Abstract

A widely used model of simultaneous luminance pattern masking is based on mechanisms that sum inputs linearly and produce a response that is an S-shaped function of that sum. This model makes two predictions about masking: (1) Changing the masker spatial waveform will shift the threshold-versus-masker contrast function horizontally by a multiplicative constant. (2) Adding a second fixed-contrast masker will shift this function horizontally by an additive constant. Experimental tests do not support these predictions. The results can be explained by a new model that incorporates broadband divisive inhibition, consistent with physiology.

© 1994 Optical Society of America

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References

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  1. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [Crossref] [PubMed]
  2. F. W. Campbell, J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
    [PubMed]
  3. N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
    [Crossref] [PubMed]
  4. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [Crossref] [PubMed]
  5. C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
    [Crossref] [PubMed]
  6. Legge and Foley1fitted their data with a version of the model in which a single mechanism mediated detection at high contrast and many similar but spatially distributed mechanisms mediated detection at low contrast. Here I consider a version of the model in which a single mechanism mediates detection in each condition.
  7. This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).
  8. R. Hecht-Nielsen, Neurocomputing (Addison-Wesley, Reading, Mass., 1990).
  9. D. E. Rummelhart, J. L. McClelland, Foundations, Vol. 1 of Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986).
  10. Equation (1) may be derived from the luminance profile of the pattern component Li(x, y) and the spatial sensitivity of the mechanism sE(x,y) as follows:Let L0 be the space average luminance of the pattern, Ci= (Li(x,y)max− Lo)/Lo be the contrast of component i, and Nij(x,y) = [Lij(x,y) − L0]/[Lij(x,y)max− Lo] be the normalized luminance profile of pattern component i.The luminance profile of a component pattern may be specified as follows:Li(x,y)=Lo+LoCiNi(x,y).The excitation of a mechanism produced by pattern component i isEi″=∫∫−∞∞Li(x,y)sE(x,y)dxdy=Lo∫∫−∞∞sE(x,y)dxdy +CiLo∫∫−∞∞Ni(x,y)sE(x,y)dxdy.The integral of sE(x,y) is assumed to be 0. So for a pattern component having a normalized luminance profile, Ni(x,y), we may writeEi″=CisEi,sEi=Lo∫∫−∞∞Ni(x,y)sE(x,y)dxdy.
  11. Legge and Foley took the absolute value here, but half-wave rectification is more consistent with the biology of cortical cells.
  12. Legge and Foley had a coefficient in the numerator. This was needed in their version of the model because they normalized sensitivity by setting maximum sensitivity to 1.
  13. K. K. DeValois, R. H. B. Tootell, “Spatial-frequency-specific inhibition in cat striate cortex cells,” J. Physiol. 336, 359–376 (1983).
  14. A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
    [Crossref]
  15. J. Robson, “Neural coding of contrast in the visual system,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 152.
  16. D. J. Heeger, “Nonlinear model of neural responses in cat visual cortex,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991.
  17. D. J. Heeger, “Normalization of cell responses in cat visual cortex,” Vis. Neurosci. 9, 181–197 (1992).
    [Crossref] [PubMed]
  18. W. S. Stiles, Mechanisms of Colour Vision (Academic, London, 1978).
  19. N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
    [Crossref]
  20. E. N. Pugh, J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
    [Crossref]
  21. C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
    [Crossref]
  22. J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
    [Crossref] [PubMed]
  23. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983),
    [Crossref] [PubMed]
  24. See J. M. Foley, Y. Yang, “Forward pattern masking: effects of spatial frequency and contrast,” J. Opt. Soc. Am. A 8, 2026–2037 (1991), for a more comprehensive description of the method.In this and all the other fits described in this paper, the data of both experiments were fitted simultaneously so that all the common parameters have the same values for both experiments. A large number of fits were made starting from different initial parameter values, and the one with the lowest value of the sum of the square error was taken as the best fit in each case. When the estimated value of a sensitivity parameter was < 1, this value was set at 0 and the data refitted. If the sum of the square error did not increase, the parameter was eliminated.
