Abstract

A two-dimensional spatially inhomogeneous model of the visual system is developed. It is based on the properties of cone spacing in the retina and on the hypothesis of uniform neural interactions (lateral inhibitions). Its quantitative predictions of the detection and discrimination (acuity) of various types of stimuli are studied. The model works well with local stimuli positioned at varied eccentricities as well as with extended stimuli (vertical cosine gratings windowed by two-dimensional windows), but a simple threshold detector was found to be insufficient to describe the increase of contrast sensitivity with the number of cycles of the cosine gratings at high frequencies. It is concluded that, even for one-dimensional stimuli, a two-dimensional approach is necessary and that other parameters such as imprecision of fixation, eye movements, and two-dimensional probability summation must be taken into account before resorting to more complex models.

© 1980 Optical Society of America

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  1. M. Davidson, "Perturbation approach to spatial brightness interaction in human vision," J. Opt. Soc. Am. 58, 1300–1308 (1968).
  2. An inhomogeneous system can be called locally homogeneous if it can be described locally by one linear filter varying with eccentricity.
  3. D. H. Kelly, "Effects of the cone-cell distribution on pattern detection experiments," J. Opt. Soc. Am. 64, 1523–1525 (1974).
  4. A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).
  5. M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).
  6. J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).
  7. H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).
  8. See Sec. III D and Conclusion.
  9. Y. Le Grand, Optique Physiologique, (Edition de la Revue d'Optique, Paris, 1956), Tome III (L'espace visuel), Chap. 8, [also in English in Y. Le Grand, Light, Colour and Vision (Chapman and Hall, London, 1968)].
  10. E. Aulhorm and H. Harms, in Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4, Chap. 5 ("Visual Perimetry").
  11. A stimulus can be called local if its extension is not more than 10–20 min of arc and extended if it exceeds, say, 1°. A stimulus can be local in one direction and extended in the other (one-dimensionally local), or local in all directions (two-dimensionally local).
  12. D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977).
  13. F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. London 197, 551–566 (1968).
  14. J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).
  15. R. L. Savoy and J. J. McCann, "Visibility of low-spatial frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).
  16. G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).
  17. O. Estévez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).
  18. H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16,957–968 (1976).
  19. B. Breitmeyer and B. Julesz, "The role of on and off transients in determining the psychophysical spatial frequency response," Vision Res. 15, 411–415 (1975).
  20. M. M. Taylor, "Visual discrimination and orientation," J. Opt. Soc. Am. 53, 763–765 (1963).
  21. F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).
  22. I. Rentschler and A. Fiorentini, "Meridional anisotropy of psychophysical spatial interactions," Vision Res. 14, 1467–1473 (1974).
  23. Taking for simplicity an infinitely thin vertical line positioned at (x,0), i.e., e(ξη) = δ(ξ–x), Eq. (7) implies s(x,y) = [σ(r)/α(r)]ω0(1))(0) with r2 = x2 + y2. The output maximum is along the line for the minimum r, that is, for y = 0.
  24. E. Pöppel, "Apparent brightness in the peripheral visual field," Naturwissenschaften 60, 110 (1973).
  25. B. Drum, "The relation of apparent brightness to contrast threshold on a photopic background: dependence on retinal position and target size," Vision Res. 16, 1401–1406 (1976).
  26. The one-dimensional acuity limit may differ from the two-dimensional acuity limit. We consider here only their relative variation from the fovea.
  27. F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
  28. D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. London 207, 351–356 (1970).
  29. J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).
  30. H. R. Blackwell, "Neural theories of simple visual discriminations," J. Opt. Soc. Am. 53, 129–160 (1963).
  31. G. Westheimer, "Spatial interaction in human cone vision," J. Physiol. London 190, 139–154 (1967).
  32. More rounded envelopes can be obtained if σ is not related to α by a power law, or if a probability summation model is used for detection, the max operator in Eq. (24) being replaced by a nonlinear summation formula: the L norm can be replaced by a Lα norm as proposed by K. F. Quick, "A vector magnitude model of contrast detection," Kybernetik 16, 65–67 (1974).
  33. This suggests a way to measure the local foveal filter using cosine gratings properly windowed by a function of x. This function must not be higher than α3. (x)/σ(x), σ(x) assumed to be known.
  34. R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
  35. P. Moon and D. E. Spencer, "The visual effect of non-uniform surround," J. Opt. Soc. Am. 35, 233–248 (1945).
  36. J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).
  37. E. R. Howell and R. F. Hess, "The functional area for summation to threshold for sinusoidal gratings," Vision Res. 18, 369–374 (1978).
  38. H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).
  39. P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. London 247, 237–271 (1975).
  40. H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).
  41. J. P. Thomas, "Model of the function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).
  42. J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).
  43. D. H. Hubel and T. N. Wiesel, "Uniformity of monkey striate cortex: a parallel relationship between field size, scatter and magnification factor," J. Comp. Neurol. 158, 295–305 (1974).
  44. L. Maffei and A. Fiorentini, "Spatial frequency rows in the striate visual cortex," Vision Res. 17, 257–264 (1977).
  45. J. L. Mannos and D. J. Sakrison, "The effects of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory 20, 525–536 (1974).
  46. A. Fiorentini, "Mach band phenomena," in Handbook of Sensory Physiology, Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4.
  47. A hexagonal network is chosen to model the retinal network. If d is the intercone distance at eccentricity (x,y), the receptor positions can be indexed as xij = x + id + j(d/2) and yij = y + j(d√3/2), (see Fig. 11); at the fovea, x0ij = id0 + jd0/2 and yij = jd0 √3/2.
  48. We consider here for simplicity that the ganglion cell outputs are the outputs of the lateral interactions and that detectors immediately follow. Parts of the lateral interactions and detectors can occur in more central visual centers. Our hypothesis is only that the neural network is homogeneous, the inhomogeneity arising from the receptor spatial distribution and the inner sensitivity.

