Abstract

The stabilized spatiotemporal threshold response surface can be modeled as the linear difference between the threshold response surfaces of two mechanisms, each of which is simply the product of a spatial and a temporal frequency response curve. With no free parameters, the resulting model is shown to be a good fit to available data.

© 1980 Optical Society of America

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References

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  1. D. H. Kelly, “New stimuli in vision,” in Abbilden und Sehen, Proceedingsof the 6th meeting of the International Commission for Optics, edited by H. Schrober and R. Rohler, Munich, 1962, pp. 119–126 (unpublished).
  2. D. H. Kelly, “Frequency doubling in visual responses,” J. Opt. Soc. Am. 56, 1628–1633 (1966).
    [CrossRef]
  3. J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
    [CrossRef]
  4. F. L. Van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
    [CrossRef] [PubMed]
  5. D. H. Kelly, “Adaptation effects on spatio-temporal sine-wave thresholds,” Vision Res. 12, 89–101 (1972).
    [CrossRef] [PubMed]
  6. D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,” J. Opt.Soc. Am. 69, 1340—1349 (1979).
    [CrossRef]
  7. J. J. Koenderink and A. J. Van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett.4, 32–34 (1979).
  8. For the origin of this term, see Flicker, edited by H. E. Henkes and L. H. van der Tweel, Junk, The Hague, 1964.
  9. For the present purpose we use the term mechanism to represent any realizable system that has the given spatial and temporal properties. Other than this, no specific physiological implications are intended.
  10. See Figs. 9, 10, and 14 of Ref. 6.
  11. The exact functions for the spatial and temporal response curves of the excitatory and inhibitory mechanisms will of course depend on the particular conditions and perhaps on the individual subject for which the surface is measured. In the case of Kelly’s interpolated surface, the excitatory spatial response SE as a function of spatial frequency u is given bySE(u)={T10(1)S19(u)/S19(10)for u≤10 cpdS1(u)for u>10 cpdand the inhibitory spatial response SI is given by SI(u) = SE(u) − S1(u). Similarly,TE(υ)={S19(0.5)T10(υ)/T10(19)for υ≤19 HzT0.5(υ)for υ>19 Hzand TI(υ) = TE(υ) − T0.5(υ), whereS19(u)=[6.1+7.3|log(19/0.05u)|3]0.14uexp(−0.07u/45.9),S1(u)=[6.1+7.3|log(1/0.05u)|3]0.02uexp(−0.07u/45.9),T10(υ)=[6.1+7.3|log(0.02υ/30)|3]0.07υexp(−0.03υ/45.9),T0.5(υ)=[6.1+7.3|log(0.02υ/1.5)|3]0.01υexp(−0.03υ/45.9).Note: The fact that, in the definition of TE, the transition from T10 to T0.5 occurs at the frequency at which SE is inferred (namely, 19 Hz) is coincidental.

1979 (2)

D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,” J. Opt.Soc. Am. 69, 1340—1349 (1979).
[CrossRef]

J. J. Koenderink and A. J. Van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett.4, 32–34 (1979).

1972 (1)

D. H. Kelly, “Adaptation effects on spatio-temporal sine-wave thresholds,” Vision Res. 12, 89–101 (1972).
[CrossRef] [PubMed]

1967 (1)

1966 (2)

Bouman, M. A.

Kelly, D. H.

D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,” J. Opt.Soc. Am. 69, 1340—1349 (1979).
[CrossRef]

D. H. Kelly, “Adaptation effects on spatio-temporal sine-wave thresholds,” Vision Res. 12, 89–101 (1972).
[CrossRef] [PubMed]

D. H. Kelly, “Frequency doubling in visual responses,” J. Opt. Soc. Am. 56, 1628–1633 (1966).
[CrossRef]

D. H. Kelly, “New stimuli in vision,” in Abbilden und Sehen, Proceedingsof the 6th meeting of the International Commission for Optics, edited by H. Schrober and R. Rohler, Munich, 1962, pp. 119–126 (unpublished).

Koenderink, J. J.

J. J. Koenderink and A. J. Van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett.4, 32–34 (1979).

F. L. Van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
[CrossRef] [PubMed]

Nas, H.

Robson, J. G.

Van Doorn, A. J.

J. J. Koenderink and A. J. Van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett.4, 32–34 (1979).

Van Nes, F. L.

