Abstract

The appearance of objects generally does not change with changes in the size of their retinal image that occur as the distance from the observer increases or decreases. Contrast constancy ensures this invariance for suprathreshold image features, but fully robust size invariance also requires invariance at threshold, so that near-threshold image features do not appear or disappear with distance changes. Since the angular size and the eccentricity of image features covary with distance changes, the threshold requirement for invariance could be satisfied approximately if contrast thresholds were to vary as the product of the spatial frequency and the eccentricity from the fovea. This model fits contrast thresholds for orientation identification over spatial frequencies of 1–16 cycles/deg and for retinal eccentricities of as much as 23 deg. Contrast detection thresholds from six different studies conform to this model over an even wider range of spatial frequencies and retinal eccentricities. The fitting variable, the fundamental eccentricity constant, was similar for all three studies that measured detection along the horizontal meridian and was higher for the orientation identification contrast thresholds along the same meridian. The eccentricity constant from studies that measured detection along the vertical meridian was higher than the constant calculated for the horizontal meridian and lower than the eccentricity constant for chromatic isoluminance gratings. Our model and these results provide new tools for analyzing the visibility of displays and for designing equal-visibility or variable-visibility displays.

© 1991 Optical Society of America

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    [Crossref]
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  3. A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
    [Crossref] [PubMed]
  4. D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
    [Crossref]
  5. T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
    [Crossref] [PubMed]
  6. J. Norman, S. Ehrlich, “Spatial frequency filtering and target identification,” Vision Res. 27, 87–96 (1987).
    [Crossref] [PubMed]
  7. M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. 252, 627–656 (1975).
    [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  15. A 5-cycle/deg feature refers to a localized image feature with a spatial spectral mean frequency of 5 cycles/deg, such as a Gabor patch or any other localized luminance patch. Although real image features may have higher frequencies, the contrast at those frequencies will generally be much lower and thus will be subthreshold and inconsequential for our discussion.
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    [Crossref] [PubMed]
  17. J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  22. J. P. Thomas, “Detection and identification: how are they related?”J. Opt. Soc. Am. A 2, 1457–1467 (1985).
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  23. H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast threshold for identification of numeric characters in direct and eccentric view.” Percept. Psychophys. (to be published).
  24. E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.
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    [Crossref]
  26. R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1337 (1974).
    [Crossref] [PubMed]
  27. J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
    [Crossref] [PubMed]
  28. D. Regan, K. I. Beverley, “Visual fields described by contrast sensitivity, by acuity, and by relative sensitivity to different orientations.” Invest. Ophthalmol. Vis. Sci. 24, 754–759 (1983).
    [PubMed]
  29. G. T. Timberlake, E. Peli, R. A. Augliere, “Visual acuity measurement with a second-generation scanning laser ophthalmoscope,” in Noninvasive Assessment of the Visual System, Vol. 4 of 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–7.
  30. J. M. Woodhouse, H. B. Barlow, “Spatial and temporal resolution and analysis,” in The Senses, H. B. Barlow, J. D. Mollon, eds. (Cambridge U. Press, Cambridge, 1982), Chap. 8, pp. 133–164.
  31. M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).
  32. A. P. Ginsburg, “Is the illusory triangle physical or imaginary?” Nature (London) 257, 291–220 (1975).
    [Crossref]
  33. C. W. Tyler, “Is the illusory triangle physical or imaginary?” Perception 6, 603–604 (1977).
    [PubMed]
  34. E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
    [Crossref] [PubMed]
  35. G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
    [PubMed]
  36. Y. Yeshurun, E. L. Schwartz, “Shape description with a space-variant sensor: algorithms for scan-path, fusion, and convergence over multiple scans,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 1217–1222 (1989).
    [Crossref]
  37. E. L. Schwartz, “Spatial mapping in the primate sensory projection: analytic structure and relevance to perception,” Biol. Cybern. 25, 181–194 (1977).
    [Crossref] [PubMed]
  38. Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).
  39. E. L. Schwartz, “Cortical anatomy, size invariance, and spatial frequency analysis,” Perception 10, 455–468 (1981).
    [Crossref] [PubMed]
  40. P. Cavanagh, “Size invariance: reply to Schwartz,” Perception 10, 469–474 (1981).
    [Crossref] [PubMed]
  41. I. Rentschler, B. Trentwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
    [Crossref]
  42. C. Braccini, “Scale-invariant image processing by means of scaled transforms or form-invariant, linear shift-variant filters,” Opt. Lett. 8, 392–394 (1983).
    [Crossref] [PubMed]
  43. J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the major oblique meridians of the human visual field,” Vision Res. 30, 497–501 (1990).
    [Crossref] [PubMed]
  44. C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
    [Crossref] [PubMed]
  45. M. A. Garcia-Perez, “Space-variant visual processing: spatially limited visual channels,” Spatial Vision 3, 129–142 (1988).
    [Crossref] [PubMed]
  46. S. N. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
    [Crossref] [PubMed]

