Abstract

In the study of perception of temporal changes in luminance, it is customary to model perceptual performance as based on one or more linear filters. The task is then to estimate the temporal impulse responses or the representation of the impulse response in the frequency domain. Previously, temporal masking data have been used to estimate the properties and numbers of these temporal mechanisms (filters) in central vision for 1-cycle-per-degree (cpd) targets [Vision Res. 38, 1023 (1998)]. The same methods have been used to explore how properties of the estimated filters change with stimulus contrast energy [J. Opt. Soc. Am. A 14, 2557 (1997)]. We present estimated properties for temporal mechanisms that detect low spatial-frequency patterns. The results indicate that two filters provide the best model for performance when mask contrast is significant. There are also differences between properties for mechanisms that detect signal spatial frequencies of 1 cpd and 1/3 cpd. The sensitivity of the low-pass mechanism relative to the bandpass mechanism is reduced at 1/3 cpd, consistent with previous findings.

© 1999 Optical Society of America

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  1. R. E. Fredericksen, R. F. Hess, “Estimating multiple temporal mechanisms in human vision,” Vision Res. 38, 1023–1040 (1998).
    [CrossRef] [PubMed]
  2. R. E. Fredericksen, R. F. Hess, “Temporal detection in human vision: dependence on stimulus energy,” J. Opt. Soc. Am. A 14, 2557–2569 (1997).
    [CrossRef]
  3. I. E. Holliday, K. H. Ruddock, “Two spatio-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
    [CrossRef] [PubMed]
  4. J. A. Roufs, F. J. Blommaert, “Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique,” Vision Res. 21, 1203–1221 (1981).
    [CrossRef] [PubMed]
  5. B. Breitmeyer, D. Levi, R. S. Harwerth, “Flicker masking in spatial vision,” Vision Res. 21, 1377–1385 (1981).
    [CrossRef] [PubMed]
  6. G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
    [CrossRef] [PubMed]
  7. U. T. Keesey, “Flicker and pattern detection: a comparison of thresholds,” J. Opt. Soc. Am. 62, 446–448 (1972).
    [CrossRef] [PubMed]
  8. J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).
  9. A. J. Pantle, “Temporal frequency response characteristic of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
    [CrossRef] [PubMed]
  10. A. J. Pantle, “Temporal determinants of spatial sine-wave masking,” Vision Res. 23, 749–757 (1983).
    [CrossRef] [PubMed]
  11. A. B. Metha, K. T. Mullen, “Temporal mechanisms underlying flicker detection and identification for red–green and achromatic stimuli,” J. Opt. Soc. Am. A 13, 1969–1980 (1996).
    [CrossRef]
  12. A. B. Metha, K. T. Mullen, “Red–green and achromatic temporal filters: a ratio model predicts contrast-dependent speed perception,” J. Opt. Soc. Am. A 14, 984–996 (1997).
    [CrossRef]
  13. S. T. Hammett, A. T. Smith, “Two temporal channels or three? A reevaluation,” Vision Res. 32, 285–291 (1992).
    [CrossRef] [PubMed]
  14. R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
    [CrossRef] [PubMed]
  15. R. J. Snowden, R. F. Hess, “Temporal frequency filters in the human peripheral visual field,” Vision Res. 32, 61–72 (1992).
    [CrossRef] [PubMed]
  16. M. B. Mandler, W. Makous, “A three channel model of temporal frequency perception,” Vision Res. 24, 1881–1887 (1984).
    [CrossRef] [PubMed]
  17. R. F. Hess, G. T. Plant, “Temporal frequency discrimination in human vision: evidence for an additional mechanism in the low spatial and high temporal frequency region,” Vision Res. 25, 1493–1500 (1985).
    [CrossRef] [PubMed]
  18. S. J. Waugh, R. F. Hess, “Suprathreshold temporal-frequency discrimination in the fovea and the periphery,” J. Opt. Soc. Am. A 11, 1199–1212 (1994).
    [CrossRef]
  19. S. R. Lehky, “Temporal properties of visual channels measured by masking,” J. Opt. Soc. Am. A 2, 1260–1272 (1985).
    [CrossRef] [PubMed]
  20. We use the term energy in the general sense of Parseval’s theorem or the integrated, squared amplitude of the signal in either the spatiotemporal or Fourier domain. Contrast energy refers to the integrated, squared contrast.
  21. D. G. Albrecht, “Visual cortex neurons in monkey and cat: effect of contrast on the spatial and temporal phase transfer functions,” Vis. Neurosci. 12, 1191–1210 (1995).