1979 (1)

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

1978 (3)

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

E. R. Howell and R. F. Hess, "The functional area for summation to threshold for sinusoidal gratings," Vision Res. 18, 369–374 (1978).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

1977 (4)

L. Maffei and A. Fiorentini, "Spatial frequency rows in the striate visual cortex," Vision Res. 17, 257–264 (1977).

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977).

1976 (6)

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

B. Drum, "The relation of apparent brightness to contrast threshold on a photopic background: dependence on retinal position and target size," Vision Res. 16, 1401–1406 (1976).

J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).

G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).

O. Estévez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16,957–968 (1976).

1975 (3)

B. Breitmeyer and B. Julesz, "The role of on and off transients in determining the psychophysical spatial frequency response," Vision Res. 15, 411–415 (1975).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. London 247, 237–271 (1975).

1974 (6)

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

D. H. Kelly, "Effects of the cone-cell distribution on pattern detection experiments," J. Opt. Soc. Am. 64, 1523–1525 (1974).

J. L. Mannos and D. J. Sakrison, "The effects of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory 20, 525–536 (1974).

D. H. Hubel and T. N. Wiesel, "Uniformity of monkey striate cortex: a parallel relationship between field size, scatter and magnification factor," J. Comp. Neurol. 158, 295–305 (1974).

I. Rentschler and A. Fiorentini, "Meridional anisotropy of psychophysical spatial interactions," Vision Res. 14, 1467–1473 (1974).

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

1973 (2)

E. Pöppel, "Apparent brightness in the peripheral visual field," Naturwissenschaften 60, 110 (1973).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

1972 (1)

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).

1970 (2)

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. London 207, 351–356 (1970).

J. P. Thomas, "Model of the function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

1968 (2)

M. Davidson, "Perturbation approach to spatial brightness interaction in human vision," J. Opt. Soc. Am. 58, 1300–1308 (1968).

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. London 197, 551–566 (1968).

1967 (1)

G. Westheimer, "Spatial interaction in human cone vision," J. Physiol. London 190, 139–154 (1967).

1966 (1)

F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).

1963 (2)

1958 (1)

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).

1945 (1)

Aulhorm, E.

E. Aulhorm and H. Harms, in Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4, Chap. 5 ("Visual Perimetry").

Bergen, J. R.

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

Bilsen, F. A.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

Blackwell, H. R.

Bouman, M. A.

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).

Breitmeyer, B.

B. Breitmeyer and B. Julesz, "The role of on and off transients in determining the psychophysical spatial frequency response," Vision Res. 15, 411–415 (1975).

Campbell, F. W.

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. London 197, 551–566 (1968).

F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).

Cavonius, C. R.

O. Estévez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

Davidson, M.

Drum, B.

B. Drum, "The relation of apparent brightness to contrast threshold on a photopic background: dependence on retinal position and target size," Vision Res. 16, 1401–1406 (1976).

Estévez, O.

O. Estévez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

Fiorentini, A.

L. Maffei and A. Fiorentini, "Spatial frequency rows in the striate visual cortex," Vision Res. 17, 257–264 (1977).

I. Rentschler and A. Fiorentini, "Meridional anisotropy of psychophysical spatial interactions," Vision Res. 14, 1467–1473 (1974).

A. Fiorentini, "Mach band phenomena," in Handbook of Sensory Physiology, Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4.

Giese, S. C.

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

Grand, Y. Le

Y. Le Grand, Optique Physiologique, (Edition de la Revue d'Optique, Paris, 1956), Tome III (L'espace visuel), Chap. 8, [also in English in Y. Le Grand, Light, Colour and Vision (Chapman and Hall, London, 1968)].