1991 (2)

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[Crossref]

K. T. Mullen, “Color vision as a post receptoral specialization of the central visual field,” Vision Res. 31, 119–130 (1991).
[Crossref]

1990 (3)

M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[Crossref] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the major oblique meridians of the human visual field,” Vision Res. 30, 497–501 (1990).
[Crossref] [PubMed]

1989 (3)

Y. Yeshurun, E. L. Schwartz, “Shape description with a space-variant sensor: algorithms for scan-path, fusion, and convergence over multiple scans,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 1217–1222 (1989).
[Crossref]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[Crossref] [PubMed]

H. J. Fleck, “Measurement and modeling of peripheral detection and discrimination thresholds,” Biol. Cybern. 61, 437–446 (1989).
[Crossref] [PubMed]

1988 (1)

M. A. Garcia-Perez, “Space-variant visual processing: spatially limited visual channels,” Spatial Vision 3, 129–142 (1988).
[Crossref] [PubMed]

1987 (4)

M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

J. Norman, S. Ehrlich, “Spatial frequency filtering and target identification,” Vision Res. 27, 87–96 (1987).
[Crossref] [PubMed]

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

J. P. Thomas, “Effect of eccentricity on the relationship between detection and identification,” J. Opt. Soc. Am. A 4, 1599–1605 (1987).
[Crossref] [PubMed]

1986 (1)

T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
[Crossref] [PubMed]

1985 (4)

B. R. Stephens, M. S. Banks, “The development of contrast constancy,” J. Exp. Child Psychol. 40, 528–547 (1985).
[Crossref] [PubMed]

J. P. Thomas, “Detection and identification: how are they related?”J. Opt. Soc. Am. A 2, 1457–1467 (1985).
[Crossref] [PubMed]

M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
[Crossref] [PubMed]

I. Rentschler, B. Trentwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
[Crossref]

1984 (1)

1983 (4)

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[Crossref] [PubMed]

R. F. Hess, A. N. Bradley, L. Piotrowski, “Contrast coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London 127, 309–330 (1983).
[Crossref]

D. Regan, K. I. Beverley, “Visual fields described by contrast sensitivity, by acuity, and by relative sensitivity to different orientations.” Invest. Ophthalmol. Vis. Sci. 24, 754–759 (1983).
[PubMed]

C. Braccini, “Scale-invariant image processing by means of scaled transforms or form-invariant, linear shift-variant filters,” Opt. Lett. 8, 392–394 (1983).
[Crossref] [PubMed]

1982 (1)

H. R. Lieberman, A. P. Pentland, “Microcomputer-based estimation of psychophysical thresholds: the best PEST,” Behav. Res. Methods Instrum. 14, 21–25 (1982).
[Crossref]

1981 (5)

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[Crossref] [PubMed]

E. L. Schwartz, “Cortical anatomy, size invariance, and spatial frequency analysis,” Perception 10, 455–468 (1981).
[Crossref] [PubMed]

P. Cavanagh, “Size invariance: reply to Schwartz,” Perception 10, 469–474 (1981).
[Crossref] [PubMed]

C. R. Carlson, R. W. Klopfenstein, C. H. Anderson, “Spatially inhomogeneous scaled transforms for vision and pattern recognition,” Opt. Lett. 6, 386–388 (1981).
[Crossref] [PubMed]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[Crossref] [PubMed]

1980 (1)

J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
[Crossref] [PubMed]

1978 (1)

C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
[Crossref] [PubMed]

1977 (2)