J. Opt. Soc. Am. (3)

J. Opt.Soc. Am. (1)

D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,” J. Opt.Soc. Am. 69, 1340—1349 (1979).
[CrossRef]

Opt. Lett. (1)

J. J. Koenderink and A. J. Van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett.4, 32–34 (1979).

Vision Res. (1)

D. H. Kelly, “Adaptation effects on spatio-temporal sine-wave thresholds,” Vision Res. 12, 89–101 (1972).
[CrossRef] [PubMed]

Other (5)

For the origin of this term, see Flicker, edited by H. E. Henkes and L. H. van der Tweel, Junk, The Hague, 1964.

For the present purpose we use the term mechanism to represent any realizable system that has the given spatial and temporal properties. Other than this, no specific physiological implications are intended.

See Figs. 9, 10, and 14 of Ref. 6.

The exact functions for the spatial and temporal response curves of the excitatory and inhibitory mechanisms will of course depend on the particular conditions and perhaps on the individual subject for which the surface is measured. In the case of Kelly’s interpolated surface, the excitatory spatial response SE as a function of spatial frequency u is given bySE(u)={T10(1)S19(u)/S19(10)for u≤10 cpdS1(u)for u>10 cpdand the inhibitory spatial response SI is given by SI(u) = SE(u) − S1(u). Similarly,TE(υ)={S19(0.5)T10(υ)/T10(19)for υ≤19 HzT0.5(υ)for υ>19 Hzand TI(υ) = TE(υ) − T0.5(υ), whereS19(u)=[6.1+7.3|log(19/0.05u)|3]0.14uexp(−0.07u/45.9),S1(u)=[6.1+7.3|log(1/0.05u)|3]0.02uexp(−0.07u/45.9),T10(υ)=[6.1+7.3|log(0.02υ/30)|3]0.07υexp(−0.03υ/45.9),T0.5(υ)=[6.1+7.3|log(0.02υ/1.5)|3]0.01υexp(−0.03υ/45.9).Note: The fact that, in the definition of TE, the transition from T10 to T0.5 occurs at the frequency at which SE is inferred (namely, 19 Hz) is coincidental.

D. H. Kelly, “New stimuli in vision,” in Abbilden und Sehen, Proceedingsof the 6th meeting of the International Commission for Optics, edited by H. Schrober and R. Rohler, Munich, 1962, pp. 119–126 (unpublished).

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Figures (6)

FIG. 1
FIG. 1

Sketch of the stabilized spatiotemporal threshold sensitivity surface, showing two orthogonal profiles: a spatial response curve at v0 Hz and a temporal response curve at u0 cycles per degree (cpd), and their intersection c.

FIG. 2
FIG. 2

(a) Theoretical temporal response curves of the excitatory (——) and inhibitory (- - -) mechanisms, (b) Theoretical spatial response curves of the excitatory (——) and inhibitory (- - -) mechanisms.

FIG. 3
FIG. 3

Contour maps of the theoretical response surface of the (a) excitatory and (b) inhibitory mechanisms. Each contour line is labeled with the sensitivity (1/threshold modulation) that it represents.

FIG. 4
FIG. 4

Contour map of the theoretical threshold response surface, generated from the excitatory and inhibitory separable mechanisms shown in Fig. 2 (and Fig. 3).

FIG. 5
FIG. 5

Comparison of the model’s prediction of sensitivity at constant temporal frequencies (solid lines) with data points. Curves are labeled with the temporal frequencies at which the data were collected and the curves calculated.

FIG. 6
FIG. 6

Comparison of model’s prediction of sensitivity at constant velocities (solid lines) with data points. Curves are labeled with the velocities at which the data were collected and the curves calculated.

Equations (7)

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F ( u , υ ) = ( 1 / c ) S υ 0 ( u ) T u 0 ( υ ) ,
( 1 / c ) S 19 ( u ) T 10 ( υ ) ,
( 1 / c ) S 19 ( u ) T 10 ( 1 ) S 1 ( u ) ,
( 1 / c ) S 1 ( 0.5 ) T 10 ( υ ) T 0.5 ( υ ) .
SE(u)={T10(1)S19(u)/S19(10)foru10cpdS1(u)foru>10cpd
TE(υ)={S19(0.5)T10(υ)/T10(19)forυ19HzT0.5(υ)forυ>19Hz
S19(u)=[6.1+7.3|log(19/0.05u)|3]0.14uexp(0.07u/45.9),S1(u)=[6.1+7.3|log(1/0.05u)|3]0.02uexp(0.07u/45.9),T10(υ)=[6.1+7.3|log(0.02υ/30)|3]0.07υexp(0.03υ/45.9),T0.5(υ)=[6.1+7.3|log(0.02υ/1.5)|3]0.01υexp(0.03υ/45.9).