    [CrossRef] [PubMed]
  22. W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
    [CrossRef] [PubMed]
  23. G. Sclar, “Expression of ‘retinal’ contrast gain control by neurones of the cat’s lateral geniculate cortex,” Exp. Brain Res. 66, 589–596 (1987).
    [CrossRef]
  24. R. M. Shapley, J. D. Victor, “The effect of contrast on the transfer properties of cat retinal ganglion cells,” J. Physiol. (London) 285, 275–298 (1978).
  25. R. M. Shapley, J. D. Victor, “The contrast gain control of the cat retina,” Vision Res. 19, 431–434 (1979).
    [CrossRef] [PubMed]
  26. R. M. Shapley, J. D. Victor, “How the contrast gain control modifies the frequency responses of cat retinal ganglion cells,” J. Physiol. (London) 318, 161–179 (1981).
  27. It is a common practice in the recent literature to refer to these filters as mechanisms. We will use the term in the appropriate context throughout this paper.
  28. J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
    [CrossRef]
  29. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  30. D. H. Kelly, “Visual responses to time-dependent stimuli. I. Amplitude sensitivity measurements,” J. Opt. Soc. Am. 51, 422–429 (1961).
    [CrossRef] [PubMed]
  31. D. H. Kelly, “Diffusion model of linear flicker responses,” J. Opt. Soc. Am. 59, 1665–1670 (1969).
    [CrossRef] [PubMed]
  32. D. H. Kelly, “Theory of flicker and transient responses. I. Uniform fields,” J. Opt. Soc. Am. 61, 537–546 (1971).
    [CrossRef] [PubMed]
  33. We use the term filter sensitivity to refer to the ability of a filter to detect the stimulus (signal). This is distinct from the filter’s gain, because signal detectability is also determined by intrinsic noise and filter efficiency.
  34. The intrinsic noise level and the filter gain (peak of the filter modulation transfer function) can be written as a ratio in our model. We can therefore know only the relative values of these two parameters. That is, we know the modulation transfer function to within only a scaling constant.
  35. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
    [CrossRef] [PubMed]
  36. W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  37. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  38. N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).
  39. Use of residual error as an acceptance metric for a model depends on whether the required assumptions have been met. See the Appendix A for a brief discussion of this topic.
  40. The low-pass ad hoc filter was constructed to have a TMTF falling slope that matched the masking data at low temporal test frequencies. The bandpass ad hoc filters were constructed to have rising and falling TMTF slopes that matched the masking data for high temporal test frequencies.
  41. We tested all combinations of one, two, and three ad hoc filters for which at least one filter was a low-pass filter. That is, one low-pass filter alone, or one low-pass filter together with one or two bandpass filters. The low-pass ad hoc filter was constructed to have a TMTF falling slope that matched the masking data at low temporal test frequencies. The bandpass filter was constructed to have rising and falling TMTF slopes that matched the masking data for high temporal test frequencies.
  42. H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974).
    [CrossRef]
  43. M. Forster, E. Sober, “How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions,” Br. J. Philos. Sci. 45, 1–35 (1994).
    [CrossRef]
  44. J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
    [CrossRef] [PubMed]
  45. J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
    [CrossRef] [PubMed]
  46. D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (Cambridge University, Cambridge, UK, 1981).
  47. Our experiments have employed temporally windowed and duration-limited signal and noise patterns. The temporal window shapes and durations were identical in all cases, and we currently do not model the temporal integration aspects of detection. Our definitions for power can therefore be considered, without loss of generality, as representing either (1) peak instantaneous power or (2) average power over the duration of the stimulus presentation.
  48. D. Lancaster, Lancaster’s Active Filter Cookbook, 2nd ed. (Biddles, Guildford, 1996).

