Abstract

A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems’ responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1−2% (5−10× pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feed forward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. C. Hood, M. A. Finkelstein, “Sensitivity to light,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Vol. 1, Chap. 5.
  2. H. R. Blackwell, “Contrast thresholds of the human eye,” J. Opt. Soc. Am. 36, 624–646 (1946).
    [CrossRef] [PubMed]
  3. E. G. Heinemann, “Simultaneous brightness induction as a function of inducing and test field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
    [CrossRef] [PubMed]
  4. G. Sperling, M. M. Sondhi, “Model for visual luminance discrimination and flicker detection,” J. Opt. Soc. Am. 58, 1133–1145 (1968).
    [CrossRef] [PubMed]
  5. P. Whittle, P. D. C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
    [CrossRef] [PubMed]
  6. G. Sperling, “Model of visual adaptation and contrast detection,” Percept. Psychophys. 8, 143–157 (1970).
    [CrossRef]
  7. E. G. Heinemann, “Simultaneous brightness induction,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvish, eds. (Springer Verlag, Berlin, 1972), Vol. VII/4, pp. 146–149.
    [CrossRef]
  8. R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. Osborne, G. Chader, eds. (Pergamon, Oxford, 1984), pp. 263–346.
    [CrossRef]
  9. G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
    [CrossRef]
  10. A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).
  11. E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,” J. Physiol. 330, 125–143 (1982).
    [PubMed]
  12. A. F. Dean, “The relationship between response amplitude and contrast for cat striate cortical neurons,” J. Physiol. (London) 318, 413–427 (1981).
  13. D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
    [PubMed]
  14. I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
    [CrossRef]
  15. G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
    [CrossRef] [PubMed]
  16. A. B. Bonds, “Temporal dynamics of contrast gain in single cells of the cat striate cortex,” Visual Neurosci. 6, 239–255 (1991).
    [CrossRef]
  17. 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]
  18. D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
    [CrossRef]
  19. D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, 1980).
  20. K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
    [CrossRef] [PubMed]
  21. J. H. Jamar, J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
    [CrossRef] [PubMed]
  22. S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
    [CrossRef] [PubMed]
  23. M. Pavel, G. Sperling, T. Riedl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987).
    [CrossRef] [PubMed]
  24. D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
    [CrossRef] [PubMed]
  25. J. G. Robson, “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
    [CrossRef]
  26. D. H. Kelly, “Adaptation effects on spatiotemporal sine-wave threshold surface,” Vision Res. 12, 89–101 (1972).
    [CrossRef] [PubMed]
  27. D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,” J. Opt. Soc. Am. 69, 1340–1349 (1979).
    [CrossRef] [PubMed]
  28. J. J. Koenderink, A. J. van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett. 4, 32–34 (1979).
    [CrossRef] [PubMed]
  29. D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
    [CrossRef]
  30. J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
    [CrossRef] [PubMed]
  31. Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
    [CrossRef] [PubMed]
  32. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  33. C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
    [CrossRef] [PubMed]
  34. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  35. C. A. Burbeck, D. H. Kelly, “Contrast gain measurements and the transient/sustained dichotomy,” J. Opt. Soc. Am. 71, 1335–1342 (1981).
    [PubMed]
  36. M. Livingstone, D. Hubel, “Segregation of form, color, movement and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
    [CrossRef] [PubMed]
  37. S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
    [CrossRef] [PubMed]
  38. A. T. Smith, “Correspondence-based and energy-based detection of second-order motion in human vision,” J. Opt. Soc. Am. A 11, 1940–1948 (1994).
    [CrossRef]
  39. W. Reichardt, “Autokorrelationsauswertung als Funktionsprinzip des Zentralnervensystems,” Z. Naturforsch. 12b, 447–457 (1957).
  40. W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.
  41. J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
    [CrossRef] [PubMed]
  42. E. H. Adelson, J. K. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
    [CrossRef] [PubMed]
  43. A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.
  44. P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
    [CrossRef]
  45. C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. (USA) 86, 2985–2989 (1989).
    [CrossRef]
  46. D. J. Heeger, “A model for the extraction of image flow,” J. Opt. Soc. Am. A 4, 1455–1471 (1987).
    [CrossRef] [PubMed]
  47. H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
    [CrossRef]
  48. S. J. Nowlan, T. J. Sejnowski, “Filter selection model for motion segmentation and velocity integration,” J. Opt. Soc. Am. A 11, 3177–3200 (1994).
    [CrossRef]
  49. C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
    [CrossRef] [PubMed]
  50. C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
    [CrossRef]
  51. V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
    [CrossRef] [PubMed]
  52. A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
    [CrossRef]
  53. A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
    [CrossRef] [PubMed]
  54. K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
    [CrossRef]
  55. J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
    [CrossRef]
  56. D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
    [CrossRef]
  57. M. S. Landy, Y. Cohen, G. Sperling, “hips: a Unix-based image processing system,” Comput. Vision Graphics Image Process. 25, 331–347 (1984a).
    [CrossRef]
  58. M. S. Landy, Y. Cohen, G. Sperling, “hips: image processing under Unix-software and applications,” Behav. Res. Methods Instrum. Comput. 16, 199–216 (1984b).
    [CrossRef]
  59. Runtime Library for Psychology Experiments, Human Information Processing Laboratory, Department of Psychology, New York University, New York 10003, 1988.
  60. R. S. Woodworth, H. Schlosberg, Experimental Psychology, rev. ed. (Holt, Rinehart & Winston, New York, 1954).
  61. K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).
  62. J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
    [PubMed]
  63. A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
    [CrossRef] [PubMed]
  64. D. H. Kelly, “Motion and vision. IV. Isotropic and anisotropic spatial responses,” J. Opt. Soc. Am. 72, 432–439 (1982).
    [CrossRef] [PubMed]
  65. C. R. Carlson, R. W. Klopfenstein, “Spatial-frequency model for hyperacuity,” J. Opt. Soc. Am. A 2, 1747–1751 (1985).
    [CrossRef]
  66. S. A. Klein, D. M. Levi, “Hyperacuity threshold of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1171–1190 (1985).
    [CrossRef]