E. L. Schwartz, “Spatial mapping in the primate sensory projection: analytic structure and relevance to perception,” Biol. Cybern. 25, 181–194 (1977).
[Crossref] [PubMed]

C. W. Tyler, “Is the illusory triangle physical or imaginary?” Perception 6, 603–604 (1977).
[PubMed]

1976 (1)

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419–1431 (1976).
[Crossref] [PubMed]

1975 (2)

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. 252, 627–656 (1975).
[PubMed]

A. P. Ginsburg, “Is the illusory triangle physical or imaginary?” Nature (London) 257, 291–220 (1975).
[Crossref]

1974 (2)

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

S. N. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
[Crossref] [PubMed]

1968 (1)

N. S. Sutherland, “Outlines of a theory of visual pattern recognition in animal and man,” Proc. R. Soc. London Ser. B 171, 297–317 (1968).
[Crossref]

Anderson, C. H.

Anstis, S. N.

S. N. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
[Crossref] [PubMed]

Arend, L. E.

E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.

Augliere, R. A.

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

G. T. Timberlake, E. Peli, R. A. Augliere, “Visual acuity measurement with a second-generation scanning laser ophthalmoscope,” in Noninvasive Assessment of the Visual System, Vol. 4 of 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–7.

Balestery, F.

C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
[Crossref] [PubMed]

Banks, M. S.

M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

B. R. Stephens, M. S. Banks, “The development of contrast constancy,” J. Exp. Child Psychol. 40, 528–547 (1985).
[Crossref] [PubMed]

Barlow, H. B.

J. M. Woodhouse, H. B. Barlow, “Spatial and temporal resolution and analysis,” in The Senses, H. B. Barlow, J. D. Mollon, eds. (Cambridge U. Press, Cambridge, 1982), Chap. 8, pp. 133–164.

Bennett, P. J.

M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Beverley, K. I.

D. Regan, K. I. Beverley, “Visual fields described by contrast sensitivity, by acuity, and by relative sensitivity to different orientations.” Invest. Ophthalmol. Vis. Sci. 24, 754–759 (1983).
[PubMed]

Braccini, C.

Bradley, A. N.

R. F. Hess, A. N. Bradley, L. Piotrowski, “Contrast coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London 127, 309–330 (1983).
[Crossref]

Burr, D. C.

T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
[Crossref] [PubMed]

Cannon, M. W.

M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).

M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
[Crossref] [PubMed]

Carlson, C. R.

Cavanagh, P.

P. Cavanagh, “Size invariance: reply to Schwartz,” Perception 10, 469–474 (1981).
[Crossref] [PubMed]

Cavonius, C. R.

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

Derrington, A. M.

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[Crossref] [PubMed]

Ehrlich, S.

J. Norman, S. Ehrlich, “Spatial frequency filtering and target identification,” Vision Res. 27, 87–96 (1987).
[Crossref] [PubMed]

Essock, E. A.

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

Fiorentini, A.

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[Crossref] [PubMed]

Fleck, H. J.

H. J. Fleck, “Measurement and modeling of peripheral detection and discrimination thresholds,” Biol. Cybern. 61, 437–446 (1989).
[Crossref] [PubMed]

Garcia-Perez, M. A.

M. A. Garcia-Perez, “Space-variant visual processing: spatially limited visual channels,” Spatial Vision 3, 129–142 (1988).
[Crossref] [PubMed]

Geisler, W. S.

M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Georgeson, M. A.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. 252, 627–656 (1975).
[PubMed]

Ginsburg, A. P.

A. P. Ginsburg, “Is the illusory triangle physical or imaginary?” Nature (London) 257, 291–220 (1975).
[Crossref]

A. P. Ginsburg, “Visual information processing based on spatial filters constrained by biological data,” Ph.D. dissertation (Cambridge University, Cambridge, 1978).

Goldstein, R. B.

E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.

Graham, N.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[Crossref] [PubMed]

Harvey, L. O.

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast threshold for identification of numeric characters in direct and eccentric view.” Percept. Psychophys. (to be published).

Hayes, T.

T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
[Crossref] [PubMed]

Henning, G. B.

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[Crossref] [PubMed]

Hess, R. F.