    [Crossref] [PubMed]
  25. J. M. Foley, G. M. Boynton, “Simultaneous pattern masking: mechanisms are revealed by threshold versus masker contrast functions and the direct measurement of masking sensitivity,” Invest. Ophthalmol. Vis. Sci. 33 Suppl., 1256 (1992).
  26. When sensitivity to the target is constant, facilitation and masking depend only on Em″, the excitation produced by the masker. Let the two maskers have contrasts C1 and C2 and sensitivities sE1 and sE2, and let C0= C2(sE2/sE1), so that C2= C0(sE1/sE2). From Eq. (3),E″=C1sE1+C2sE2=C1sE1+C0sE1+(C1+C0)sE1.Thus adding a constant second masker is equivalent to adding a constant C0 to the contrast of the first masker. C0 may be positive or negative, depending on the sign of sE2. The TvC function will shift left or right by this same constant. Because the experimental range of masker contrast is limited, only a segment of this function may be manifested in the data. For example, in experiment 2 when there are two maskers, facilitation is predicted to occur at masker contrasts below the range used.
  27. A. I. Khuri, J. A. Cornell, Response Surfaces: Designs and Analysis (Dekker, New York, 1987).
  28. S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detector units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
    [Crossref] [PubMed]
  29. F. W. Campbell, J. J. Kulilowski, “Orientation selectivity of the human visual system,” J. Physiol. (London) 336, 359–376 (1966).
  30. G. C. Phillips, H. R. Wilson, “Orientation bandwidths of spatial mechanisms measured by masking,” J. Opt. Soc. Am. A 2, 226–232 (1984).
    [Crossref]
  31. J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc R. Soc. London Ser. B 246, 61–69 (1991).
    [Crossref]
  32. J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
    [Crossref] [PubMed]
  33. J. Nachmias, “Masked detection of gratings: the standard model revisited,” Vision Res. 33, 1359–1365 (1993).
    [Crossref] [PubMed]
  34. G. Sperling, M. M. Sondhi, “Model for visual luminance discrimination and flicker detection,” J. Opt. Soc. Am. 58, 1133–1145 (1968).
    [Crossref] [PubMed]
  35. D. P. Andrews, “Perception of contour orientation in the central fovea,” Vision Res. 7, 975–1013 (1967).
    [Crossref] [PubMed]
  36. R. H. S. Carpenter, C. Blakemore, “Interaction between orientations in human vision,” Exp. Brain Res. 18, 287–303 (1973).
    [Crossref] [PubMed]
  37. S. Grossberg, E. Mingolla, “Neural dynamics of perceptual grouping: textures, boundaries, and emergent segmentations,” Percept. Psychophys. 38, 141–171 (1985).
    [Crossref] [PubMed]
  38. S. Grossberg, E. Mingolla, “Neural dynamics of surface perception: boundary webs, illuminants, and shape-from-shading,” Computer Vision Graphics Image Process. 37, 116–165 (1987).
    [Crossref]
  39. S. Grossberg, E. Mingolla, D. Todorovic, “A neural network architecture for preattentive vision,” IEEE Trans. Biomed. Eng. 36, 65–84 (1989).
    [Crossref] [PubMed]
  40. J. Lubin, “Discrimination contours in an opponent motion space,” Invest. Ophthalmol. Vis. Sci. 30 Suppl., 426 (1989).
  41. J. R. Bergin, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).
  42. N. Graham, “Complex channels, early local nonlinearities, and normalization in texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).
  43. L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
    [Crossref] [PubMed]
  44. L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
    [Crossref] [PubMed]
  45. J. P. Thomas, L. A. Olzak, T. D. Wickens, “The bridge between Fourier and feature codes: some interferences from discrimination data,” presented at the European Conference on Visual Perception, Pisa, Italy, 1992.
  46. B. G. Breitmeyer, Visual Masking: An Integrative Approach (Oxford U. Press, New York, 1984).
  47. M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time course and contrast dependence,” Vision Res. 27, 369–379 (1987).
    [Crossref]
  48. R. L. DeValois, K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).
  49. D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
    [Crossref]
  50. W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
    [Crossref] [PubMed]

