Unbiased estimation of ellipses by bootstrapping

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 18, Issue 7, 1996, Pages 752-756

  Cabrera, Javier ^a   Meer, Peter ^a,b  

^a RUTGERS UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Bootstrap; Curve fitting; Implicit models; Low level processing

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; CURVE FITTING; ERRORS; IMAGE SEGMENTATION; MATHEMATICAL MODELS;

BOOTSTRAP; LOW LEVEL PROCESSING; NONLINEAR ESTIMATORS; UNBIASED ESTIMATION;

COMPUTER VISION;

EID: 0030196288     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.506797     Document Type: Article

References (24)

1. F.L. Bookstein, " Fitting Conic Sections to Scattered Data," Computer Graphics and Image Processing, vol. 9, pp. 56-71, 1979.
2. J. Cabrera and G.S. Watson, " Simulation Methods for Mean and Median Bias Reduction," Statistical Planning and Inference, to appear 1996.
3. J. Cabrera and L.T. FernhuU, " Applications of Von-Mises Expansions to the Mean and Median Bias Reduction Methods," Proc. 1995 ConJ. ISA, pp. 134-135, Beijmg, China, Aug. 1995.
4. J.M. Chambers and T.J. Hastie, Statistical Models in S. New York: Wadsworth, 1992.
5. K. Cho, P. Meer, and J. Cabrera, " Quantitative Evaluation of Performance through Bootstrapping: Edge Detection," IF.FF. Int'l Symp. Computer Vision, pp. 491-496, Coral Gables, Fla., Nov. 1995.
6. T. Ellis, A. Abbood, and B. Brillault, " Ellipse Detection and Matching with Uncertainty," Image Mid Vision Computing, vol. 10, pp. 271-276,1992.
7. B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, London: Chapman & Hall, 1993.
8. J.H. Friedman, " Multivariate Adaptive Regression Splines," The Annals of Statistics, vol. 19, pp. 1-141,1991.
9. W.A. Fuller, Measurement Error Models. New York: Wiley, 1987.
10. R.M. Haralick and L.G. Shapiro, Computer and Rannt Vision. Rpading, Mass.: Addison-Wesley, 1992.
11. A.K. Jain, R.C. Dubes, and C.-C. Chen. "Bootstrap Techniques for Error Estimation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, pp. 628-633,1987.
12. S.H- Joseph, " Unbiased Least Squares Fitting of Circular Arcs," CVGIP: Graphical Models and Image Processing, vol. 56, pp. 424-432, 1994.
13. K. Kanatani, Geometric Computation for Machine Vision. Oxford: Clarendon Press, 1993.
14. K. Kanatani, " Statistical Bias of Conic Fitting and Renormalization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, pp. 320-326, 1994.
15. Y. Kanazawa and K. Kanatani, " Reliability of Conic Fitting," Proc. Second Asian Conf. Computer Vision, Singapore, vol. Ill, pp. 397- 401, Dec. 1995
16. Q.-T. Luong and O. Faugeras, " The Fundamental Matrix: Theory, Algorithms, and Stability Analysis," Int'l J. Computer Vision, vol. 17, pp. 43-76,1996.
17. W.G. Manteigna, J.M.P. Sanchez, and J. Romo, " The Bootstrap-A Review," Computational Statistics, vol. 9, pp. 165-205,1994.
18. D.M. Politis and J.P. Romano, " Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions" The Annals of Statistics, vol. 22, pp. 2031-2050,1994.
19. J. Porrill, " Fitting Ellipses and Predicting Confidence Envelopes Using a Bias Corrected Kaiman Filter/' Image and Vision Computing, pp. 37-41,1990.
20. P.L. Rosin, " A Note on Least Squares Fitting of Ellipses," Pattern Recognition Letters, vol. 14, pp. 799-808,1993.
21. R. Safaee-Rad, I. Tchoukanov, B. Benhabib, and K.C. Smith, " Accurate Parameter Estimation of Quadratic Curves from GreyLevel Images," CVGIP: Image Understanding, vol. 54, pp. 259-274, 1991.
22. RA. Trusted, Elements of Statistical Computing. New York: Chapman & Hall, 1985.
23. VI. Werman and Z. Geyzel, " Fitting a Second Degree Curve in the Presence of Error," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 207-211,1995.
24. G.A. Young, " Bootstrap: More than a Stab in the Dark," Statistical Science, vol. 9, pp. 382-415, 1994; with discussion: R. Beran, B. Efron, P.M. Grambsch et al., D. Hinkley, M.P. Meredith and J.G. Morel, W. Navidi, M.J. Schervish.