1998

R. E. Fredericksen, R. F. Hess, “Estimating multiple temporal mechanisms in human vision,” Vision Res. 38, 1023–1040 (1998).
[CrossRef] [PubMed]

1997

1996

1995

D. G. Albrecht, “Visual cortex neurons in monkey and cat: effect of contrast on the spatial and temporal phase transfer functions,” Vis. Neurosci. 12, 1191–1210 (1995).
[CrossRef] [PubMed]

1994

M. Forster, E. Sober, “How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions,” Br. J. Philos. Sci. 45, 1–35 (1994).
[CrossRef]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

S. J. Waugh, R. F. Hess, “Suprathreshold temporal-frequency discrimination in the fovea and the periphery,” J. Opt. Soc. Am. A 11, 1199–1212 (1994).
[CrossRef]

1992

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

S. T. Hammett, A. T. Smith, “Two temporal channels or three? A reevaluation,” Vision Res. 32, 285–291 (1992).
[CrossRef] [PubMed]

R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
[CrossRef] [PubMed]

R. J. Snowden, R. F. Hess, “Temporal frequency filters in the human peripheral visual field,” Vision Res. 32, 61–72 (1992).
[CrossRef] [PubMed]

1987

G. Sclar, “Expression of ‘retinal’ contrast gain control by neurones of the cat’s lateral geniculate cortex,” Exp. Brain Res. 66, 589–596 (1987).
[CrossRef]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

1985

S. R. Lehky, “Temporal properties of visual channels measured by masking,” J. Opt. Soc. Am. A 2, 1260–1272 (1985).
[CrossRef] [PubMed]

R. F. Hess, G. T. Plant, “Temporal frequency discrimination in human vision: evidence for an additional mechanism in the low spatial and high temporal frequency region,” Vision Res. 25, 1493–1500 (1985).
[CrossRef] [PubMed]

1984

M. B. Mandler, W. Makous, “A three channel model of temporal frequency perception,” Vision Res. 24, 1881–1887 (1984).
[CrossRef] [PubMed]

1983

A. J. Pantle, “Temporal determinants of spatial sine-wave masking,” Vision Res. 23, 749–757 (1983).
[CrossRef] [PubMed]

I. E. Holliday, K. H. Ruddock, “Two spatio-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef] [PubMed]

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

1981

R. M. Shapley, J. D. Victor, “How the contrast gain control modifies the frequency responses of cat retinal ganglion cells,” J. Physiol. (London) 318, 161–179 (1981).

J. A. Roufs, F. J. Blommaert, “Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique,” Vision Res. 21, 1203–1221 (1981).
[CrossRef] [PubMed]

B. Breitmeyer, D. Levi, R. S. Harwerth, “Flicker masking in spatial vision,” Vision Res. 21, 1377–1385 (1981).
[CrossRef] [PubMed]

1979

R. M. Shapley, J. D. Victor, “The contrast gain control of the cat retina,” Vision Res. 19, 431–434 (1979).
[CrossRef] [PubMed]

1978

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

A. J. Pantle, “Temporal frequency response characteristic of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

R. M. Shapley, J. D. Victor, “The effect of contrast on the transfer properties of cat retinal ganglion cells,” J. Physiol. (London) 285, 275–298 (1978).

1974

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974).
[CrossRef]

1973

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

1972

1971

1969

1968

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

1966

1961

Akaike, H.

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974).
[CrossRef]

Albrecht, D. G.

D. G. Albrecht, “Visual cortex neurons in monkey and cat: effect of contrast on the spatial and temporal phase transfer functions,” Vis. Neurosci. 12, 1191–1210 (1995).
[CrossRef] [PubMed]

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

Blommaert, F. J.

J. A. Roufs, F. J. Blommaert, “Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique,” Vision Res. 21, 1203–1221 (1981).
[CrossRef] [PubMed]

Breitmeyer, B.

B. Breitmeyer, D. Levi, R. S. Harwerth, “Flicker masking in spatial vision,” Vision Res. 21, 1377–1385 (1981).
[CrossRef] [PubMed]

Campbell, F. W.

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

Creelman, C. D.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Field, D. J.

Flannery, B. P.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Forster, M.

M. Forster, E. Sober, “How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions,” Br. J. Philos. Sci. 45, 1–35 (1994).
[CrossRef]

Fredericksen, R. E.

R. E. Fredericksen, R. F. Hess, “Estimating multiple temporal mechanisms in human vision,” Vision Res. 38, 1023–1040 (1998).
[CrossRef] [PubMed]

R. E. Fredericksen, R. F. Hess, “Temporal detection in human vision: dependence on stimulus energy,” J. Opt. Soc. Am. A 14, 2557–2569 (1997).
[CrossRef]

Geisler, W. S.

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

Hammett, S. T.

