Abstract

We have implemented a model of contrast gain control in human vision that incorporates a number of key features, including a contrast sensitivity function, multiple oriented bandpass channels, accelerating nonlinearities, and a divisive inhibitory gain control pool. The parameters of this model have been optimized through a fit to the recent data that describe masking of a Gabor function by cosine and Gabor masks [J. M. Foley, “Human luminance pattern mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710 (1994)]. The model achieves a good fit to the data. We also demonstrate how the concept of recruitment may accommodate a variant of this model in which excitatory and inhibitory paths have a common accelerating nonlinearity, but which include multiple channels tuned to different levels of contrast [P. C. Teo and D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE 2179, 127 (1994)].

© 1997 Optical Society of America

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References

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  1. J. Nachmias, R. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  2. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  3. P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 127–139 (1994).
    [CrossRef]
  4. H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
    [CrossRef] [PubMed]
  5. J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
    [CrossRef]
  6. G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
    [PubMed]
  7. W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
    [CrossRef] [PubMed]
  8. D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–198 (1992).
    [PubMed]
  9. M. W. Cannon, S. C. Fullenkamp, “A transducer model for contrast perception,” Vision Res. 31, 983–998 (1991).
    [CrossRef] [PubMed]
  10. A. Ahumada, “Computational image quality metrics: a review,” in SID International Symposium 1993, Vol. 24 of Digest of Technical Papers (Society for Information Display, Santa Ana, Calif., 1993), pp. 305–308.
  11. S. Daly, “The visible differences predictor: an algorithm for the assessment of image fidelity quality,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).
  12. J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).
  13. J. W. Woods, Subband Image Coding (Kluwer Academic, Norwell, Mass., 1991).
  14. J. M. Valeton, A. B. Watson, “Contrast detection does not have a local spatial scale,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 428 (1990).
  15. A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graphics Image Process. 39, 311–327 (1987).
    [CrossRef]
  16. D. J. Heeger, “Half-squaring in responses of cat simple cells,” Visual Neurosci. 9, 427–443 (1992).
  17. A. B. Watson, “Efficiency of an image code based on human vision,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
    [CrossRef] [PubMed]
  18. A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
    [CrossRef] [PubMed]
  19. S. Wolfram, The Mathematica Book (Wolfram Media/Cambridge U. Press, Champaign, Ill., 1996).
  20. J. M. Foley, G. M. Boynton, “A new model of human luminance pattern vision mechanisms: analysis of the effects of pattern orientation, spatial phase and temporal frequency,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 32–42 (1994).
    [CrossRef]
  21. R. J. Snowden, “The effect of contrast surrounds on contrast centres: merely normal masking?” Invest. Ophthalmol. Visual Sci. Suppl. 36, S438 (1995).
  22. J. A. Solomon, A. B. Watson, “Spatial and spatial frequency spreads of masking: measurements and a contrast gain-control model,” Perception (Suppl.) 24, 37 (1995).
  23. M. D’Zmura, B. Singer, “Spatial pooling of contrast gain control,” J. Opt. Soc. Am. A 13, 2135–2140 (1996).
    [CrossRef]
  24. J. M. Foley, “Simultaneous pattern masking: How come threshold elevation bandwidth decreases as stimulus duration increases?” Invest. Ophthalmol. Visual Sci. Suppl. 37, S912 (1996).
  25. J. Nachmias, “Masked detection of gratings: the standard model revisited,” Vision Res. 33, 1359–1365 (1993).
    [CrossRef] [PubMed]

1996 (2)

M. D’Zmura, B. Singer, “Spatial pooling of contrast gain control,” J. Opt. Soc. Am. A 13, 2135–2140 (1996).
[CrossRef]

J. M. Foley, “Simultaneous pattern masking: How come threshold elevation bandwidth decreases as stimulus duration increases?” Invest. Ophthalmol. Visual Sci. Suppl. 37, S912 (1996).

1995 (2)

R. J. Snowden, “The effect of contrast surrounds on contrast centres: merely normal masking?” Invest. Ophthalmol. Visual Sci. Suppl. 36, S438 (1995).

J. A. Solomon, A. B. Watson, “Spatial and spatial frequency spreads of masking: measurements and a contrast gain-control model,” Perception (Suppl.) 24, 37 (1995).

1994 (1)

1993 (2)

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

H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
[CrossRef] [PubMed]

1992 (4)

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

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

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–198 (1992).
[PubMed]

D. J. Heeger, “Half-squaring in responses of cat simple cells,” Visual Neurosci. 9, 427–443 (1992).

1991 (1)

M. W. Cannon, S. C. Fullenkamp, “A transducer model for contrast perception,” Vision Res. 31, 983–998 (1991).
[CrossRef] [PubMed]

1990 (1)

J. M. Valeton, A. B. Watson, “Contrast detection does not have a local spatial scale,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 428 (1990).

1987 (2)

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graphics Image Process. 39, 311–327 (1987).
[CrossRef]

A. B. Watson, “Efficiency of an image code based on human vision,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

1985 (1)

1980 (1)

1974 (1)

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

Ahumada, A.