1995 (1)

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

1994 (2)

1992 (2)

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

1991 (5)

A. B. Bonds, “Temporal dynamics of contrast gain in single cells of the cat striate cortex,” Visual Neurosci. 6, 239–255 (1991).
[CrossRef]

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]

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
[CrossRef]

S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
[CrossRef] [PubMed]

1990 (1)

G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

1989 (5)

G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
[CrossRef]

K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
[CrossRef]

J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
[CrossRef]

P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
[CrossRef]

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. (USA) 86, 2985–2989 (1989).
[CrossRef]

1988 (2)

M. Livingstone, D. Hubel, “Segregation of form, color, movement and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

1987 (2)

1986 (1)

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

1985 (7)

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

J. H. Jamar, J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

S. A. Klein, D. M. Levi, “Hyperacuity threshold of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1171–1190 (1985).
[CrossRef]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. K. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

C. R. Carlson, R. W. Klopfenstein, “Spatial-frequency model for hyperacuity,” J. Opt. Soc. Am. A 2, 1747–1751 (1985).
[CrossRef]

1984 (3)

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
[CrossRef] [PubMed]

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
[CrossRef]

1982 (5)

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef]

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,” J. Physiol. 330, 125–143 (1982).
[PubMed]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
[CrossRef]

D. H. Kelly, “Motion and vision. IV. Isotropic and anisotropic spatial responses,” J. Opt. Soc. Am. 72, 432–439 (1982).
[CrossRef] [PubMed]

1981 (3)

C. A. Burbeck, D. H. Kelly, “Contrast gain measurements and the transient/sustained dichotomy,” J. Opt. Soc. Am. 71, 1335–1342 (1981).
[PubMed]

A. F. Dean, “The relationship between response amplitude and contrast for cat striate cortical neurons,” J. Physiol. (London) 318, 413–427 (1981).

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

1980 (2)

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

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

1979 (2)

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)

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

1972 (1)

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

1970 (1)

G. Sperling, “Model of visual adaptation and contrast detection,” Percept. Psychophys. 8, 143–157 (1970).
[CrossRef]

1969 (1)

P. Whittle, P. D. C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

1968 (1)

1966 (2)

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

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

1957 (1)

W. Reichardt, “Autokorrelationsauswertung als Funktionsprinzip des Zentralnervensystems,” Z. Naturforsch. 12b, 447–457 (1957).

