Abstract

The detectability of a sinusoidal grating was measured in a standard two-interval forced-choice experiment against backgrounds of noise gratings of the same orientation as the signal. The noise gratings were either spatially high-pass or low-pass filtered and were either unchanged in each observation interval (static) or flickering at a rate that depended on their cutoff frequency (dynamic). Spatial-frequency-selective mechanisms are inferred from the data and their characteristics shown to depend on assumptions concerning the detection process thought to follow the spatial-frequency-selective device.

© 1981 Optical Society of America

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  1. F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of grating,” J. Physiol. London 197, 551–556 (1968).
  2. L. Maffei, “Spatial frequency channels: neural mechanisms,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, and H. L. Teuber, eds. (Springer-Verlag, Berlin, 1978), Chap. VIII.
  3. R. De Valois, “Spatial processing of luminance and colour,” Invest Ophthamol. 17, 834–835 (1978).
  4. J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).
  5. H. L. F. Helmholtz, The Sensations of Tone, A. J. Ellis, trans. (Dover, New York, 1954).
  6. C. Blakernore and F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. London 200, 11P–13P (1967).
  7. M. B. Sachs, J. Nachmias, and J. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
    [CrossRef] [PubMed]
  8. C. F. Stromeyer and B. Julesz, “Spatial-frequency masking in vision: critical bands and the spread of masking,” J. Opt. Soc. Am. 62, 1221–1232 (1972).
    [CrossRef] [PubMed]
  9. R. D. Patterson and G. B. Henning, “Stimulus variability and auditory filter shape,” J. Acoust. Soc. Am. 62, 649–664 (1977).
    [CrossRef] [PubMed]
  10. J. Nachmias, “Effects of exposure duration on visual contrast sensitivity with square-wave gratings,” J. Opt. Soc. Am. 67, 421–427 (1967).
    [CrossRef]
  11. R. D. Patterson, “Auditory filter shape,” J. Acoust. Soc. Am. 55, 802–809 (1974).
    [CrossRef] [PubMed]
  12. U. Greis and R. Röhler, “Untersuchung der subjectiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970).
    [CrossRef]
  13. B. G. Hertz and G. B. Henning.
  14. F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).
  15. G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
    [CrossRef] [PubMed]
  16. Stromeyer and Julesz kept the product of the square of the noise contrast and the bandwidth of their masking noise constant when changing cutoff frequencies.17 If we assume that masking is proportional to noise-contrast density, then we might adjust the data in Fig. 6 to show the contrast elevation that would have occurred had Stomeyer and Julesz kept their noise-contrast density constant. The correction steepens the low-frequency side from about 0.35-log-unit change of contrast per halving of spatial frequency to 0.52 log unit per halving. The steepening of the high-frequency side is negligible when the correction is applied on the basis of the bandwidths used by Stromeyer and Julesz.
  17. C. F. Stromeyer, Division of Applied Sciences, Harvard University, Cambridge, Mass. 02138, personal communication.
  18. D. G. Pelli, Department of Psychology, University of Minnesota, Minneapolis, Minn. 55455, personal communication (1980).
  19. We are unable to reject the hypothesis that our data are linear on semilogarithmic coordinates. The more extensive adjusted data16 of Stromeyer and Julesz are more nearly linear on double-logarithmic coordinates.
  20. R. D. Patterson, “Auditory filter shapes derived with noise stimuli,” J. Acoust. Soc. Am. 59, 640–654 (1976).
    [CrossRef] [PubMed]
  21. D. G. Pelli, “Channel properties revealed by noise masking,” Invest. Ophthalmol. 19, Suppl. 44A (1980).
  22. J. Nachmias, “Signal detection theory and its application to problems in vision,” in Handbook of Sensory Physiology, D. Jameson and L. M. Hurvich, eds. (Springer-Verlag, Berlin, 1972), Chap. VIII/4.
    [CrossRef]
  23. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).
  24. B. E. Carter and G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. London 219, 355–365 (1971).
  25. F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).
  26. G. B. Henning, “Effect of interaural phase on frequency and amplitude discrimination,” J. Acoust. Soc. Am. 54, 1160–1178 (1973).
    [CrossRef] [PubMed]
  27. G. B. Henning, “A model of auditory discrimination and detection,” J. Acoust. Soc. Am. 41, 774–777 (1967).
    [CrossRef] [PubMed]
  28. J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,” J. Opt. Soc. Am. 65, 1141–1142 (1966).
    [CrossRef]
  29. D. H. Kelly, “Flickering patterns and lateral inhibition,” J. Opt. Soc. Am. 59, 1361–1369 (1969).
    [CrossRef]
  30. J. L. Hinton and G. B. Henning.
  31. P. Lennie, Laboratory of Experimental Psychology, University of Sussex, Brighton, Sussex, U.K., personal communication (1979).