Green, D. G.

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. London 207, 351–356 (1970).

Hall, Jr., J. A.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

Harms, H.

E. Aulhorm and H. Harms, in Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4, Chap. 5 ("Visual Perimetry").

Hess, R. F.

E. R. Howell and R. F. Hess, "The functional area for summation to threshold for sinusoidal gratings," Vision Res. 18, 369–374 (1978).

Hilz, R.

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

Hines, M.

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

Hoekstra, J.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

Howell, E. R.

E. R. Howell and R. F. Hess, "The functional area for summation to threshold for sinusoidal gratings," Vision Res. 18, 369–374 (1978).

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, "Uniformity of monkey striate cortex: a parallel relationship between field size, scatter and magnification factor," J. Comp. Neurol. 158, 295–305 (1974).

Julesz, B.

B. Breitmeyer and B. Julesz, "The role of on and off transients in determining the psychophysical spatial frequency response," Vision Res. 15, 411–415 (1975).

Keemink, C. J.

G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).

Kelly, D. H.

King-Smith, P. E.

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. London 247, 237–271 (1975).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

Koenderink, J. J.

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).

Kulikowski, J. J.

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. London 247, 237–271 (1975).

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).

Levinson, J.

F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).

Limb, J. O.

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

Maffei, L.

L. Maffei and A. Fiorentini, "Spatial frequency rows in the striate visual cortex," Vision Res. 17, 257–264 (1977).

Mannos, J. L.

J. L. Mannos and D. J. Sakrison, "The effects of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory 20, 525–536 (1974).

McCann, J. J.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

Moon, P.

Mostafavi, H.

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16,957–968 (1976).

Pöppel, E.

E. Pöppel, "Apparent brightness in the peripheral visual field," Naturwissenschaften 60, 110 (1973).

Rentschler, I.

I. Rentschler and A. Fiorentini, "Meridional anisotropy of psychophysical spatial interactions," Vision Res. 14, 1467–1473 (1974).

Robson, J. G.

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. London 197, 551–566 (1968).

Rubinstein, C. B.

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

Sakrison, D. J.

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16,957–968 (1976).

J. L. Mannos and D. J. Sakrison, "The effects of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory 20, 525–536 (1974).

Savoy, R. L.

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

R. L. Savoy and J. J. McCann, "Visibility of low-spatial frequency sine-wave targets: dependence on number of cycles," J. Opt. Soc. Am. 65, 343–350 (1975).

Spencer, D. E.

Taylor, M. M.

Thomas, J. P.

J. P. Thomas, "Model of the function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

van den Brink, G.

G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).

van der Brink, G.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

van der Goot, D. P. J.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

van der Wildt, G. T.

G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).

van Doorn, A. J.

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).

van Meeteren, A.

J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).

Vos, J. J.

J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).

Walraven, J.

J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).

Westheimer, G.

G. Westheimer, "Spatial interaction in human cone vision," J. Physiol. London 190, 139–154 (1967).

Weymouth, F. W.

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, "Uniformity of monkey striate cortex: a parallel relationship between field size, scatter and magnification factor," J. Comp. Neurol. 158, 295–305 (1974).

Wilson, H. R.

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

Am. J. Ophthalmol. (1)

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).

IEEE Trans. Inf. Theory (1)

J. L. Mannos and D. J. Sakrison, "The effects of a visual fidelity criterion on the encoding of images," IEEE Trans. Inf. Theory 20, 525–536 (1974).

J. Comp. Neurol. (1)

D. H. Hubel and T. N. Wiesel, "Uniformity of monkey striate cortex: a parallel relationship between field size, scatter and magnification factor," J. Comp. Neurol. 158, 295–305 (1974).

J. Opt. Soc. Am. (6)

J. Physiol. London (5)

P. E. King-Smith and J. J. Kulikowski, "The detection of gratings by independent activation of line detectors," J. Physiol. London 247, 237–271 (1975).

G. Westheimer, "Spatial interaction in human cone vision," J. Physiol. London 190, 139–154 (1967).

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. London 207, 351–356 (1970).

F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. London 197, 551–566 (1968).

F. W. Campbell, J. J. Kulikowski, and J. Levinson, "The effect of orientation on the visual resolution of gratings," J. Physiol. London 187, 427–436 (1966).

Kybernetic (1)

A. J. van Doorn, J. J. Koenderink, and M. A. Bouman, "The influence of the retinal inhomogeneity on the perception of spatial patterns," Kybernetic 10, 223–230 (1972).

Naturwissenschaften (1)

E. Pöppel, "Apparent brightness in the peripheral visual field," Naturwissenschaften 60, 110 (1973).

Opt. Acta (1)

D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977).