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the major oblique meridians of the human visual field,” Vision Res. 30, 497–501 (1990).
[Crossref] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[Crossref] [PubMed]

R. F. Hess, A. N. Bradley, L. Piotrowski, “Contrast coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London 127, 309–330 (1983).
[Crossref]

Hilz, R.

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

Johnson, C. A.

C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
[Crossref] [PubMed]

Keltner, J. L.

C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
[Crossref] [PubMed]

Klopfenstein, R. W.

Kroon, J. N.

J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
[Crossref] [PubMed]

Kulikowski, J. J.

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419–1431 (1976).
[Crossref] [PubMed]

Lieberman, H. R.

H. R. Lieberman, A. P. Pentland, “Microcomputer-based estimation of psychophysical thresholds: the best PEST,” Behav. Res. Methods Instrum. 14, 21–25 (1982).
[Crossref]

Maffei, L.

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[Crossref] [PubMed]

Morrone, M. C.

T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
[Crossref] [PubMed]

Mullen, K. T.

K. T. Mullen, “Color vision as a post receptoral specialization of the central visual field,” Vision Res. 31, 119–130 (1991).
[Crossref]

Norman, J.

J. Norman, S. Ehrlich, “Spatial frequency filtering and target identification,” Vision Res. 27, 87–96 (1987).
[Crossref] [PubMed]

Parish, D. H.

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[Crossref]

Peli, E.

E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A 7, 2032–2040 (1990).
[Crossref] [PubMed]

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

G. T. Timberlake, E. Peli, R. A. Augliere, “Visual acuity measurement with a second-generation scanning laser ophthalmoscope,” in Noninvasive Assessment of the Visual System, Vol. 4 of 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–7.

E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.

Pentland, A. P.

H. R. Lieberman, A. P. Pentland, “Microcomputer-based estimation of psychophysical thresholds: the best PEST,” Behav. Res. Methods Instrum. 14, 21–25 (1982).
[Crossref]

Peterfreund, N.

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

Piotrowski, L.

R. F. Hess, A. N. Bradley, L. Piotrowski, “Contrast coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London 127, 309–330 (1983).
[Crossref]

Pointer, J. S.

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the major oblique meridians of the human visual field,” Vision Res. 30, 497–501 (1990).
[Crossref] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[Crossref] [PubMed]

Regan, D.

D. Regan, K. I. Beverley, “Visual fields described by contrast sensitivity, by acuity, and by relative sensitivity to different orientations.” Invest. Ophthalmol. Vis. Sci. 24, 754–759 (1983).
[PubMed]

Rentschler, I.

I. Rentschler, B. Trentwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
[Crossref]

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast threshold for identification of numeric characters in direct and eccentric view.” Percept. Psychophys. (to be published).

Rijsdijk, J. P.

J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
[Crossref] [PubMed]

Robson, J. G.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[Crossref] [PubMed]

Sandini, G.

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[Crossref] [PubMed]

Schwartz, E. L.

Y. Yeshurun, E. L. Schwartz, “Shape description with a space-variant sensor: algorithms for scan-path, fusion, and convergence over multiple scans,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 1217–1222 (1989).
[Crossref]

E. L. Schwartz, “Cortical anatomy, size invariance, and spatial frequency analysis,” Perception 10, 455–468 (1981).
[Crossref] [PubMed]

E. L. Schwartz, “Spatial mapping in the primate sensory projection: analytic structure and relevance to perception,” Biol. Cybern. 25, 181–194 (1977).
[Crossref] [PubMed]

Shlomot, E.

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

Sperling, G.

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[Crossref]

Stephens, B. R.

B. R. Stephens, M. S. Banks, “The development of contrast constancy,” J. Exp. Child Psychol. 40, 528–547 (1985).
[Crossref] [PubMed]

Strasburger, H.

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast threshold for identification of numeric characters in direct and eccentric view.” Percept. Psychophys. (to be published).

Sullivan, G. D.

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. 252, 627–656 (1975).
[PubMed]

Sutherland, N. S.

N. S. Sutherland, “Outlines of a theory of visual pattern recognition in animal and man,” Proc. R. Soc. London Ser. B 171, 297–317 (1968).
[Crossref]

Thibos, L. N.

M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).

Thomas, J. P.

Timberlake, G. T.