A. Ahumada, “Computational image quality metrics: a review,” in SID International Symposium 1993, Vol. 24 of Digest of Technical Papers (Society for Information Display, Santa Ana, Calif., 1993), pp. 305–308.

Ahumada, A. J.

Albrecht, D. G.

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

Boynton, G. M.

J. M. Foley, G. M. Boynton, “A new model of human luminance pattern vision mechanisms: analysis of the effects of pattern orientation, spatial phase and temporal frequency,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 32–42 (1994).
[CrossRef]

Cannon, M. W.

M. W. Cannon, S. C. Fullenkamp, “A transducer model for contrast perception,” Vision Res. 31, 983–998 (1991).
[CrossRef] [PubMed]

D’Zmura, M.

Daly, S.

S. Daly, “The visible differences predictor: an algorithm for the assessment of image fidelity quality,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).

DeAngelis, G. C.

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

Foley, J. M.

J. M. Foley, “Simultaneous pattern masking: How come threshold elevation bandwidth decreases as stimulus duration increases?” Invest. Ophthalmol. Visual Sci. Suppl. 37, S912 (1996).

J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
[CrossRef]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

J. M. Foley, G. M. Boynton, “A new model of human luminance pattern vision mechanisms: analysis of the effects of pattern orientation, spatial phase and temporal frequency,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 32–42 (1994).
[CrossRef]

Freeman, R. D.

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

Fullenkamp, S. C.

M. W. Cannon, S. C. Fullenkamp, “A transducer model for contrast perception,” Vision Res. 31, 983–998 (1991).
[CrossRef] [PubMed]

Geisler, W. S.

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

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–198 (1992).
[PubMed]

D. J. Heeger, “Half-squaring in responses of cat simple cells,” Visual Neurosci. 9, 427–443 (1992).

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 127–139 (1994).
[CrossRef]

Humanski, R.

H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
[CrossRef] [PubMed]

Legge, G. E.

Lubin, J.

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).

Nachmias, J.

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

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

Ohzawa, I.

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

Robson, J. G.

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

Sansbury, R.

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

Singer, B.

Snowden, R. J.

R. J. Snowden, “The effect of contrast surrounds on contrast centres: merely normal masking?” Invest. Ophthalmol. Visual Sci. Suppl. 36, S438 (1995).

Solomon, J. A.

J. A. Solomon, A. B. Watson, “Spatial and spatial frequency spreads of masking: measurements and a contrast gain-control model,” Perception (Suppl.) 24, 37 (1995).

Teo, P. C.

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 127–139 (1994).
[CrossRef]

Valeton, J. M.

J. M. Valeton, A. B. Watson, “Contrast detection does not have a local spatial scale,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 428 (1990).

Watson, A. B.

J. A. Solomon, A. B. Watson, “Spatial and spatial frequency spreads of masking: measurements and a contrast gain-control model,” Perception (Suppl.) 24, 37 (1995).

J. M. Valeton, A. B. Watson, “Contrast detection does not have a local spatial scale,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 428 (1990).

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graphics Image Process. 39, 311–327 (1987).
[CrossRef]

A. B. Watson, “Efficiency of an image code based on human vision,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
[CrossRef] [PubMed]

Wolfram, S.

S. Wolfram, The Mathematica Book (Wolfram Media/Cambridge U. Press, Champaign, Ill., 1996).

Woods, J. W.

J. W. Woods, Subband Image Coding (Kluwer Academic, Norwell, Mass., 1991).

Comput. Vision Graphics Image Process. (1)

A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graphics Image Process. 39, 311–327 (1987).
[CrossRef]

Invest. Ophthalmol. Visual Sci. Suppl. (3)

R. J. Snowden, “The effect of contrast surrounds on contrast centres: merely normal masking?” Invest. Ophthalmol. Visual Sci. Suppl. 36, S438 (1995).

J. M. Foley, “Simultaneous pattern masking: How come threshold elevation bandwidth decreases as stimulus duration increases?” Invest. Ophthalmol. Visual Sci. Suppl. 37, S912 (1996).

J. M. Valeton, A. B. Watson, “Contrast detection does not have a local spatial scale,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 428 (1990).

J. Neurophysiol. (1)

G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Perception (Suppl.) (1)

J. A. Solomon, A. B. Watson, “Spatial and spatial frequency spreads of masking: measurements and a contrast gain-control model,” Perception (Suppl.) 24, 37 (1995).

Vision Res. (5)

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

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

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

H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “A transducer model for contrast perception,” Vision Res. 31, 983–998 (1991).
[CrossRef] [PubMed]

Visual Neurosci. (2)

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–198 (1992).
[PubMed]

D. J. Heeger, “Half-squaring in responses of cat simple cells,” Visual Neurosci. 9, 427–443 (1992).

Other (7)

S. Wolfram, The Mathematica Book (Wolfram Media/Cambridge U. Press, Champaign, Ill., 1996).

J. M. Foley, G. M. Boynton, “A new model of human luminance pattern vision mechanisms: analysis of the effects of pattern orientation, spatial phase and temporal frequency,” in Computational Vision Based on Neurobiology, T. B. Lawton, ed., Proc. SPIE2054, 32–42 (1994).
[CrossRef]

A. Ahumada, “Computational image quality metrics: a review,” in SID International Symposium 1993, Vol. 24 of Digest of Technical Papers (Society for Information Display, Santa Ana, Calif., 1993), pp. 305–308.