1955 (2)

J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
[PubMed]

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing and test field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef] [PubMed]

1946 (1)

Adelson, E. H.

Ahumada, A. J.

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

Albrecht, D. G.

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]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Anderson, S. J.

Badcock, D. R.

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

Bergen, J. K.

Blackwell, H. R.

Bonds, A. B.

A. B. Bonds, “Temporal dynamics of contrast gain in single cells of the cat striate cortex,” Visual Neurosci. 6, 239–255 (1991).
[CrossRef]

Burbeck, C. A.

Burr, D. C.

Carlson, C. R.

Cavanagh, P.

P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
[CrossRef]

Challands, P. D. C.

P. Whittle, P. D. C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

Chubb, C.

C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
[CrossRef]

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. (USA) 86, 2985–2989 (1989).
[CrossRef]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

Cohen, Y.

M. S. Landy, Y. Cohen, G. Sperling, “hips: image processing under Unix-software and applications,” Behav. Res. Methods Instrum. Comput. 16, 199–216 (1984b).
[CrossRef]

M. S. Landy, Y. Cohen, G. Sperling, “hips: a Unix-based image processing system,” Comput. Vision Graphics Image Process. 25, 331–347 (1984a).
[CrossRef]

Conte, M. M.

J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
[CrossRef]

Coombs, J. S.

J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
[PubMed]

Dean, A. F.

A. F. Dean, “The relationship between response amplitude and contrast for cat striate cortical neurons,” J. Physiol. (London) 318, 413–427 (1981).

Derrington, A. M.

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Eccles, J. C.

J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
[PubMed]

Enroth-Cugell, C.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. Osborne, G. Chader, eds. (Pergamon, Oxford, 1984), pp. 263–346.
[CrossRef]

Fatt, P.

J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
[PubMed]

Ferrera, V. P.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Finkelstein, M. A.

D. C. Hood, M. A. Finkelstein, “Sensitivity to light,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Vol. 1, Chap. 5.

Foley, J. M.

Freeman, R. D.

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
[CrossRef]

Geisler, W. S.

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]

Hamilton, D. B.

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

D. J. Heeger, “A model for the extraction of image flow,” J. Opt. Soc. Am. A 4, 1455–1471 (1987).
[CrossRef] [PubMed]

Heinemann, E. G.

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing and test field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef] [PubMed]

E. G. Heinemann, “Simultaneous brightness induction,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvish, eds. (Springer Verlag, Berlin, 1972), Vol. VII/4, pp. 146–149.
[CrossRef]

Hood, D. C.

D. C. Hood, M. A. Finkelstein, “Sensitivity to light,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Vol. 1, Chap. 5.

Hubel, D.

M. Livingstone, D. Hubel, “Segregation of form, color, movement and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Jamar, J. H.

J. H. Jamar, J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

Kaplan, E.

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,” J. Physiol. 330, 125–143 (1982).
[PubMed]

Kelly, D. H.

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]

Klein, S. A.

S. A. Klein, D. M. Levi, “Hyperacuity threshold of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1171–1190 (1985).
[CrossRef]

Klopfenstein, R. W.

Koenderink, J. J.

J. H. Jamar, J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, “Spatiotemporal contrast detection threshold surface is bimodal,” Opt. Lett. 4, 32–34 (1979).
[CrossRef] [PubMed]

Landy, M. S.

M. S. Landy, Y. Cohen, G. Sperling, “hips: image processing under Unix-software and applications,” Behav. Res. Methods Instrum. Comput. 16, 199–216 (1984b).
[CrossRef]

M. S. Landy, Y. Cohen, G. Sperling, “hips: a Unix-based image processing system,” Comput. Vision Graphics Image Process. 25, 331–347 (1984a).
[CrossRef]

Legge, G. E.

Lelkens, A. M. M.

A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
[CrossRef]

Lennie, P.

G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Levi, D. M.

S. A. Klein, D. M. Levi, “Hyperacuity threshold of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1171–1190 (1985).
[CrossRef]

Livingstone, M.

M. Livingstone, D. Hubel, “Segregation of form, color, movement and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Lu, Z.-L.

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

Marr, D.

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

Mather, G.

P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
[CrossRef]

Maunsell, J. H.

G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

McKee, S. P.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

Morrone, M. C.