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

G. T. Timberlake, E. Peli, R. A. Augliere, “Visual acuity measurement with a second-generation scanning laser ophthalmoscope,” in Noninvasive Assessment of the Visual System, Vol. 4 of 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–7.

Trentwein, B.

I. Rentschler, B. Trentwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
[Crossref]

Tyler, C. W.

C. W. Tyler, “Is the illusory triangle physical or imaginary?” Perception 6, 603–604 (1977).
[PubMed]

van der Wildt, G. J.

J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
[Crossref] [PubMed]

Wilkinson, M. D.

M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).

Woodhouse, J. M.

J. M. Woodhouse, H. B. Barlow, “Spatial and temporal resolution and analysis,” in The Senses, H. B. Barlow, J. D. Mollon, eds. (Cambridge U. Press, Cambridge, 1982), Chap. 8, pp. 133–164.

Yeshurun, Y.

Y. Yeshurun, E. L. Schwartz, “Shape description with a space-variant sensor: algorithms for scan-path, fusion, and convergence over multiple scans,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 1217–1222 (1989).
[Crossref]

Young, G. M.

E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.

Zeevi, Y. Y.

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

Behav. Res. Methods Instrum. (1)

H. R. Lieberman, A. P. Pentland, “Microcomputer-based estimation of psychophysical thresholds: the best PEST,” Behav. Res. Methods Instrum. 14, 21–25 (1982).
[Crossref]

Biol. Cybern. (2)

E. L. Schwartz, “Spatial mapping in the primate sensory projection: analytic structure and relevance to perception,” Biol. Cybern. 25, 181–194 (1977).
[Crossref] [PubMed]

H. J. Fleck, “Measurement and modeling of peripheral detection and discrimination thresholds,” Biol. Cybern. 61, 437–446 (1989).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Y. Yeshurun, E. L. Schwartz, “Shape description with a space-variant sensor: algorithms for scan-path, fusion, and convergence over multiple scans,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 1217–1222 (1989).
[Crossref]

Invest. Ophthalmol. Vis. Sci. (2)

G. T. Timberlake, E. Peli, E. A. Essock, R. A. Augliere, “Reading with macular scotoma. II. Retinal locus for scanning text,” Invest. Ophthalmol. Vis. Sci. 28, 1268–1274 (1987).
[PubMed]

D. Regan, K. I. Beverley, “Visual fields described by contrast sensitivity, by acuity, and by relative sensitivity to different orientations.” Invest. Ophthalmol. Vis. Sci. 24, 754–759 (1983).
[PubMed]

Invest. Ophthalmol. Vis. Sci. Suppl. (1)

M. D. Wilkinson, L. N. Thibos, M. W. Cannon, “Contrast constancy: neural compensation for image attenuation,” Invest. Ophthalmol. Vis. Sci. Suppl. 31, 323 (1990).

J. Exp. Child Psychol. (1)

B. R. Stephens, M. S. Banks, “The development of contrast constancy,” J. Exp. Child Psychol. 40, 528–547 (1985).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (5)

J. Physiol. (1)

M. A. Georgeson, G. D. Sullivan, “Contrast constancy: deblurring in human vision by spatial frequency channels,” J. Physiol. 252, 627–656 (1975).
[PubMed]

Nature (London) (2)

A. P. Ginsburg, “Is the illusory triangle physical or imaginary?” Nature (London) 257, 291–220 (1975).
[Crossref]

I. Rentschler, B. Trentwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
[Crossref]

Opt. Lett. (2)

Perception (5)

E. L. Schwartz, “Cortical anatomy, size invariance, and spatial frequency analysis,” Perception 10, 455–468 (1981).
[Crossref] [PubMed]

P. Cavanagh, “Size invariance: reply to Schwartz,” Perception 10, 469–474 (1981).
[Crossref] [PubMed]

C. W. Tyler, “Is the illusory triangle physical or imaginary?” Perception 6, 603–604 (1977).
[PubMed]

T. Hayes, M. C. Morrone, D. C. Burr, “Recognition of positive and negative bandpass-filtered images,” Perception 15, 595–602 (1986).
[Crossref] [PubMed]

A. Fiorentini, L. Maffei, G. Sandini, “The role of high spatial frequencies in face perception,” Perception 12, 195–201 (1983).
[Crossref] [PubMed]