1993 (3)

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[Crossref] [PubMed]

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[Crossref] [PubMed]

J. Nachmias, “Masked detection of gratings: the standard model revisited,” Vision Res. 33, 1359–1365 (1993).
[Crossref] [PubMed]

1992 (4)

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[Crossref] [PubMed]

W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
[Crossref] [PubMed]

J. M. Foley, G. M. Boynton, “Simultaneous pattern masking: mechanisms are revealed by threshold versus masker contrast functions and the direct measurement of masking sensitivity,” Invest. Ophthalmol. Vis. Sci. 33 Suppl., 1256 (1992).

D. J. Heeger, “Normalization of cell responses in cat visual cortex,” Vis. Neurosci. 9, 181–197 (1992).
[Crossref] [PubMed]

1991 (4)

1989 (4)

S. Grossberg, E. Mingolla, D. Todorovic, “A neural network architecture for preattentive vision,” IEEE Trans. Biomed. Eng. 36, 65–84 (1989).
[Crossref] [PubMed]

J. Lubin, “Discrimination contours in an opponent motion space,” Invest. Ophthalmol. Vis. Sci. 30 Suppl., 426 (1989).

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detector units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[Crossref] [PubMed]

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[Crossref]

1987 (2)

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[Crossref]

S. Grossberg, E. Mingolla, “Neural dynamics of surface perception: boundary webs, illuminants, and shape-from-shading,” Computer Vision Graphics Image Process. 37, 116–165 (1987).
[Crossref]

1985 (2)

S. Grossberg, E. Mingolla, “Neural dynamics of perceptual grouping: textures, boundaries, and emergent segmentations,” Percept. Psychophys. 38, 141–171 (1985).
[Crossref] [PubMed]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[Crossref]

1984 (1)

1983 (2)

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983),
[Crossref] [PubMed]

K. K. DeValois, R. H. B. Tootell, “Spatial-frequency-specific inhibition in cat striate cortex cells,” J. Physiol. 336, 359–376 (1983).

1980 (1)

1979 (1)

E. N. Pugh, J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

1974 (2)

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

1973 (1)

R. H. S. Carpenter, C. Blakemore, “Interaction between orientations in human vision,” Exp. Brain Res. 18, 287–303 (1973).
[Crossref] [PubMed]

1971 (1)

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

1968 (2)

F. W. Campbell, J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

G. Sperling, M. M. Sondhi, “Model for visual luminance discrimination and flicker detection,” J. Opt. Soc. Am. 58, 1133–1145 (1968).
[Crossref] [PubMed]

1967 (1)

D. P. Andrews, “Perception of contour orientation in the central fovea,” Vision Res. 7, 975–1013 (1967).
[Crossref] [PubMed]

1966 (1)

F. W. Campbell, J. J. Kulilowski, “Orientation selectivity of the human visual system,” J. Physiol. (London) 336, 359–376 (1966).

Albrecht, D. G.

W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
[Crossref] [PubMed]

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[Crossref]

Anderson, S. J.

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detector units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[Crossref] [PubMed]

Andrews, D. P.

D. P. Andrews, “Perception of contour orientation in the central fovea,” Vision Res. 7, 975–1013 (1967).
[Crossref] [PubMed]

Bergin, J. R.

J. R. Bergin, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

Blakemore, C.

R. H. S. Carpenter, C. Blakemore, “Interaction between orientations in human vision,” Exp. Brain Res. 18, 287–303 (1973).
[Crossref] [PubMed]

Bonds, A. B.

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[Crossref]

Boynton, G. M.

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[Crossref] [PubMed]

J. M. Foley, G. M. Boynton, “Simultaneous pattern masking: mechanisms are revealed by threshold versus masker contrast functions and the direct measurement of masking sensitivity,” Invest. Ophthalmol. Vis. Sci. 33 Suppl., 1256 (1992).

Breitmeyer, B. G.

B. G. Breitmeyer, Visual Masking: An Integrative Approach (Oxford U. Press, New York, 1984).

Burr, D. C.