Psychol. Rev. (1)

J. P. Thomas, "Model of the function of receptive fields in human vision," Psychol. Rev. 77, 121–134 (1970).

Vision Res. (18)

J. J. Kulikowski and P. E. King-Smith, "Spatial arrangement of line, edge and grating detectors revealed by subthreshold summation," Vision Res. 13, 1455–1478 (1973).

H. R. Wilson and J. R. Bergen, "A four mechanism model for threshold spatial vision," Vision Res. 19, 19–32 (1979).

B. Drum, "The relation of apparent brightness to contrast threshold on a photopic background: dependence on retinal position and target size," Vision Res. 16, 1401–1406 (1976).

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).

J. J. McCann, R. L. Savoy, and J. A. Hall, Jr, "Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters," Vision Res. 18, 891–894 (1978).

E. R. Howell and R. F. Hess, "The functional area for summation to threshold for sinusoidal gratings," Vision Res. 18, 369–374 (1978).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

H. R. Wilson and S. C. Giese, "Threshold visibility of frequency gradient patterns," Vision Res. 17, 1177–1190 (1977).

I. Rentschler and A. Fiorentini, "Meridional anisotropy of psychophysical spatial interactions," Vision Res. 14, 1467–1473 (1974).

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, and F. A. Bilsen, "The influence of the number of cycles upon the visual contrast threshold for spatial sine wave patterns," Vision Res. 14, 365–368 (1974).

J. J. Vos, J. Walraven, and A. van Meeteren, "Light profiles of the foveal image of a point source," Vision Res. 16, 215–219 (1976).

G. T. van der Wildt, C. J. Keemink, and G. van den Brink, "Gradient detection and contrast transfer by the human eye," Vision Res. 16, 1047–1053 (1976).

O. Estévez and C. R. Cavonius, "Low-frequency attenuation in the detection of gratings: sorting out the artifacts," Vision Res. 16, 497–500 (1976).

H. Mostafavi and D. J. Sakrison, "Structure and properties of a single channel in the human visual system," Vision Res. 16,957–968 (1976).

B. Breitmeyer and B. Julesz, "The role of on and off transients in determining the psychophysical spatial frequency response," Vision Res. 15, 411–415 (1975).

L. Maffei and A. Fiorentini, "Spatial frequency rows in the striate visual cortex," Vision Res. 17, 257–264 (1977).

Other (12)

Taking for simplicity an infinitely thin vertical line positioned at (x,0), i.e., e(ξη) = δ(ξ–x), Eq. (7) implies s(x,y) = [σ(r)/α(r)]ω0(1))(0) with r2 = x2 + y2. The output maximum is along the line for the minimum r, that is, for y = 0.

See Sec. III D and Conclusion.

Y. Le Grand, Optique Physiologique, (Edition de la Revue d'Optique, Paris, 1956), Tome III (L'espace visuel), Chap. 8, [also in English in Y. Le Grand, Light, Colour and Vision (Chapman and Hall, London, 1968)].

E. Aulhorm and H. Harms, in Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4, Chap. 5 ("Visual Perimetry").

A stimulus can be called local if its extension is not more than 10–20 min of arc and extended if it exceeds, say, 1°. A stimulus can be local in one direction and extended in the other (one-dimensionally local), or local in all directions (two-dimensionally local).

The one-dimensional acuity limit may differ from the two-dimensional acuity limit. We consider here only their relative variation from the fovea.

More rounded envelopes can be obtained if σ is not related to α by a power law, or if a probability summation model is used for detection, the max operator in Eq. (24) being replaced by a nonlinear summation formula: the L norm can be replaced by a Lα norm as proposed by K. F. Quick, "A vector magnitude model of contrast detection," Kybernetik 16, 65–67 (1974).

This suggests a way to measure the local foveal filter using cosine gratings properly windowed by a function of x. This function must not be higher than α3. (x)/σ(x), σ(x) assumed to be known.

A. Fiorentini, "Mach band phenomena," in Handbook of Sensory Physiology, Visual Psychophysics (Springer, Heidelberg, 1972), Vol. VII/4.

A hexagonal network is chosen to model the retinal network. If d is the intercone distance at eccentricity (x,y), the receptor positions can be indexed as xij = x + id + j(d/2) and yij = y + j(d√3/2), (see Fig. 11); at the fovea, x0ij = id0 + jd0/2 and yij = jd0 √3/2.

We consider here for simplicity that the ganglion cell outputs are the outputs of the lateral interactions and that detectors immediately follow. Parts of the lateral interactions and detectors can occur in more central visual centers. Our hypothesis is only that the neural network is homogeneous, the inhomogeneity arising from the receptor spatial distribution and the inner sensitivity.

An inhomogeneous system can be called locally homogeneous if it can be described locally by one linear filter varying with eccentricity.

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