Murphy, B. J.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

Nachmias, J.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

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

Naka, K. I.

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

Nakayama, K.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

Nowlan, S. J.

Ohzawa, I.

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
[CrossRef]

Pantle, A.

K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
[CrossRef]

Parish, D. H.

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef] [PubMed]

Pavel, M.

Pelli, D. G.

D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, 1980).

Ramachandran, V. S.

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

Rau, M. V.

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

Reichardt, W.

W. Reichardt, “Autokorrelationsauswertung als Funktionsprinzip des Zentralnervensystems,” Z. Naturforsch. 12b, 447–457 (1957).

W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.

Riedl, T.

Robson, J. G.

Ross, J.

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef]

Rushton, W. A.

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

Sansbury, R. V.

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

Schlosberg, H.

R. S. Woodworth, H. Schlosberg, Experimental Psychology, rev. ed. (Holt, Rinehart & Winston, New York, 1954).

Sclar, G.

G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
[CrossRef]

Sejnowski, T. J.

Shapley, R.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. Osborne, G. Chader, eds. (Pergamon, Oxford, 1984), pp. 263–346.
[CrossRef]

Shapley, R. M.

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,” J. Physiol. 330, 125–143 (1982).
[PubMed]

Silverman, G. H.

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

Smith, A. T.

Sondhi, M. M.

Sperling, G.

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
[CrossRef]

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef] [PubMed]

G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
[CrossRef]

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. (USA) 86, 2985–2989 (1989).
[CrossRef]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

M. Pavel, G. Sperling, T. Riedl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987).
[CrossRef] [PubMed]

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

M. S. Landy, Y. Cohen, G. Sperling, “hips: image processing under Unix-software and applications,” Behav. Res. Methods Instrum. Comput. 16, 199–216 (1984b).
[CrossRef]

M. S. Landy, Y. Cohen, G. Sperling, “hips: a Unix-based image processing system,” Comput. Vision Graphics Image Process. 25, 331–347 (1984a).
[CrossRef]

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
[CrossRef] [PubMed]

G. Sperling, “Model of visual adaptation and contrast detection,” Percept. Psychophys. 8, 143–157 (1970).
[CrossRef]

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

Stromeyer, C. F.

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

Thompson, P. G.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

Turano, K.

K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
[CrossRef]

Ullman, S.

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

van Doorn, A. J.

van Santen, J. P. H.

Vanderbeek, A.

Victor, J. D.

J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
[CrossRef]

Vidyasagar, T. R.

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

Whittle, P.

P. Whittle, P. D. C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Woodworth, R. S.

R. S. Woodworth, H. Schlosberg, Experimental Psychology, rev. ed. (Holt, Rinehart & Winston, New York, 1954).

Yo, C.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Behav. Res. Methods Instrum. Comput. (1)

M. S. Landy, Y. Cohen, G. Sperling, “hips: image processing under Unix-software and applications,” Behav. Res. Methods Instrum. Comput. 16, 199–216 (1984b).
[CrossRef]

Comput. Vision Graphics Image Process. (1)

M. S. Landy, Y. Cohen, G. Sperling, “hips: a Unix-based image processing system,” Comput. Vision Graphics Image Process. 25, 331–347 (1984a).
[CrossRef]

J. Exp. Psychol. (1)

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing and test field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef] [PubMed]

J. Math. Psychol. (1)

C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
[CrossRef]

J. Neurophysiol. (1)

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

J. Opt. Soc. Am. (7)

J. Opt. Soc. Am. A (12)

C. R. Carlson, R. W. Klopfenstein, “Spatial-frequency model for hyperacuity,” J. Opt. Soc. Am. A 2, 1747–1751 (1985).
[CrossRef]

S. A. Klein, D. M. Levi, “Hyperacuity threshold of 1 sec: theoretical predictions and empirical validation,” J. Opt. Soc. Am. A 2, 1171–1190 (1985).
[CrossRef]

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. K. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

D. J. Heeger, “A model for the extraction of image flow,” J. Opt. Soc. Am. A 4, 1455–1471 (1987).
[CrossRef] [PubMed]

S. J. Nowlan, T. J. Sejnowski, “Filter selection model for motion segmentation and velocity integration,” J. Opt. Soc. Am. A 11, 3177–3200 (1994).
[CrossRef]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
[CrossRef] [PubMed]