1980 (1)

D. G. Pelli, “Channel properties revealed by noise masking,” Invest. Ophthalmol. 19, Suppl. 44A (1980).

1978 (2)

R. De Valois, “Spatial processing of luminance and colour,” Invest Ophthamol. 17, 834–835 (1978).

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).

1977 (1)

R. D. Patterson and G. B. Henning, “Stimulus variability and auditory filter shape,” J. Acoust. Soc. Am. 62, 649–664 (1977).
[CrossRef] [PubMed]

1976 (1)

R. D. Patterson, “Auditory filter shapes derived with noise stimuli,” J. Acoust. Soc. Am. 59, 640–654 (1976).
[CrossRef] [PubMed]

1975 (1)

G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

1974 (1)

R. D. Patterson, “Auditory filter shape,” J. Acoust. Soc. Am. 55, 802–809 (1974).
[CrossRef] [PubMed]

1973 (1)

G. B. Henning, “Effect of interaural phase on frequency and amplitude discrimination,” J. Acoust. Soc. Am. 54, 1160–1178 (1973).
[CrossRef] [PubMed]

1972 (1)

1971 (2)

B. E. Carter and G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. London 219, 355–365 (1971).

M. B. Sachs, J. Nachmias, and J. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

1970 (1)

U. Greis and R. Röhler, “Untersuchung der subjectiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970).
[CrossRef]

1969 (2)

F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).

D. H. Kelly, “Flickering patterns and lateral inhibition,” J. Opt. Soc. Am. 59, 1361–1369 (1969).
[CrossRef]

1968 (1)

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of grating,” J. Physiol. London 197, 551–556 (1968).

1967 (3)

C. Blakernore and F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. London 200, 11P–13P (1967).

J. Nachmias, “Effects of exposure duration on visual contrast sensitivity with square-wave gratings,” J. Opt. Soc. Am. 67, 421–427 (1967).
[CrossRef]

G. B. Henning, “A model of auditory discrimination and detection,” J. Acoust. Soc. Am. 41, 774–777 (1967).
[CrossRef] [PubMed]

1966 (1)

1965 (1)

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).

Blakernore, C.

C. Blakernore and F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. London 200, 11P–13P (1967).

Broadbent, D. E.

G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of grating,” J. Physiol. London 197, 551–556 (1968).

C. Blakernore and F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. London 200, 11P–13P (1967).

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).

Carpenter, R. H.

F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).

Carter, B. E.

B. E. Carter and G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. London 219, 355–365 (1971).

Davenport, W. B.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

De Valois, R.

R. De Valois, “Spatial processing of luminance and colour,” Invest Ophthamol. 17, 834–835 (1978).

Green, D. G.

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).

Greis, U.

U. Greis and R. Röhler, “Untersuchung der subjectiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970).
[CrossRef]

Helmholtz, H. L. F.

H. L. F. Helmholtz, The Sensations of Tone, A. J. Ellis, trans. (Dover, New York, 1954).

Henning, G. B.

R. D. Patterson and G. B. Henning, “Stimulus variability and auditory filter shape,” J. Acoust. Soc. Am. 62, 649–664 (1977).
[CrossRef] [PubMed]

G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

G. B. Henning, “Effect of interaural phase on frequency and amplitude discrimination,” J. Acoust. Soc. Am. 54, 1160–1178 (1973).
[CrossRef] [PubMed]

B. E. Carter and G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. London 219, 355–365 (1971).

G. B. Henning, “A model of auditory discrimination and detection,” J. Acoust. Soc. Am. 41, 774–777 (1967).
[CrossRef] [PubMed]

B. G. Hertz and G. B. Henning.

J. L. Hinton and G. B. Henning.

Hertz, B. G.

G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

B. G. Hertz and G. B. Henning.

Hinton, J. L.

J. L. Hinton and G. B. Henning.

Julesz, B.

Kelly, D. H.

Lennie, P.

