OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 43, Iss. 31 — Nov. 1, 2004
  • pp: 5796–5805

Influence of Thresholding on Centroid Statistics: Full Analytical Description

Jorge Ares and Justo Arines  »View Author Affiliations

Applied Optics, Vol. 43, Issue 31, pp. 5796-5805 (2004)

View Full Text Article

Acrobat PDF (702 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The centroid method is a common procedure for subpixel location that is applied to a large number of optical sensors. In practice, it is always accompanied by thresholding algorithms used to eliminate undesirable background that may decrease precision. We present a full analytical description of the interaction between centroiding and thresholding applied over an intensity distribution corrupted by additive Gaussian noise. An in depth analysis of the most outstanding statistical properties of this relation (mean and variance) is also presented by means of simulated and experimental data. This work provides fundamental concepts to the designers of sensors that are based on centroid measurements to allow them to use thresholding correctly before centroid computation.

© 2004 Optical Society of America

OCIS Codes
(100.5010) Image processing : Pattern recognition
(150.5670) Machine vision : Range finding
(150.6910) Machine vision : Three-dimensional sensing

Jorge Ares and Justo Arines, "Influence of Thresholding on Centroid Statistics: Full Analytical Description," Appl. Opt. 43, 5796-5805 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. R. Armstrong and D. Taley, “A survey of current solid state star tracker technology,” J. Astronaut. Sci. 33, 341–352 (1985).
  2. R. C. Stone, “A comparison of digital centering algorithms,” Astron. J. 97, 1227–1237 (1989).
  3. R. H. Garstang, “Hyperfine structure and the broadening of sunspot spectral lines,” J. Opt. Soc. Am. B 2, 311–313 (1984).
  4. C. S. Fraser and M. R. Shortis, “Metric exploitation of still video imagery,” Photogrammet. Rec. 15, 107–122 (1995).
  5. G. A. West and T. A. Clarke, “A survey and examination of subpixel measurement techniques,” in Close-Range Photogrammetry Meets Machine Vision, A. Gruen and E. P. Baltsavias, eds., Proc. SPIE 1395, 456–463 (1990).
  6. M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target images,” in Videometrics II, S. F. El-Hakim, ed., Proc. SPIE 2350, 239–250 (1994).
  7. J. P. Fillard, “Subpixel accuracy location estimation from digital signals,” Opt. Eng. 31, 2465–2471 (1992).
  8. W. Ruyten, “Subpixel localization of synthetic references in digital images by use of an augmented template,” Opt. Eng. 41, 601–607 (2002).
  9. J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
  10. B. Platt and R. V. Shack, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).
  11. J. Ares, T. Mancebo, and S. Bará, “Position and displacement sensing with Shack-Hartmann wave-front sensors,” Appl. Opt. 39, 1511–1520 (2000).
  12. R. G. Dorsch, G. Häusler, and J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
  13. Y. Pu and H. Meng, “An advanced off-axis holographic particle image velocimetry (HPIV) system,” Exp. Fluids 29, 184–197 (2000).
  14. R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
  15. R. Navarro and M. A. Losada, “Aberrations and relative efficiency of ray pencils in the living human eye,” Optom. Vis. Sci. 74, 540–547 (1997).
  16. B. F. Alexander and K. Chew, “Elimination of systematic error in subpixel accuracy estimation,” Opt. Eng. 30, 1320–1331 (1991).
  17. G. A. Tyller and D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. A 72, 804–808 (1982).
  18. J. Morgan, D. C. Slater, J. G. Timothy, and E. B. Jenkins, “Centroid position measurements and subpixel sensitivity variations with the MAMA detector,” Appl. Opt. 28, 1178–1192 (1989).
  19. G. Cao and X. Yu, “Accuracy analysis of Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994); (some small typographical errors in the formula appeared in the original paper and were corrected here).
  20. J. Ares and J. Arines, “Effective noise in thresholded intensity distribution: influence on centroid statistics,” Opt. Lett. 26, 1831–1833 (2001).
  21. R. C. González and R. E. Woods, “Image segmentation,” in Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 443–455.
  22. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).
  23. J. F. Kenney and E. S. Keeping, Mathematics of Statistics, 2nd ed. (Van Nostrand, Princeton, N.J., 1951), Part II.
  24. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures (Wiley-Interscience, New York, 1971).
  25. J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett. 27, 497–499 (2002).
  26. G. Luo, O. Chutatape, and H. Fang, “Experimental study on nonuniformity on line jitter in CCD images,” Appl. Opt. 40, 4716–4720 (2001).
  27. R. M. Haralick and L. G. Shapiro, “Binary machine vision,” in Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1992), Vol. I, pp. 14–28.
  28. T. A. Clarke, “A frame grabber related error in subpixel target location,” Photogramet. Rec. 15, 315–322 (1995).
  29. T. Metz, J. Walewski, and C. F. Kaminski, “Maximum-likelihood curve fitting scheme for experiments with pulsed laser subject to intensity fluctuations,” Appl. Opt. 42, 1551–1563 (2003).
  30. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited