Asymptotic global confidence regions for 3-D parametric shape estimation in inverse problems

IEEE Transactions on Image Processing

Volumn 15, Issue 10, 2006, Pages 2904-2919

  Ye, Jong Chul ^a   Moulin, Pierre ^b   Bresler, Yoram ^b  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Confidence regions; Cram r Rao bounds (CRBs); Exceedence probability; Maximum likelihood estimation (MLE); Random fields; Surface estimation

Indexed keywords

COMPUTER SIMULATION; INVERSE PROBLEMS; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; PROBABILITY; RANDOM PROCESSES;

CONVENTIONAL IMAGE RECONSTRUCTION; CRAMER-RAO BOUNDS (CRBS); EXCEEDENCE PROBABILITY; PIXEL-BASED IMAGE RECONSTRUCTION; RANDOM FIELDS; SURFACE ESTIMATION;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; CONFIDENCE INTERVAL; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; STATISTICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; CONFIDENCE INTERVALS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED;

EID: 33749171380     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2006.877524     Document Type: Article

References (30)

1. G. Farin, Curves and Surfaces for Computer Aided Geometric Design, 4th ed. San Diego, CA: Academic, 2001.
2. B. Horn, "Extended Gaussian images," Proc. IEEE, vol. 72, no. 12, pp. 1656-1678, Dec. 1984.
3. K. Kanatani, "Statistical bias of conic fitting and renormalization," IEEE Trans. Pattern Anal. Mach. Intell., vol. 16, no. 3, pp. 320-326, Mar. 1994.
4. H. L. VanTrees, Detection, Estimation and Modulation Theory, Part I: Detection, Estimation, and Linear Modulation Theory. New York: Wiley, 1968.
5. J. C. Ye, Y. Bresler, and P. Moulin, "Asymptotic global confidence regions in parametric shape estimation problems," IEEE Trans. Inf. Theory, vol. 46, no. 5, pp. 1881-1895, Aug. 2000.
6. J. C. Ye, Y. Bresler, and P. Moulin, "Cramér-Rao bounds for 2-D target shape estimation in non-linear inverse scattering problems with application to passive radar," IEEE Trans. Antennas Propagat., vol. 49, no. 5, pp. 771-783, May 2001.
7. J. C. Ye, Y. Bresler, and P. Moulin, "Cramér-Rao bound of parametric shape estimation in inverse problems," IEEE Trans. Image Process., vol. 12, no. 1, pp. 71-84, Jan. 2003.
8. T. Tasdizen and R. Whitaker, "Cramer-Rao Bounds for nonparametric surface reconstruction from range data," Tech. Rep. UUCS-03-006, School Comput., Univ. Utah, Salt Lake City, 2003.
9. A. Poonawala, P. Milanfar, and R. Gardner, "A statistical analysis of shape reconstruction from areas of shadows," presented at the 36th Asilomar Conf. Signals, Systems and Computers Pacific Grove, CA, Nov. 2002.
10. J. Sun, "Tail probabilities of the maxima of Gaussian random fields," Ann. Prob., vol. 21, no. 1, pp. 34-71, Jan. 1993.
11. R. J. Adler, "On excursion sets, tube formulae, and maxima of random fields," Ann. Appl. Prob., vol. 10, no. 1, pp. 1-74, 2000.
12. H. Weyl, "On the volume of tubes," Amer. J. Math., no. 61, pp. 461-472, 1939.
13. H. Hotelling, "Tubes and spheres in n-space, a class of statistical problems," Amer. J. Math., vol. 61, no. 9, pp. 440-460, 1939.
14. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. New York: Dover, 1971.
15. R. E. Blahut, Theory of Remote Image Formation. Cambridge, U.K.: Cambridge Univ. Press, 2004.
16. G. T. Herman and A. Kuba, "Discrete tomography in medical imaging," Proc. IEEE, vol. 91, no. 10, pp. 1612-1626, Oct. 2003.
17. E. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed. New York: Springer-Verlag, 2003.
18. J. Gorman and A. Hero, "Lower bounds for parametric estimation with constraints," IEEE Trans. Inf. Theory, vol. 6, no. 6, pp. 1285-1301, Nov. 1990.
19. P. Stoica and B. C. Ng, "On the Cramer-Rao bound under parametric constraints," IEEE Signal Process. Lett., vol. 5, pp. 177-179, Jul. 1998.
20. S. Basu and Y. Bresler, "Stability of nonlinear least squares problems and the Cramér-Rao bound," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3426-3436, Dec. 2000.
21. S. S. Wilks and J. F. Daly, "An optimum property of confidence regions associated with the likelihood function," Ann. Math. Statist., no. 10, pp. 225-235, 1939.
22. V. I. Piterbarg, "High excursions for nonstationary generalized chi-square processes," Stochastic Process. Appl., no. 53, pp. 307-337, 1994.
23. 2, F and t fields," Adv. Appl. Prob., no. 26, pp. 13-42, 1994.
24. K. J. Worsley, "Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics," Adv. Appl. Prob., no. 27, pp. 943-959, 1995.
25. K. J. Worsley, "Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images," Ann. Statist., no. 23, pp. 640-669, 1995.
26. 2 fields," Ann. Statist., vol. 27, no. 3, pp. 925-942, 1999.
27. C. Loader, Libtube: Software for the Volume-of-Tube Formula 2002 [Online]. Available: http://www.herine.net/stat/tube/
28. C. Loader, "The volume-of-tube formula: Computational methods and statistical applications," presented at the Interface Conf.: Computational Biology and Bioinformatics 2004.
29. J. Nelder and R. Mead, "A simplex method for function minimization," The Comput. J., vol. 7, no. 4, pp. 308-313, 1965.
30. M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, and F. Rossi, TheGNU Scientific Library Reference Manual 2002 [Online]. Available: http://sources.redhat.com/gsl