P. Lennie, Laboratory of Experimental Psychology, University of Sussex, Brighton, Sussex, U.K., personal communication (1979).

Levinson, J. Z.

F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).

Maffei, L.

L. Maffei, “Spatial frequency channels: neural mechanisms,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, and H. L. Teuber, eds. (Springer-Verlag, Berlin, 1978), Chap. VIII.

Movshon, J. A.

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).

Nachmias, J.

Patterson, R. D.

R. D. Patterson and G. B. Henning, “Stimulus variability and auditory filter shape,” J. Acoust. Soc. Am. 62, 649–664 (1977).
[CrossRef] [PubMed]

R. D. Patterson, “Auditory filter shapes derived with noise stimuli,” J. Acoust. Soc. Am. 59, 640–654 (1976).
[CrossRef] [PubMed]

R. D. Patterson, “Auditory filter shape,” J. Acoust. Soc. Am. 55, 802–809 (1974).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, “Channel properties revealed by noise masking,” Invest. Ophthalmol. 19, Suppl. 44A (1980).

D. G. Pelli, Department of Psychology, University of Minnesota, Minneapolis, Minn. 55455, personal communication (1980).

Robson, J.

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of grating,” J. Physiol. London 197, 551–556 (1968).

J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,” J. Opt. Soc. Am. 65, 1141–1142 (1966).
[CrossRef]

Röhler, R.

U. Greis and R. Röhler, “Untersuchung der subjectiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970).
[CrossRef]

Root, W. L.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

Sachs, M. B.

Stromeyer, C. F.

Thompson, I. D.

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).

Tolhurst, D. J.

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).

Invest Ophthamol. (1)

R. De Valois, “Spatial processing of luminance and colour,” Invest Ophthamol. 17, 834–835 (1978).

Invest. Ophthalmol. (1)

D. G. Pelli, “Channel properties revealed by noise masking,” Invest. Ophthalmol. 19, Suppl. 44A (1980).

J. Acoust. Soc. Am. (5)

G. B. Henning, “Effect of interaural phase on frequency and amplitude discrimination,” J. Acoust. Soc. Am. 54, 1160–1178 (1973).
[CrossRef] [PubMed]

G. B. Henning, “A model of auditory discrimination and detection,” J. Acoust. Soc. Am. 41, 774–777 (1967).
[CrossRef] [PubMed]

R. D. Patterson and G. B. Henning, “Stimulus variability and auditory filter shape,” J. Acoust. Soc. Am. 62, 649–664 (1977).
[CrossRef] [PubMed]

R. D. Patterson, “Auditory filter shape,” J. Acoust. Soc. Am. 55, 802–809 (1974).
[CrossRef] [PubMed]

R. D. Patterson, “Auditory filter shapes derived with noise stimuli,” J. Acoust. Soc. Am. 59, 640–654 (1976).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (5)

J. Physiol. London (6)

B. E. Carter and G. B. Henning, “The detection of gratings in narrow-band visual noise,” J. Physiol. London 219, 355–365 (1971).

F. W. Campbell, R. H. Carpenter, and J. Z. Levinson, “Visibility of aperiodic patterns compared with that of sinusoidal grating,” J. Physiol. London 204, 283–298 (1969).

J. A. Movshon, I. D. Thompson, and D. J. Tolhurst, “Spatial summation in the receptive fields of simple cells in the cat’s striate cortex,” J. Physiol. London 283, 53–78 (1978).

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of grating,” J. Physiol. London 197, 551–556 (1968).

C. Blakernore and F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. London 200, 11P–13P (1967).

F. W. Campbell and D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).

Opt. Acta (1)

U. Greis and R. Röhler, “Untersuchung der subjectiven Detailerkennbarkeit mit Hilfe der Ortsfrequenzfilterung,” Opt. Acta 17, 515–526 (1970).
[CrossRef]

Vision Res. (1)

G. B. Henning, B. G. Hertz, and D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Other (11)

Stromeyer and Julesz kept the product of the square of the noise contrast and the bandwidth of their masking noise constant when changing cutoff frequencies.17 If we assume that masking is proportional to noise-contrast density, then we might adjust the data in Fig. 6 to show the contrast elevation that would have occurred had Stomeyer and Julesz kept their noise-contrast density constant. The correction steepens the low-frequency side from about 0.35-log-unit change of contrast per halving of spatial frequency to 0.52 log unit per halving. The steepening of the high-frequency side is negligible when the correction is applied on the basis of the bandwidths used by Stromeyer and Julesz.

