Ellipse fitting with hyperaccuracy

IEICE Transactions on Information and Systems

Volumn E89-D, Issue 10, 2006, Pages 2653-2660

  Kanatani, Kenichi ^a  

^a OKAYAMA UNIVERSITY   (Japan)

Author keywords

Ellipse fitting; Error analysis; Hyperaccuracy correction; KCR lower bound; Maximum likelihood estimation

Indexed keywords

ERROR ANALYSIS; INFORMATION THEORY; MAXIMUM LIKELIHOOD ESTIMATION;

ELLIPSE FITTING; HYPERACCURACY CORRECTION; KCR LOWER BOUND;

CURVE FITTING;

EID: 33750090729     PISSN: 09168532     EISSN: 17451361     Source Type: Journal    
DOI: 10.1093/ietisy/e89-d.10.2653     Document Type: Article

References (38)

1. S. Amari and M. Kawanabe, "Information geometry of estimating functions in semiparametric statistical models," Bernoulli, vol.3, no.1, pp.29-54, March 1997.
2. F.J. Bookstein, "Fitting conic sections to scattered data," Comput. Graph. Image Process., vol.9, no.1, pp.56-71, 1979.
3. J. Cabrera and P. Meer, "Unbiased estimation of ellipses by boot-strapping," IEEE Trans. Pattern Anal. Mach. Intell., vol.18, no.7, pp.752-756, July 1996.
4. N. Chernov and C. Lesort, "Statistical efficiency of curve fitting algorithms," Comput. Stat. Data Anal., vol.47, no.4, pp.713-728, Nov. 2004.
5. W. Chojnacki, M.J. Brooks, A. van den Hengel, and D. Gawley, "On the fitting of surfaces to data with covariances," IEEE Trans. Pattern Anal. Mach. Intell., vol.22, no.11, pp.1294-1303, Nov. 2000.
6. D.B. Cooper and N. Yalabik, "On the computational cost of approximating and recognizing nose-perturbed straight lines and quadratic arcs in the plane," IEEE Trans. Comput., vol.C-25, no. 10, pp.1020-1032, Oct. 1976.
7. B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, 1994.
8. T. Endoh, T. Toriu, and N. Tagawa, "A superior estimator to the maximum likelihood estimator on 3-D motion estimation from noisy optical flow," IEICE Trans. Inf. & Syst., vol.E77-D, no. 11, pp.1240-1246, Nov. 1994.
9. A. Fitzgibbon, M. Pilu, and R.B. Fisher, "Direct least square fitting of ellipses," IEEE Trans. Pattern Anal. Mach. Intell., vol.21, no.5, pp.476-480, May 1999.
10. J. Illingworth and J. Kittler, "The adaptive Hough transform," IEEE Trans. Pattern Anal. Mach. Intell., vol.9, no.5, pp.690-698, Sept. 1999.
11. D. Ioannou, W. Huda, and A.F. Laine, "Circle recognition through a 2D Hough transform and radius histogramming," Image Vis. Comput., vol.17, no.1, pp.15-26, Jan. 1999.
12. S.H. Joseph, "Unbiased least squares fitting of circular arcs," CVGIP: Models Image Process., vol.56, no.5, pp.424-432, Sept. 1994.
13. K. Kanatani, Geometric Computation for Machine Vision, Oxford University Press, Oxford, U.K., 1993.
14. K. Kanatani, "Statistical bias of conic fitting and renormalization," IEEE Trans. Pattern Anal. Mach. Intell., vol. 16, no.3, pp.320-326, Mgarch 1994.
15. K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice, Elsevier Science, Amsterdam, The Netherlands, 1996, reprinted by Dover, New York, 2005.
16. K. Kanatani, "Ellipse fitting with hyperaccuracy," Proc. 9th Euro Conf. Comput. Vision, vol.1, pp.484-495, Graz, Austria, May 2006.
17. K. Kanatani, "Cramer-Rao lower bounds for curve fitting," Graphical Models Image Process., vol.60, no.2, pp.93-99, March 1998.
18. K. Kanatani, "Further improving geometric fitting," Proc. 5th Int. Conf. 3-D Digital Imaging and Modeling, pp.2-13, Ottawa, Ontario, Canada, June 2005.
19. K. Kanatani and N. Ohta, "Automatic detection of circular objects by ellipse growing," Int. J. Image Graphics, vol.4, no.1, pp.35-50, Jan. 2004.