S. Daly, “The visible differences predictor: an algorithm for the assessment of image fidelity quality,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).

J. Lubin, “The use of psychophysical data and models in the analysis of display system performance,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).

J. W. Woods, Subband Image Coding (Kluwer Academic, Norwell, Mass., 1991).

P. C. Teo, D. J. Heeger, “Perceptual image distortion,” in Human Vision, Visual Processing, and Digital Display V, B. E. Rogowitz, J. P. Allebach, eds., Proc. SPIE2179, 127–139 (1994).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

Outline of the generic image discrimination model incorporating contrast gain control.

Fig. 2
Fig. 2

Outline of the specific model used in our contrast gain control model of pattern masking. CSF, contrast sensitivity function.

Fig. 3
Fig. 3

Example stimuli to illustrate the operation of the model: (a) cosine mask at 45-deg orientation, (b) Gabor target, (c) mask at 25% contrast, (d) mask at 25% contrast plus target at 50% contrast.

Fig. 4
Fig. 4

Contrast sensitivities for 1-octave Gabor targets as a function of spatial frequency, fit by a parabola in log-log coordinates (from Ref. 14). The parameters are peak sensitivity, 62.24; peak frequency, 1.04 c/deg; and log bandwidth at half-height, 1.118.

Fig. 5
Fig. 5

Gabor array filter bank, with three spatial frequencies and four orientations. (a) The transfer functions and (b) the even impulse responses of each filter are shown, all scaled to unit amplitude.

Fig. 6
Fig. 6

Responses of the Gabor filter bank (a) to mask alone and (b) to mask plus target.

Fig. 7
Fig. 7

Responses after the excitatory nonlinearity (a) to mask alone and (b) to mask plus target.

Fig. 8
Fig. 8

(a) Example set of three inhibitory pooling kernels, one for each level, and (b) their corresponding 3D Fourier transforms.

Fig. 9
Fig. 9

Response of inhibitory path (a) to mask alone and (b) to mask plus target.

Fig. 10
Fig. 10

Normalized responses (a) to mask alone and (b) mask plus target.

Fig. 11
Fig. 11

Differential response raised to the power β=4 for the example stimuli: (a) target contrast, 50%; (b) target contrast, 17%. For clarity, both images are displayed at full contrast; in (a) the largest value is 195.3; in (b) it is 1.3.

Fig. 12
Fig. 12

Stimuli from Foley and Boynton.20 The first row shows a Gabor target added to cosine masks at orientations of 0, 11.25, 22.5, 45, and 90 deg. The second row shows the same Gabor target added to an identical Gabor mask or a Gabor mask plus a cosine mask at 45 or 90 deg.

Fig. 13
Fig. 13

Data and simulations for observer KMF. Each graph contains an absolute threshold (no mask) plotted on the vertical axis; the corresponding model prediction is indicated by a horizontal line.

Fig. 14
Fig. 14

Data and simulations for observer JYS, as in Fig. 13.

Fig. 15
Fig. 15

Effect of mask phase. Target was a 2-c/deg Gabor function; mask was a cosine at either 0 or 90 deg phase relative to the center of the Gabor. The curves are fits of the model. The 0-deg prediction is also reproduced on the right for comparison.

Fig. 16
Fig. 16

Thin curves show the responses of a set of saturating neurons with p=q, and input gains ranging between 0 and 1.5 log units in 0.5-log-unit steps. The thick solid curve is the sum of these responses. The dashed curve is the response of a single, nonsaturating neuron with p=2.4, q=2, a=1, b=1, g=0.0316. (a) p=q=2; a=1; b=1. (b) p=q=2.4; a={0.850606, 1.01095, 1.20151, 1.428}; b=1.

Fig. 17
Fig. 17

Neural response functions for several values of b (0.01, 0.0316, 0.1, 0.316, 1). The corner of each curve, which occurs at c=b/(gν), is plotted as a point. Other parameters are ν=0.5, a=1, g=10, p=2.4, q=2.

Tables (2)

Tables Icon

Table 1 Model Notation

Tables Icon

Table 2 Estimated Model Parameters and Rms Error for the Two Observers in Foley and Boynton (Ref. 20) a

Equations (13)

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

tu¯,x¯,ϕq*Hu¯,x¯,ϕ.
ru¯,x¯,ϕ=tu¯,x¯,ϕpbq+tu¯,x¯,ϕq*Hu¯,x¯,ϕ.
d=|r1u¯,x¯,ϕ-r2u¯,x¯,ϕ|β1/β.
d=b-q|Gf|β1/β.
a(gkc)piwi(gic)q+bq.
ν=iwi(gi/gk)q1/q.
a(gc)p(gcν)p+bq.
a=agp-q,
b=b/g.
a=abp-q,
g=g/b.
g=ga1/(p-q),
b=ba1/(p-q).

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