S. J. Anderson, D. C. Burr, “Receptive field properties of human motion detector units inferred from spatial frequency masking,” Vision Res. 29, 1343–1358 (1989).
[Crossref] [PubMed]

Campbell, F. W.

F. W. Campbell, J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

F. W. Campbell, J. J. Kulilowski, “Orientation selectivity of the human visual system,” J. Physiol. (London) 336, 359–376 (1966).

Carpenter, R. H. S.

R. H. S. Carpenter, C. Blakemore, “Interaction between orientations in human vision,” Exp. Brain Res. 18, 287–303 (1973).
[Crossref] [PubMed]

Cole, G. R.

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[Crossref]

Cornell, J. A.

A. I. Khuri, J. A. Cornell, Response Surfaces: Designs and Analysis (Dekker, New York, 1987).

DeValois, K.

R. L. DeValois, K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

DeValois, K. K.

K. K. DeValois, R. H. B. Tootell, “Spatial-frequency-specific inhibition in cat striate cortex cells,” J. Physiol. 336, 359–376 (1983).

DeValois, R.

This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).

DeValois, R. L.

R. L. DeValois, K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

Foley, J. M.

Geisler, W. S.

W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
[Crossref] [PubMed]

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[Crossref]

Georgeson, J. M.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[Crossref]

Georgeson, M. A.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[Crossref]

Graham, N.

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
[Crossref]

N. Graham, “Complex channels, early local nonlinearities, and normalization in texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

Grossberg, S.

S. Grossberg, E. Mingolla, D. Todorovic, “A neural network architecture for preattentive vision,” IEEE Trans. Biomed. Eng. 36, 65–84 (1989).
[Crossref] [PubMed]

S. Grossberg, E. Mingolla, “Neural dynamics of surface perception: boundary webs, illuminants, and shape-from-shading,” Computer Vision Graphics Image Process. 37, 116–165 (1987).
[Crossref]

S. Grossberg, E. Mingolla, “Neural dynamics of perceptual grouping: textures, boundaries, and emergent segmentations,” Percept. Psychophys. 38, 141–171 (1985).
[Crossref] [PubMed]

Hecht-Nielsen, R.

R. Hecht-Nielsen, Neurocomputing (Addison-Wesley, Reading, Mass., 1990).

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat visual cortex,” Vis. Neurosci. 9, 181–197 (1992).
[Crossref] [PubMed]

D. J. Heeger, “Nonlinear model of neural responses in cat visual cortex,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991.

Khuri, A. I.

A. I. Khuri, J. A. Cornell, Response Surfaces: Designs and Analysis (Dekker, New York, 1987).

Klein, S.

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

Kronauer, R. E.

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[Crossref]

Kulilowski, J. J.

F. W. Campbell, J. J. Kulilowski, “Orientation selectivity of the human visual system,” J. Physiol. (London) 336, 359–376 (1966).

Landy, M. S.

J. R. Bergin, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

Legge, G. E.

Levi, D.

This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).

Lubin, J.

J. Lubin, “Discrimination contours in an opponent motion space,” Invest. Ophthalmol. Vis. Sci. 30 Suppl., 426 (1989).

MafFei, L.

This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).

McClelland, J. L.

D. E. Rummelhart, J. L. McClelland, Foundations, Vol. 1 of Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986).

Mingolla, E.

S. Grossberg, E. Mingolla, D. Todorovic, “A neural network architecture for preattentive vision,” IEEE Trans. Biomed. Eng. 36, 65–84 (1989).
[Crossref] [PubMed]

S. Grossberg, E. Mingolla, “Neural dynamics of surface perception: boundary webs, illuminants, and shape-from-shading,” Computer Vision Graphics Image Process. 37, 116–165 (1987).
[Crossref]

S. Grossberg, E. Mingolla, “Neural dynamics of perceptual grouping: textures, boundaries, and emergent segmentations,” Percept. Psychophys. 38, 141–171 (1985).
[Crossref] [PubMed]

Mollon, J. D.

E. N. Pugh, J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

Morgan, M. J.