Proc. R. Soc. London (1)

R. F. Hess, A. N. Bradley, L. Piotrowski, “Contrast coding in amblyopia. I. Differences in the neural basis of human amblyopia,” Proc. R. Soc. London 127, 309–330 (1983).
[Crossref]

Proc. R. Soc. London Ser. B (1)

N. S. Sutherland, “Outlines of a theory of visual pattern recognition in animal and man,” Proc. R. Soc. London Ser. B 171, 297–317 (1968).
[Crossref]

Spatial Vision (1)

M. A. Garcia-Perez, “Space-variant visual processing: spatially limited visual channels,” Spatial Vision 3, 129–142 (1988).
[Crossref] [PubMed]

Vision Res. (13)

S. N. Anstis, “A chart demonstrating variations in acuity with retinal position,” Vision Res. 14, 589–592 (1974).
[Crossref] [PubMed]

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[Crossref] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the major oblique meridians of the human visual field,” Vision Res. 30, 497–501 (1990).
[Crossref] [PubMed]

C. A. Johnson, J. L. Keltner, F. Balestery, “Effects of target size and eccentricity on visual detection and resolution,” Vision Res. 18, 1217–1222 (1978).
[Crossref] [PubMed]

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

J. P. Rijsdijk, J. N. Kroon, G. J. van der Wildt, “Contrast sensitivity as a function of position on the retina,” Vision Res. 20, 235–241 (1980).
[Crossref] [PubMed]

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[Crossref]

J. Norman, S. Ehrlich, “Spatial frequency filtering and target identification,” Vision Res. 27, 87–96 (1987).
[Crossref] [PubMed]

J. J. Kulikowski, “Effective contrast constancy and linearity of contrast sensation,” Vision Res. 16, 1419–1431 (1976).
[Crossref] [PubMed]

K. T. Mullen, “Color vision as a post receptoral specialization of the central visual field,” Vision Res. 31, 119–130 (1991).
[Crossref]

M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: with emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[Crossref] [PubMed]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[Crossref] [PubMed]

Other (7)

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast threshold for identification of numeric characters in direct and eccentric view.” Percept. Psychophys. (to be published).

E. Peli, R. B. Goldstein, G. M. Young, L. E. Arend, “Contrast sensitivity functions for analysis and simulation of visual perception,” in Noninvasive Assessment of the Visual System, Vol. 3 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 126–129.

A 5-cycle/deg feature refers to a localized image feature with a spatial spectral mean frequency of 5 cycles/deg, such as a Gabor patch or any other localized luminance patch. Although real image features may have higher frequencies, the contrast at those frequencies will generally be much lower and thus will be subthreshold and inconsequential for our discussion.

A. P. Ginsburg, “Visual information processing based on spatial filters constrained by biological data,” Ph.D. dissertation (Cambridge University, Cambridge, 1978).

G. T. Timberlake, E. Peli, R. A. Augliere, “Visual acuity measurement with a second-generation scanning laser ophthalmoscope,” in Noninvasive Assessment of the Visual System, Vol. 4 of 1987 Technical Digest Series (Optical Society of America, Washington, D.C., 1987), pp. 4–7.

J. M. Woodhouse, H. B. Barlow, “Spatial and temporal resolution and analysis,” in The Senses, H. B. Barlow, J. D. Mollon, eds. (Cambridge U. Press, Cambridge, 1982), Chap. 8, pp. 133–164.

Y. Y. Zeevi, N. Peterfreund, E. Shlomot, “Pyramidal image representation in nonuniform systems,” in Visual Communications and Image Processing ’88, T. R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1001, 563–571 (1988).

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Figures (8)

Fig. 1
Fig. 1

Hypothetical contrast threshold as a function of eccentricity for various spatial frequencies that would maintain invariant image perception with distance. The slopes of the lines have the same ratios as the corresponding spatial frequencies. If a threshold feature at spatial frequency 2f and an eccentricity of 20 deg is shifted by the change of distance to spatial frequency 4f but at the same time approaches an eccentricity of 10 deg from the fovea, then it will remain at the threshold level despite these changes.