A. T. Smith, “Correspondence-based and energy-based detection of second-order motion in human vision,” J. Opt. Soc. Am. A 11, 1940–1948 (1994).
[CrossRef]

M. Pavel, G. Sperling, T. Riedl, A. Vanderbeek, “Limits of visual communication: the effect of signal-to-noise ratio on the intelligibility of American Sign Language,” J. Opt. Soc. Am. A 4, 2355–2365 (1987).
[CrossRef] [PubMed]

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

J. Physiol. (2)

E. Kaplan, R. M. Shapley, “X and Y cells in the lateral geniculate nucleus of macaque monkeys,” J. Physiol. 330, 125–143 (1982).
[PubMed]

J. S. Coombs, J. C. Eccles, P. Fatt, “The specific ionic conductances and ionic movements across the motoneuronal membrane that produce the inhibitory post-synaptic potential,” J. Physiol. 130, 326–373 (1955).
[PubMed]

J. Physiol. (London) (3)

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

A. F. Dean, “The relationship between response amplitude and contrast for cat striate cortical neurons,” J. Physiol. (London) 318, 413–427 (1981).

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–240 (1984).

Nature (London) (1)

I. Ohzawa, G. Sclar, R. D. Freeman, “Contrast gain control in the cat visual cortex,” Nature (London) 298, 266–268 (1982).
[CrossRef]

Opt. Lett. (1)

Percept. Psychophys. (1)

G. Sperling, “Model of visual adaptation and contrast detection,” Percept. Psychophys. 8, 143–157 (1970).
[CrossRef]

Proc. Natl. Acad. Sci. (USA) (1)

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. (USA) 86, 2985–2989 (1989).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

Science (1)

M. Livingstone, D. Hubel, “Segregation of form, color, movement and depth: anatomy, physiology, and perception,” Science 240, 740–749 (1988).
[CrossRef] [PubMed]

Spatial Vision (2)

G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
[CrossRef]

P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
[CrossRef]

Vision Res. (16)

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
[CrossRef]

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
[CrossRef]

J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
[CrossRef]

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–347 (1980).
[CrossRef] [PubMed]

P. Whittle, P. D. C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

G. Sclar, J. H. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

J. H. Jamar, J. J. Koenderink, “Contrast detection and detection of contrast modulation for noise gratings,” Vision Res. 25, 511–521 (1985).
[CrossRef] [PubMed]

S. P. McKee, G. H. Silverman, K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609–619 (1986).
[CrossRef] [PubMed]

D. C. Burr, J. Ross, “Contrast sensitivity at high velocities,” Vision Res. 22, 479–484 (1982).
[CrossRef]

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[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]

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef] [PubMed]

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

Visual Neurosci. (4)

A. B. Bonds, “Temporal dynamics of contrast gain in single cells of the cat striate cortex,” Visual Neurosci. 6, 239–255 (1991).
[CrossRef]

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]

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Z. Naturforsch. (1)

W. Reichardt, “Autokorrelationsauswertung als Funktionsprinzip des Zentralnervensystems,” Z. Naturforsch. 12b, 447–457 (1957).

Other (8)

W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.

D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, 1980).

D. C. Hood, M. A. Finkelstein, “Sensitivity to light,” in Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Vol. 1, Chap. 5.

E. G. Heinemann, “Simultaneous brightness induction,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvish, eds. (Springer Verlag, Berlin, 1972), Vol. VII/4, pp. 146–149.
[CrossRef]

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” in Progress in Retinal Research, N. Osborne, G. Chader, eds. (Pergamon, Oxford, 1984), pp. 263–346.
[CrossRef]

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotos, ed. (Association for Computing Machinery, New York, 1983), pp. 1–10.

Runtime Library for Psychology Experiments, Human Information Processing Laboratory, Department of Psychology, New York University, New York 10003, 1988.