20. Y. Kanazawa and K. Kanatani, "Optimal conic fitting and reliability evaluation," IEICE Trans. Inf. & Syst., vol.E79-D, no.9, pp.1323-1328, Sept. 1996.
21. D. Keren, D. Cooper, and J. Subrahmonia, "Describing complicated objects by implicit polynomials," IEEE Trans. Pattern Anal. Mach. Intell., vol.16, no.1, pp.38-53, Jan. 1994.
22. A. Kukush, I. Markovsky, and S. Van Huffel, "Consistent estimation in an implicit quadratic measurement error model," Comput. Stat. Data Anal., vol.47, no.1, pp. 123-147, Aug. 2004.
23. A. Kukush and E.O. Maschlce, "The efficiency of adjusted least squares in the linear functional relationship," J. Multivariate Anal., vol.87, no.2, pp.261-274, Oct. 2003.
24. Y. Leedan and P. Meer, "Heteroscedastic regression in computer vision: Problems with bilinear constraint," Int. J. Comput. Vis., vol.37, no.2, pp. 127-150, June 2000.
25. M. Mühlich and R. Mester, "Unbiased errors-in-variables estimation using generalized eigensystem analysis," Proc. 2nd Workshop Statistical Methods in Video Processing, pp.38-49, Prague, Czech, May 2004.
26. N. Ohta, "Motion parameter estimation from optical flow without nuisance parameters," 3rd Int. Workshop on Statistical and Computational Theory of Vision, Nice, France, Oct. 2003, http://www.stat.ucla.edu/~sczhu/ Workshops/SCTV2003.html
27. T. Okatani and K. Deguchi, "Toward a statistically optimal method for estimating geometric relations from noisy data: Cases of linear relations," Proc. IEEE Conf. Comput. Vision Pattern Recog., vol.1, pp.432-439, Madison, WI, U.S.A., June 2003.
28. J. Porrill, "Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter," Image Vis. Comput., vol.8, no.1, pp.37-41, Feb. 1990.
29. V. Pratt, "Direct least-squares fitting of algebraic surfaces," Comput. Graph., vol.21, no.4, pp.145-152, July 1987.
30. G. Roth and M.D. Levine, "Extracting geometric primitives," CVGIP: Image Understand., vol.58, no.1, pp.1-22, July 1993.
31. G. Roth and M.D. Levine, "Geometric primitive extraction using a genetic algorithm," IEEE Trans. Pattern Anal. Mach. Intell., vol.16, no.9, pp.901-905, Sept. 1994.
32. P.L. Rosin and G.A.W. West, "Nonparametric segmentation of curves into various representations," IEEE Trans. Pattern Anal. Mach. Intell., vol.17, no. 12, pp. 1140-1153, Dec. 1995.
33. R. Safee-Rad, I. Tchoukanov, B. Benhabib, and K.C. Smith, "Accurate parameter estimation of quadratic curves from gray-level images," CVGIP: Image Understand., vol.54, no.2, pp.259-274, Sept. 1991.
34. P.D. Sampson, "Fitting conic sections to "very scattered" data: An iterative refinement of the Bookstein algorithm," Comput. Graph. Image Process., vol.18, no.1, pp.97-108, Jan. 1982.
35. G. Taubin, "Estimation of planar curves, surfaces, and non-planar space curves defined by implicit equations with applications to edge and range image segmentation," IEEE Trans. Pattern Anal. Mach. Intell., vol.13, no.11, pp.1115-1138, Nov. 1991.
36. S. Tsuji and F. Matsumoto, "Detection of ellipses by a modified Hough transform," IEEE Trans. Comput., vol.C-27, no.8, pp.777-781, Aug. 1978.
37. M. Werman and D. Keren, "A Bayesian method for filtering parametric and nonparametric models to noisy data," IEEE Trans. Pattern Anal. Mach. Intell., vol.23, no.5, pp.528-534, May 2001.
38. H.K. Yuen, J. Illingworth, and J. Kittler, "Detecting partially occluded ellipses using the Hough transform," Image Vis. Comput., vol.7, no. 1, pp.31-37, Feb. 1989.