C. F. Stromeyer, Division of Applied Sciences, Harvard University, Cambridge, Mass. 02138, personal communication.

D. G. Pelli, Department of Psychology, University of Minnesota, Minneapolis, Minn. 55455, personal communication (1980).

We are unable to reject the hypothesis that our data are linear on semilogarithmic coordinates. The more extensive adjusted data16 of Stromeyer and Julesz are more nearly linear on double-logarithmic coordinates.

B. G. Hertz and G. B. Henning.

L. Maffei, “Spatial frequency channels: neural mechanisms,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, and H. L. Teuber, eds. (Springer-Verlag, Berlin, 1978), Chap. VIII.

H. L. F. Helmholtz, The Sensations of Tone, A. J. Ellis, trans. (Dover, New York, 1954).

J. Nachmias, “Signal detection theory and its application to problems in vision,” in Handbook of Sensory Physiology, D. Jameson and L. M. Hurvich, eds. (Springer-Verlag, Berlin, 1972), Chap. VIII/4.
[CrossRef]

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

J. L. Hinton and G. B. Henning.

P. Lennie, Laboratory of Experimental Psychology, University of Sussex, Brighton, Sussex, U.K., personal communication (1979).

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Figures (8)

Fig. 1
Fig. 1

The percentage-correct detection of a 6 cycles/deg grating in a standard 2IFC experiment as a function of the signal contrast. The parameter is the cutoff frequency of the low-pass filtered visual noise against which the grating was detected. Each data point is based on 100 observations from observer BGH.

Fig. 2
Fig. 2

The percentage-correct detection of a 1 cycle/deg grating in a standard 2IFC experiment as a function of the signal contrast. The parameter is the cutoff frequency of the high-pass filtered visual noise against which the grating was detected. Each data point is based on 100 observations from observer GBH.

Fig. 3
Fig. 3

The log signal contrast corresponding to 75% correct detection of a 3 cycles/deg grating as a function of the cutoff frequency of the visual masking noise. Data for (a) GBH and (b) BGH. Solid symbols, low-pass noise conditions; open symbols, high-pass noise conditions. The contrasts corresponding to 75% correct were obtained by interpolation from psychometric function based on 100 observations per point. (The signal contrasts have been adjusted between high- and low-pass conditions by a factor that depends on the noise-power density used in the two conditions.)

Fig. 4
Fig. 4

The log contrast corresponding to 75% correct responses as a function of both high- and low-pass filtered visual noise at three different signal frequencies for observer GBH.

Fig. 5
Fig. 5

The log contrast corresponding to 75% correct responses as a function of both high- and low-pass filtered visual noise at three different signal frequencies for observer BGH.

Fig. 6
Fig. 6

Data calculated from Stromeyer and Julesz (Ref. 8). The ordinate, to facilitate comparison with Figs. 4 and 5, shows the ratio of the threshold contrast for masked signals to that for unmasked signals. The abscissa shows cutoff frequency, and both coordinates are logarithmic.

Fig. 7
Fig. 7

Solid lines show the attenuation characteristics of the frequency-selective mechanisms inferred from the data of BGH on the assumption that observers use a decision statistic that is a monotonic function of the peak-to-trough ratio of the filtered stimulus. Dotted lines show the characteristics inferred from the same data when observers use a decision statistic that is a monotonic function of the energy in the filtered stimulus.

Fig. 8
Fig. 8

Log masked sensitivity (the reciprocal of masked contrast) as a function of the cutoff frequency of the visual masking noise. Data for three different observers are shown. The noise was continously present and continuously changing.

Equations (6)

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

D = - S 0 / 2 S 0 / 2 [ - x ( s ) h ( σ - s ) d s ] 2 d σ ,
D = - X ( f ) H ( f ) 2 d f ,
D = 2 0 F c N ( f ) H ( f ) 2 d f ,
P ( c ) = ( 1 / σ x 2 ) 0 V t exp [ ( V t 2 + C s 2 ) / 2 σ x 2 ] × [ 1 - exp ( - V t 2 / 2 σ x 2 ) ] I 0 ( C s V t / σ x ) d V t ,
σ x 2 = N 0 0 F c H ( f ) 2 d f .
H ( f ) 2 = d ( σ x 2 ) / d F c ,