S. T. Hammett, A. T. Smith, “Two temporal channels or three? A reevaluation,” Vision Res. 32, 285–291 (1992).
[CrossRef] [PubMed]

Harwerth, R. S.

B. Breitmeyer, D. Levi, R. S. Harwerth, “Flicker masking in spatial vision,” Vision Res. 21, 1377–1385 (1981).
[CrossRef] [PubMed]

Hess, R. F.

R. E. Fredericksen, R. F. Hess, “Estimating multiple temporal mechanisms in human vision,” Vision Res. 38, 1023–1040 (1998).
[CrossRef] [PubMed]

R. E. Fredericksen, R. F. Hess, “Temporal detection in human vision: dependence on stimulus energy,” J. Opt. Soc. Am. A 14, 2557–2569 (1997).
[CrossRef]

S. J. Waugh, R. F. Hess, “Suprathreshold temporal-frequency discrimination in the fovea and the periphery,” J. Opt. Soc. Am. A 11, 1199–1212 (1994).
[CrossRef]

R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
[CrossRef] [PubMed]

R. J. Snowden, R. F. Hess, “Temporal frequency filters in the human peripheral visual field,” Vision Res. 32, 61–72 (1992).
[CrossRef] [PubMed]

R. F. Hess, G. T. Plant, “Temporal frequency discrimination in human vision: evidence for an additional mechanism in the low spatial and high temporal frequency region,” Vision Res. 25, 1493–1500 (1985).
[CrossRef] [PubMed]

Holliday, I. E.

I. E. Holliday, K. H. Ruddock, “Two spatio-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef] [PubMed]

Keesey, U. T.

Kelly, D. H.

Kulikowski, J. J.

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

Lancaster, D.

D. Lancaster, Lancaster’s Active Filter Cookbook, 2nd ed. (Biddles, Guildford, 1996).

Legge, G. E.

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

Lehky, S. R.

Levi, D.

B. Breitmeyer, D. Levi, R. S. Harwerth, “Flicker masking in spatial vision,” Vision Res. 21, 1377–1385 (1981).
[CrossRef] [PubMed]

Macmillan, N. A.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Makous, W.

J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

M. B. Mandler, W. Makous, “A three channel model of temporal frequency perception,” Vision Res. 24, 1881–1887 (1984).
[CrossRef] [PubMed]

Mandler, M. B.

M. B. Mandler, W. Makous, “A three channel model of temporal frequency perception,” Vision Res. 24, 1881–1887 (1984).
[CrossRef] [PubMed]

Metha, A. B.

Mullen, K. T.

Pantle, A. J.

A. J. Pantle, “Temporal determinants of spatial sine-wave masking,” Vision Res. 23, 749–757 (1983).
[CrossRef] [PubMed]

A. J. Pantle, “Temporal frequency response characteristic of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

Pelli, D. G.

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

D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (Cambridge University, Cambridge, UK, 1981).

Plant, G. T.

R. F. Hess, G. T. Plant, “Temporal frequency discrimination in human vision: evidence for an additional mechanism in the low spatial and high temporal frequency region,” Vision Res. 25, 1493–1500 (1985).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Robson, J. G.

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

J. G. Robson, “Spatial and temporal contrast sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
[CrossRef]

Roufs, J. A.

J. A. Roufs, F. J. Blommaert, “Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique,” Vision Res. 21, 1203–1221 (1981).
[CrossRef] [PubMed]

Ruddock, K. H.

I. E. Holliday, K. H. Ruddock, “Two spatio-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef] [PubMed]

Sclar, G.

G. Sclar, “Expression of ‘retinal’ contrast gain control by neurones of the cat’s lateral geniculate cortex,” Exp. Brain Res. 66, 589–596 (1987).
[CrossRef]

Shapley, R. M.

R. M. Shapley, J. D. Victor, “How the contrast gain control modifies the frequency responses of cat retinal ganglion cells,” J. Physiol. (London) 318, 161–179 (1981).

R. M. Shapley, J. D. Victor, “The contrast gain control of the cat retina,” Vision Res. 19, 431–434 (1979).
[CrossRef] [PubMed]

R. M. Shapley, J. D. Victor, “The effect of contrast on the transfer properties of cat retinal ganglion cells,” J. Physiol. (London) 285, 275–298 (1978).

Smith, A. T.