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[Crossref] [PubMed]

Nachmias, J.

J. Nachmias, “Masked detection of gratings: the standard model revisited,” Vision Res. 33, 1359–1365 (1993).
[Crossref] [PubMed]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

Olzak, L. A.

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[Crossref] [PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[Crossref] [PubMed]

J. P. Thomas, L. A. Olzak, T. D. Wickens, “The bridge between Fourier and feature codes: some interferences from discrimination data,” presented at the European Conference on Visual Perception, Pisa, Italy, 1992.

Pelli, D. G.

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983),
[Crossref] [PubMed]

Phillips, G. C.

Pugh, E. N.

E. N. Pugh, J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

Robson, J.

J. Robson, “Neural coding of contrast in the visual system,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 152.

Robson, J. R.

F. W. Campbell, J. R. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Ross, J.

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[Crossref] [PubMed]

J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc R. Soc. London Ser. B 246, 61–69 (1991).
[Crossref]

Rovamo, J.

This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).

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D. E. Rummelhart, J. L. McClelland, Foundations, Vol. 1 of Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986).

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J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

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Speed, H. D.

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[Crossref] [PubMed]

J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc R. Soc. London Ser. B 246, 61–69 (1991).
[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[Crossref] [PubMed]

J. P. Thomas, L. A. Olzak, T. D. Wickens, “The bridge between Fourier and feature codes: some interferences from discrimination data,” presented at the European Conference on Visual Perception, Pisa, Italy, 1992.

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J. P. Thomas, L. A. Olzak, T. D. Wickens, “The bridge between Fourier and feature codes: some interferences from discrimination data,” presented at the European Conference on Visual Perception, Pisa, Italy, 1992.

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[Crossref] [PubMed]

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[Crossref]

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[Crossref]

C. F. Stromeyer, G. R. Cole, R. E. Kronauer, “Second-site adaptation in the red–green chromatic pathways,” Vision Res. 25, 219–237 (1985).
[Crossref]

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[Crossref] [PubMed]

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[Crossref] [PubMed]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[Crossref] [PubMed]

J. Nachmias, “Masked detection of gratings: the standard model revisited,” Vision Res. 33, 1359–1365 (1993).
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[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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Other (18)

J. Robson, “Neural coding of contrast in the visual system,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 152.

D. J. Heeger, “Nonlinear model of neural responses in cat visual cortex,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991.

W. S. Stiles, Mechanisms of Colour Vision (Academic, London, 1978).

N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
[Crossref]

Legge and Foley1fitted their data with a version of the model in which a single mechanism mediated detection at high contrast and many similar but spatially distributed mechanisms mediated detection at low contrast. Here I consider a version of the model in which a single mechanism mediates detection in each condition.

This literature is reviewed by H. R. Wilson, D. Levi, L. MafFei, J. Rovamo, R. DeValois, “The perception of form: retina to striate cortex,” in L. Spillmann, J. S. Werner, eds., Visual Perception: The Neurophysiological Foundations (Academic, San Diego, Calif., 1990).

R. Hecht-Nielsen, Neurocomputing (Addison-Wesley, Reading, Mass., 1990).

D. E. Rummelhart, J. L. McClelland, Foundations, Vol. 1 of Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986).

Equation (1) may be derived from the luminance profile of the pattern component Li(x, y) and the spatial sensitivity of the mechanism sE(x,y) as follows:Let L0 be the space average luminance of the pattern, Ci= (Li(x,y)max− Lo)/Lo be the contrast of component i, and Nij(x,y) = [Lij(x,y) − L0]/[Lij(x,y)max− Lo] be the normalized luminance profile of pattern component i.The luminance profile of a component pattern may be specified as follows:Li(x,y)=Lo+LoCiNi(x,y).The excitation of a mechanism produced by pattern component i isEi″=∫∫−∞∞Li(x,y)sE(x,y)dxdy=Lo∫∫−∞∞sE(x,y)dxdy +CiLo∫∫−∞∞Ni(x,y)sE(x,y)dxdy.The integral of sE(x,y) is assumed to be 0. So for a pattern component having a normalized luminance profile, Ni(x,y), we may writeEi″=CisEi,sEi=Lo∫∫−∞∞Ni(x,y)sE(x,y)dxdy.

