (1997).
6. G. N. Newsam and N. J. Redding, "Fitting the most probable curve to noisy observations," in IEEE Proc. ICIP'97, pp. 752-755 (1997).
7. W. Gander, G. H. Golub, and R. Strebel, "Least-squares fitting of circles and ellipses," BIT 34, 558-578 (1994).
8. P. S. Modenov and A. S. Parkhomenko, Geometric Transformations, Academic Press, New York (1965).
9. J. A. Brandon and A. Cowley, "A weighted least squares method for circle fitting to frequency response data," J. Sound Vib. 83(3), 419-424 (1983).
10. I. Kasa, "A circle fitting procedure and its error analysis," IEEE Trans. Instrum. Meas., 8-14 (Mar. 1976).
11. N. I. Chernov and G. A. Ososkov, "Effective algorithms for circle fitting," Comput. Phys. Commun. 33, 329-333 (1984).
12. C. A. Corral and C. S. Lindquist, "On implementing Kasa's circle fit procedure," IEEE Trans. Instrum. Meas. 47(3), 789-795 (1998).
13. G. Casella and R. L. Berger, Statistical Inference, Duxburry Press, Belmont, CA (1990).
14. M. Berman and D. Culpin, "The statistical behaviour of some least squares estimators of the centre and radius of a circle," J. R. Stat. Soc. Ser. B. Methodol. 48, 183-196 (1986).
15. M. Berman, "Large sample bias in least squares estimators of a circular arc center and its radius," Comput. Vis. Graph. Image Process. 45, 126-128 (1989).
16. Th. Caronnet, Exercise de geometrie-complements, Librarie Vuibert, Paris (1946).
17. H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, The Mathematical Association of America, Yale University, (1967).
18. W. Gander, G. H. Golub, and R. Strebel, "Fitting of circles and ellipses - least-squares solution," Technical Report 217, Institut fur Wisenschaftliches ETH Zurich, (June 1994).