S. T. Hammett, A. T. Smith, “Two temporal channels or three? A reevaluation,” Vision Res. 32, 285–291 (1992).
[CrossRef] [PubMed]

Snowden, R. J.

R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
[CrossRef] [PubMed]

R. J. Snowden, R. F. Hess, “Temporal frequency filters in the human peripheral visual field,” Vision Res. 32, 61–72 (1992).
[CrossRef] [PubMed]

Sober, E.

M. Forster, E. Sober, “How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions,” Br. J. Philos. Sci. 45, 1–35 (1994).
[CrossRef]

Teukolsky, A. A.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Tolhurst, D. J.

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

Vetterling, W. T.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipies in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Victor, J. D.

R. M. Shapley, J. D. Victor, “How the contrast gain control modifies the frequency responses of cat retinal ganglion cells,” J. Physiol. (London) 318, 161–179 (1981).

R. M. Shapley, J. D. Victor, “The contrast gain control of the cat retina,” Vision Res. 19, 431–434 (1979).
[CrossRef] [PubMed]

R. M. Shapley, J. D. Victor, “The effect of contrast on the transfer properties of cat retinal ganglion cells,” J. Physiol. (London) 285, 275–298 (1978).

Watson, A. B.

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

Waugh, S. J.

Yang, J.

J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

Biol. Cybern.

I. E. Holliday, K. H. Ruddock, “Two spatio-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef] [PubMed]

Br. J. Philos. Sci.

M. Forster, E. Sober, “How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions,” Br. J. Philos. Sci. 45, 1–35 (1994).
[CrossRef]

Exp. Brain Res.

G. Sclar, “Expression of ‘retinal’ contrast gain control by neurones of the cat’s lateral geniculate cortex,” Exp. Brain Res. 66, 589–596 (1987).
[CrossRef]

IEEE Trans. Autom. Control.

H. Akaike, “A new look at statistical model identification,” IEEE Trans. Autom. Control. 19, 716–723 (1974).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

J. J. Kulikowski, D. J. Tolhurst, “Psychophysical evidence for sustained and transient detectors in human vision,” J. Physiol. (London) 232, 149–162 (1973).

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

R. M. Shapley, J. D. Victor, “How the contrast gain control modifies the frequency responses of cat retinal ganglion cells,” J. Physiol. (London) 318, 161–179 (1981).

R. M. Shapley, J. D. Victor, “The effect of contrast on the transfer properties of cat retinal ganglion cells,” J. Physiol. (London) 285, 275–298 (1978).

Percept. Psychophys.

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

A. J. Pantle, “Temporal frequency response characteristic of motion channels measured with three different psychophysical techniques,” Percept. Psychophys. 24, 285–294 (1978).
[CrossRef] [PubMed]

Vis. Neurosci.

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Our experiments have employed temporally windowed and duration-limited signal and noise patterns. The temporal window shapes and durations were identical in all cases, and we currently do not model the temporal integration aspects of detection. Our definitions for power can therefore be considered, without loss of generality, as representing either (1) peak instantaneous power or (2) average power over the duration of the stimulus presentation.

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We use the term energy in the general sense of Parseval’s theorem or the integrated, squared amplitude of the signal in either the spatiotemporal or Fourier domain. Contrast energy refers to the integrated, squared contrast.

It is a common practice in the recent literature to refer to these filters as mechanisms. We will use the term in the appropriate context throughout this paper.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Use of residual error as an acceptance metric for a model depends on whether the required assumptions have been met. See the Appendix A for a brief discussion of this topic.

The low-pass ad hoc filter was constructed to have a TMTF falling slope that matched the masking data at low temporal test frequencies. The bandpass ad hoc filters were constructed to have rising and falling TMTF slopes that matched the masking data for high temporal test frequencies.

We tested all combinations of one, two, and three ad hoc filters for which at least one filter was a low-pass filter. That is, one low-pass filter alone, or one low-pass filter together with one or two bandpass filters. The low-pass ad hoc filter was constructed to have a TMTF falling slope that matched the masking data at low temporal test frequencies. The bandpass filter was constructed to have rising and falling TMTF slopes that matched the masking data for high temporal test frequencies.

We use the term filter sensitivity to refer to the ability of a filter to detect the stimulus (signal). This is distinct from the filter’s gain, because signal detectability is also determined by intrinsic noise and filter efficiency.