Legge and Foley took the absolute value here, but half-wave rectification is more consistent with the biology of cortical cells.

Legge and Foley had a coefficient in the numerator. This was needed in their version of the model because they normalized sensitivity by setting maximum sensitivity to 1.

J. R. Bergin, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

N. Graham, “Complex channels, early local nonlinearities, and normalization in texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991).

When sensitivity to the target is constant, facilitation and masking depend only on Em″, the excitation produced by the masker. Let the two maskers have contrasts C1 and C2 and sensitivities sE1 and sE2, and let C0= C2(sE2/sE1), so that C2= C0(sE1/sE2). From Eq. (3),E″=C1sE1+C2sE2=C1sE1+C0sE1+(C1+C0)sE1.Thus adding a constant second masker is equivalent to adding a constant C0 to the contrast of the first masker. C0 may be positive or negative, depending on the sign of sE2. The TvC function will shift left or right by this same constant. Because the experimental range of masker contrast is limited, only a segment of this function may be manifested in the data. For example, in experiment 2 when there are two maskers, facilitation is predicted to occur at masker contrasts below the range used.

A. I. Khuri, J. A. Cornell, Response Surfaces: Designs and Analysis (Dekker, New York, 1987).

J. P. Thomas, L. A. Olzak, T. D. Wickens, “The bridge between Fourier and feature codes: some interferences from discrimination data,” presented at the European Conference on Visual Perception, Pisa, Italy, 1992.

B. G. Breitmeyer, Visual Masking: An Integrative Approach (Oxford U. Press, New York, 1984).

R. L. DeValois, K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

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Figures (7)

Fig. 1
Fig. 1

A version of the Legge–Foley model of the human pattern-vision mechanisms.

Fig. 2
Fig. 2

Model 3: a new model of the human pattern-vision mechanisms. The principal difference is the divisive inhibitory input (shown at upper left). This input is raised to a power before it is summed across different orientations.

Fig. 3
Fig. 3

Experiment 1: TvC functions for simultaneous masking with masker orientation re target as the parameter. The function for relative orientation = 0 deg is shown in both panels for both observers. a, Masker at 0, 11.25, and 22.5 deg; b, masker at 0, 45, and 90 deg. Smooth curves correspond to the best-fitting version of model 1.

Fig. 4
Fig. 4

Experiment 2: TvC functions for a vertical target and vertical Gabor masker as a function of the orientation of a second fixed-contrast masker (C = 0.1). Smooth curves correspond to the best-fitting version of model 1.

Fig. 5
Fig. 5

Experiment 1; the data are the same as in Fig. 3. Smooth curves correspond to the best-fitting version of model 3.

Fig. 6
Fig. 6

Experiment 2; the data are the same as in Fig. 4. Smooth curves correspond to the best-fitting version of model 3.

Fig. 7
Fig. 7

Excitatory sensitivity, sEmj, and inhibitory sensitivity, sImj, as a function of masker orientation re target.

Tables (2)

Tables Icon

Table 1 Experimental Variables

Equations (13)

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E i = C i s E i ,
E = i E i = i C i s E i ,
E = max ( E , 0 ) .
R = E p / ( E 2 + Z ) ,
I = i I i = i C i s I i , I = max ( I , 0 ) .
R = E p / ( I q + Z ) .
I j = i I i j = i C i j s I i j , I j = max ( I , 0 ) .
R = E p / ( j I j q + Z ) .
δ R = R m + t R m = 1 ,
Li(x,y)=Lo+LoCiNi(x,y).
Ei=Li(x,y)sE(x,y)dxdy=LosE(x,y)dxdy+CiLoNi(x,y)sE(x,y)dxdy.
Ei=CisEi,sEi=LoNi(x,y)sE(x,y)dxdy.
E=C1sE1+C2sE2=C1sE1+C0sE1+(C1+C0)sE1.

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