R. S. Woodworth, H. Schlosberg, Experimental Psychology, rev. ed. (Holt, Rinehart & Winston, New York, 1954).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Elaborated Reichardt detector. It computes motion direction from two inputs that sample the visual display at two adjacent spatial locations A and B. SF1 and SF2 denote linear spatiotemporal filters (receptive fields) that may be different from each other. In the right (R) subunit of the detector, the output of SF1 is delayed by the temporal delay filter TF and then multiplied (×) by the direct output of SF2. The output of the multiplier is temporally averaged over a temporal window (defined by a linear filter TA) to produce the final output of the R subunit. In the L subunit of the detector, the output of SF2 is delayed by TF, multiplied (×) by the direct output of SF1 and temporally averaged by TA. The difference (R minus L) defines the output of the detector. Outputs greater than zero indicate stimulus motion from A to B; outputs less than zero indicate stimulus motion from B to A.

Fig. 2
Fig. 2

First-order (luminance-modulation) motion stimuli, with and without pedestals. (a) The pedestal: a static sine wave. (b) The motion stimulus: a moving sine wave with half the amplitude of a, frozen at one instant in time. (c) Five frames of pedestaled motion: the sum of (a) and (b). From frame to frame the moving sine wave travels 90 deg to the right. The wobbling movement of a peak of the compound waveform is indicated by the dotted–dashed line. Any mechanism that computes motion from stimulus features such as peaks, valleys, or zero crossings perceives only the wobble. (d, e, f) The five stimulus frames shown separately for each component. Each horizontal segment (1–5) shows a slice of the component as it would have appeared to the subject, except that the contrast has been enormously exaggerated for the purpose of reproductive clarity. (d) The static sine-wave pedestal, as diagrammed in (a). (e) The drifting luminance modulation, as in (b); consecutive frames are shifted to the right by 90 deg. (f) Pedestaled motion: the sum of modulations (d) and (e). The five frames correspond to those shown schematically in (c).

Fig. 3
Fig. 3

Second-order (texture-contrast-modulation) motion stimuli, with and without pedestals. (a) The pedestal: a static sinusoidal modulation of texture contrast. (b) The motion stimulus: a moving sinusoidal texture-contrast modulation with half the amplitude of (a) frozen at one instant in time. (c) Five frames of pedestaled motion: the sum of (a) and (b). From frame to frame the moving sinusoidal modulation travels 90 deg to the right. The wobbling movement of a peak of the compound waveform is indicated by the dotted–dashed line. Any mechanism that computes motion from stimulus features such as peaks, valleys, or zero crossings perceives only the wobble. (d, e, f) The five stimulus frames shown separately for each component. Each horizontal segment (1–5) shows a slice of the component as it would have appeared to the subject, except that the contrast has been exaggerated for the purpose of reproductive clarity. (d) The static sine-wave pedestal, as diagrammed in (a). (e) The drifting texture-contrast modulation, as in (b); consecutive frames are shifted to the right by 90 deg. (f) Pedestaled motion: the sum of modulations (d) and (e). The five frames correspond to those shown schematically in (c).

Fig. 4
Fig. 4

Contrast-modulation threshold for 75%-correct motion-direction judgments versus pedestal-modulation amplitudes for first-order stimuli. Both axes are logarithmic. Each panel represents a different subject. The smooth curve drawn though the data represents Eq. (7f) in the text: The level of the horizontal asymptote is k′, the threshold without a pedestal (0.25% and 0.28% for subjects ZL and EB, respectively). At large pedestal amplitudes, motion threshold for drifting luminance modulation is approximately proportional to the amplitude of the pedestals: η′ is the slope of the diagonal asymptote (1.01 and 1.25 for subjects ZL and EB, respectively). The intersection of the asymptotes at mped = (λ′/k′)η is the reciprocal of the generalized Weber fraction (the number of times that pedestal amplitude exceeds threshold amplitude: 0.75% and 1.2% for subjects ZL and EB, respectively).

Fig. 5
Fig. 5

Contrast-modulation threshold for 75%-correct motion-direction judgments versus pedestal-modulation amplitudes for second-order stimuli. Both axes are linear. Throughout the investigated pedestal-amplitude range, motion threshold for a drifting texture-contrast grating is constant for both subjects (diamonds connected by solid lines). Data from Experiment 1 are shown for comparison (dots connected by dotted lines).

Fig. 6
Fig. 6

Threshold for 75%-correct motion-direction judgments versus baseline contrast for second-order stimuli. There is no pedestal—no contrast modulation except for the motion stimulus. The coordinates are logarithmic. The horizontal axis denotes baseline root-mean-square amplitude.

