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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 7 — Jul. 1, 2003
  • pp: 1371–1381

Bayesian model of Snellen visual acuity

Oscar Nestares, Rafael Navarro, and Beatriz Antona  »View Author Affiliations

JOSA A, Vol. 20, Issue 7, pp. 1371-1381 (2003)

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A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eye’s optical aberrations, and standard values are used for all other parameters, including the Stiles–Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VA in refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.

© 2003 Optical Society of America

OCIS Codes
(330.1070) Vision, color, and visual optics : Vision - acuity
(330.4060) Vision, color, and visual optics : Vision modeling
(330.5000) Vision, color, and visual optics : Vision - patterns and recognition
(330.5370) Vision, color, and visual optics : Physiological optics
(330.6110) Vision, color, and visual optics : Spatial filtering

Original Manuscript: June 20, 2002
Revised Manuscript: January 6, 2003
Manuscript Accepted: January 6, 2003
Published: July 1, 2003

Oscar Nestares, Beatriz Antona, and Rafael Navarro, "Bayesian model of Snellen visual acuity," J. Opt. Soc. Am. A 20, 1371-1381 (2003)

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  1. G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 398–404 (1982).
  2. H. B. Peters, “The relationship between refractive error and visual acuity at three age levels,” Am. J. Ophthalmol. 38, 194–199 (1961).
  3. A. Bradley, T. Thomas, M. Kalaher, M. Hoerres, “Effects of spherical and astigmatic defocus on acuity and contrast sensitivity: a comparison of three clinical charts,” Optom. Vision Sci. 68, 418–426 (1991). [CrossRef]
  4. J. Liang, B. Grimm, S. Goelz, J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994). [CrossRef]
  5. R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997). [CrossRef]
  6. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998). [CrossRef]
  7. E. Moreno-Barriuso, R. Navarro, “Laser ray tracing versus Hartmann–Shack sensor for measuring optical aberrations in the human eye,” J. Opt. Soc. Am. A 17, 974–985 (2000). [CrossRef]
  8. P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “Measuring device for determining monochromatic aberration of the human eye,” Ophthalmologe 94, 441–445 (1997). [CrossRef] [PubMed]
  9. T. Seiler, M. Kaemmerer, P. Mierdel, H. E. Krinke, “Ocular optical aberrations after photorefractive keratectomy for myopia and myopic astigmatism,” Arch. Ophthalmol. 118, 17–21 (2000). [CrossRef] [PubMed]
  10. E. Moreno-Barriuso, J. Merayo-Lloves, S. Marcos, R. Navarro, L. Llorente, S. Barbero, “Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing,” Invest. Ophthalmol. Visual Sci. 42, 1396–1403 (2001).
  11. W. Verdon, M. Bullimore, R. K. Maloney, “Visual performance after photorefractive keratectomy,” Arch. Ophthalmol. 114, 1465–1472 (1996). [CrossRef] [PubMed]
  12. J. T. Holladay, D. R. Dudeja, J. Chang, “Functional vision and corneal changes after laser in situ keratomileusis determined by contrast sensitivity, glare testing and corneal topography,” J. Cataract Refract. Surg. 25, 663–669 (1999). [CrossRef] [PubMed]
  13. R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations and visual performance after radial keratotomy,” J. Refract. Surg. 14, 397–407 (1998). [PubMed]
  14. M. Giles, “Aberration tolerances for visual optical systems,” J. Opt. Soc. Am. 67, 634–643 (1977). [CrossRef] [PubMed]
  15. M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surg. 16, 116–121 (2000). [PubMed]
  16. J. E. Greivenkamp, J. Schwiegerling, J. M. Miller, M. D. Mellinger, “Visual acuity modeling using optical raytracing of schematic eyes,” Am. J. Ophthalmol. 120, 227–240 (1995). [PubMed]
  17. A. Guirao, J. Porter, D. R. Williams, I. G. Cox, “Calculated impact of higher-order monochromatic aberrations on retinal image quality in a population of human eyes,” J. Opt. Soc. Am. A 19, 1–9 (2002). [CrossRef]
  18. W. S. Geisler, “Ideal-observer analysis of visual discrimination,” in Frontiers of Visual Science (National Academy Press, Washington, D.C., 1987).
  19. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1993).
  20. A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987). [CrossRef] [PubMed]
  21. M. S. Landy, J. A. Movshon, Computational Models of Visual Processing (MIT Press, Cambridge, Mass., 1991).
  22. F. W. G. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  23. M. A. Losada, R. Navarro, J. Santamaria, “Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels,” Vision Res. 33, 2321–2336 (1993). [CrossRef] [PubMed]
  24. J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997). [CrossRef]
  25. A. Vargas, J. Campos, R. Navarro, “Invariant pattern recognition against defocus based on subband decomposition of the filter,” Opt. Commun. 185, 33–40 (2000). [CrossRef]
  26. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  27. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990). [CrossRef] [PubMed]
  28. H. H. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970). [CrossRef]
  29. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 232–244.
  30. R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993). [CrossRef] [PubMed]
  31. A. Van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974). [CrossRef]
  32. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).
  33. R. Navarro, J. Santamarı́a, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985). [CrossRef] [PubMed]
  34. S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999). [CrossRef]
  35. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990). [CrossRef] [PubMed]
  36. O. Nestares, R. Navarro, J. Portilla, A. Tabernero, “Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions,” J. Electron. Imaging 7, 166–173 (1998). [CrossRef]
  37. C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1990). [CrossRef] [PubMed]
  38. D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985). [CrossRef] [PubMed]
  39. P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994). [CrossRef]

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