Fig. 2
Fig. 2

Contrast thresholds for orientation identification of two observers at different spatial frequencies, measured as a function of eccentricity. Lines represent the fit of the model to the data. All five lines were fitted together, and the slopes of the lines were constrained to have the same ratios as the corresponding spatial frequencies (factors of 2, in this case). The eccentricity constant a, representing the slope at 1 cycle/deg, is 0.048 and 0.053 for subjects JY and GY, respectively. Error bars represent the estimate of the standard error of the mean, se ˆ.

Fig. 3
Fig. 3

Contrast detection threshold data (symbols) as a function of eccentricity together with the fit of our model (lines) to data from three different studies: (a) data from Ref. 18, (b) data from Ref. 17, (c) data from Ref. 19. (d) The same data and fits as in (c), displayed as normalized thresholds, i.e., threshold divided by (calculated) foveal thresholds. The normalized graph makes it easier to appreciate visually the closeness of the fit of our model to these data.

Fig. 4
Fig. 4

(a) Retinal contrast detection thresholds as a function of eccentricity, measured with a laser interferometric technique by Hilz and Cavonius.26 The lines represent the fit of our model to their data. The crossing of the lines here, compared with distal contrast threshold measurements (Fig. 3), represents the effect of neural compensation for the optical degradation of the image. (b) The same data and fits as in (a), displayed in terms of normalized thresholds. This should have been the result of such retinal contrast threshold measurements without neural compensation for the optical modulation transfer function.

Fig. 5
Fig. 5

(a) Changes in the appearance of a face with a large change in observation distance are illustrated for a normal observer (top) and for a patient with 10-deg-diameter central scotoma (bottom). Images at the left represent the appearance of the face at 25 cm (10 in.) from the observer, where it spans 32 deg of visual angle. Images at the right represent the appearance of the same face 4.3 m (14 ft) from the observer, where it spans only 2 deg of visual angle. The normal observer is assumed to fixate at the center of the face in both cases. The patient is assumed to place the edge of his or her scotoma at the edge of the image in both cases. The changes in appearance for the normal observer are small, limited to the high spatial frequencies and compatible with the filtration of the image by the eye’s optical media. The effect of change in distance is much more detrimental for the patient with a central scotoma. At close range the appearance of the face to the patient is almost identical to its appearance to the normal observer. (b) A schematic diagram of the image in (a) and the relation of scotoma and foveal positions to the various images.

Fig. 6
Fig. 6

Simulations presented in Fig. 5 are illustrated here for the cable-car scene that contains more relevant high-frequency information. Both the image invariance for the normal observer and the degradation of the image for the low-vision patient are more dramatic in this case.

Fig. 7
Fig. 7

Simulation of the appearance of newspaper-sized text at a normal reading distance of 25 cm. The section of text illustrated is assumed to span 16 deg of visual angle at a normal reading distance. Fixation is held at the center of the image, and the processing is identical to the one used for Figs. 4 and 5. In this higher-resolution image, it is possible to appreciate the nonuniform aspect of the simulation, which is difficult to note in the previous figures. However, the degradation of image visibility with eccentricity illustrated here is much smaller than the degradation simulated by Yeshurun and Schwartz.36

Fig. 8
Fig. 8

Equal-visibility chart, including variations in both size and contrast. When fixation is maintained at the center, all patches should be of equal visibility (the contrast is three times the threshold contrast). In this chart, for any eccentricity we may trade size for contrast and maintain visibility. The threshold chart corresponding to Anstis’s46 letter chart cannot be reproduced in print because of the low contrasts. This image was generated under the assumption that the full frame spans 32 deg of visual angle. However, the effect should be largely distance invariant. The orientation discrimination data (subject JY) were used. Thus the discrimination of patch orientation should be equal for all eccentricities and sizes presented on the chart.

Tables (1)

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Table 1 Fundamental Eccentricity Constant a, Calculated for the Data from Various studiesa

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

T ( θ , f ) = G ( θ f ) ,
T ( θ , f ) = A exp ( a θ f ) ,
T r ( θ , f ) = T ( θ , f ) T ( 0 , f ) = exp ( a θ f ) ,
p ( x , y ) = L 0 [ 1 + m cos ( 2 π f 0 x ) exp ( x 2 + y 2 σ 2 ) ] ,
ln [ T ( θ , f ) ] = a θ f + b ( f ) ,

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