The intrinsic noise level and the filter gain (peak of the filter modulation transfer function) can be written as a ratio in our model. We can therefore know only the relative values of these two parameters. That is, we know the modulation transfer function to within only a scaling constant.

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Figures (4)

Fig. 1
Fig. 1

Complete data for two observers (the two authors). Each data point represents the 81.6% correct signal contrast threshold for data grouped by signal and noise temporal frequency. Successive curves are displaced downward by 15 dB to simplify presentation. Thin solid curves, model comprising two filters chosen from our standard basis set; thin dashed curves, model comprising two arbitrarily chosen linear filters; thick solid curves, model comprising a single ad hoc filter applied separately to subsets of the data grouped by signal temporal frequency.

Fig. 2
Fig. 2

(a) Comparison of all model fits in terms of absolute χ2 likelihood. The result shows a clear difference between the two-filter model fits and the single-filter model fits to each signal temporal frequency: The single-filter fits produce an acceptable fit to the data. The model-generated thresholds in Fig. 1 (solid curves) and the goodness-of-fit measures in (a) reinforce this conclusion. (b) Comparison of the models by use of the Akaike information criterion,42 a metric designed for comparing nonnested models by inclusion of a penalty on parameter count. The version of the AIC used here is the sum of the χ2 value and twice the parameter count, divided by the total number of fitted data points. The result is consistent with the finding that the two-filter models produce equal fits but that the by-signal-frequency model produces a significantly improved fit even when penalized for its extra flexibility.

Fig. 3
Fig. 3

(a) Shows how the filter cutoff frequency fc for the single-filter fits varies with signal temporal frequency fs. The filter cutoff frequency is a measure of the filter’s knee point for low-pass filters and of the TMTF peak frequency for high-pass filters. (b) Shows how the damping factor d, a measure of filter shape (peakiness, or width), varies with fs. A damping factor above 1 indicates a flattened or rounded shape, whereas damping factors below 1 indicate a peaked or narrowed bandpass shape.

Fig. 4
Fig. 4

TMTF’s for the best-fitting single hi filters for data collected at 1 cpd and at 1/3 cpd. TMTF’s are presented as normalized to allow comparison of peak positions, shapes, and bandwidths. The filters underlying signals at 24 Hz appear to be identical in shape. There is perhaps some inconsistent variation at low temporal frequencies (2 Hz), while the 7/8 Hz comparison indicates a nearly identical underlying mechanism. The difference in peak position in the 7 and 8 Hz data is likely due to the difference in signal temporal frequency, because the peak masking position follows the signal very well in that temporal frequency range.1 There may be some narrowing of underlying mechanism bandwidth.

Tables (1)

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Table 1 Intrinsic Noise Ratios and Efficiency Changes for the Best ad hoc Filter Models

Equations (22)

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L(x, y, t)=Lm×[1+Cs×G(x, y, t)×cos(2πfxx)×cos(2πftt)],
G(x, y, t)=exp[-(x/Sx)2-(y/Sy)2-(t/St)2],
σs2=1F×(σn2+η2)
F×σs2/(σn2+η2)=1,
σsj2=Cs2×Gj2×-|S(f)|2|Hj(f)|2df,
σnj2=Cn2×Gj2×-|N(f)|2|Hj(f)|2df+ηj,
Pj=Φ{[log10(σsj2/σnj2)+Ej]×βj}
Pj=Φ{log10[(10Ej×σsj2/σnj2)βj]},
Pd=1-j(1-Pj).
hg(t)=exp{-[ln(t/τ)/σ]2},
hi(t)=ihg(t)/it,i0.
|L1(f)| = |(1+ω2)-1/2|,
|H1(f)| = |ω(1+ω2)-1/2|,
|L2(f)| = |[ω4+(d2-2)ω2+1]-1/2|,
|H2(f)| = |[ω-4+(d2-2)ω-2+1]-1/2|
Oi(t)=si(t)+ni(t)=[Si(t)+Ni(t)]*hi+ηi(t),
SNRi=[si(t)]2[ni(t)]2,
[fi(t)]2=1T T[fi(t)]2dt,
SNRopt=iαisi(t)2/iαini(t)2.
SNRopt=αTCsααTCnα,
SNRopt=α2C1,1s+(1-α)2C2,2s+2α(1-α)C1,2sα2C1,1n+(1-α)2C2,2n+2α(1-α)C1,2n,
SNRoptα=0

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