Fig. 7
Fig. 7

Three models of motion gain control. In all the models the input signal first passes through a stage of light adaptation A and then divides into two paths which both arrive at a gain-control mechanism before the signal continues forward to the motion-detection component. (a) Model for first-order motion with pedestals derived from Experiment 1. The direct signal u arrives at the gain control, where it is divided by the controlling signal, k+w, which is first derived by filtering the input with a linear spatial filter F2, rectifying the output (the actual exponent, the average of two subjects, η = 1.1), and then by forming a weighted sum to represent the spatial neighborhood of the motion detector (∫∫). The controlling signal k + w(x, t) is the denominator of Eq. (6a) in the text. A Reichardt (motion-energy) detector receives the gain-controlled input u(k + w)−1, and its output (support for rightward minus leftward motion) is subjected to additive noise and submitted to a decision mechanism. The linear filters in the gain-controlling F2 and motion F1 pathways are shown in gray to represent the fact that they are not constrained by Experiment 1. (b) Model representing the masking data of Anderson et al.37 This model is identical to a except in the following details. The linear filter F2 in the gain-controlling pathway is now defined by jittering mask stimuli, the linear filter F1 in the motion pathway is now defined by moving mask stimuli, and the exponent of the rectification process is η = 0.83 (versus 1.1 for model a). (c) Model representing the second-order motion system as derived from Experiments 2 and 3. Radially symmetric spatial filters represent the center-surround receptive fields that define the range of spatial-frequency channels. Each filter is followed by rectification; the rectified channel outputs are summed (+) to produce the internal representation of the carrier plus modulator. The remainder of the model is as in (a) and (b)

Fig. 8
Fig. 8

Modulation thresholds for two-flash presentations of a sinusoidal grating as a function of the translation between flashes. Data are taken from Fig. 5A of Nakayama and Silverman20 [2 cycles per degree (cpd) condition]. The horizontal axis denotes the phase angle θ between the two frames. The vertical axis denotes contrast sensitivity (1/threshold). Solid curve, prediction of Nakayama and Silverman [Eq. (8) in the text]; dotted curve, direct prediction based on the model of Fig. 7a (shunting feedforward gain control with a Reichardt motion detector) with the parameters taken directly from subject ZL in Experiment 1. One parameter was estimated from the data—a slight (0.95) sensitivity reduction in the two-flash (versus the present five-flash) experiment. Although both theories give statistically excellent predictions, only the shunting-plus-Reichardt theory generalizes to other paradigms (see text for details).

Equations (17)

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

s ( x , y , t ) = L ( x , y , t ) L 0 L 0 ,
M ( x , t ) = m b + m p sin ( 2 π α x + θ p ) + m sin [ 2 π ( α x + β f t ) + θ ] .
M 1 ( x , t ) = m b 1 + m p 1 sin ( 2 π α x + θ p 1 ) + m 1 sin [ 2 π ( α x + β f t ) + θ ] ,
M 2 ( x , y ) = m b 2 + m p 2 sin ( 2 π α x + θ p 2 ) + m 2 sin [ 2 π ( α x + β f t ) + θ ] ,
M 3 ( x , t ) = m b 3 + m p 3 sin ( 2 π α x + θ p 3 ) + m 3 sin [ 2 π ( α x + β f t ) + θ ] .
υ ( x , t ) = u ( x , t ) k + w ( x , t ) ,
w ( x , t ) = Fc [ test ( x , t ) + pedestal ( x , t ) ] 1 . Fc [ pedestal ( x , t ) ] ,
u ( x , t ) = test ( x , t ) + pedestal ( x , t ) 2 . test ( x , t ) .
υ eff ( x , t ) = test ( x , t ) k + Fc [ pedestal ( x , t ) ] .
test ( x , t ) = m test , 75 sin ( α x ± f t ) ,
pedestal ( x , t ) = m ped sin ( α x ) .
υ eff ( x , t ) = m test , 75 ( m ped ) k + Fc [ m ped sin ( α x ) ] sin ( α x ± f t ) = υ 75 sin ( α x ± f t ) ,
υ 75 = m test , 75 ( m ped ) k + Fc [ m ped sin ( α x ) ] .
υ 75 = m test , 75 ( m ped ) k + λ m ped η .
m test , 75 ( m ped ) = k + λ m ped η .
y = α m 2 sin ( θ ) ,
Reichardt + Expt . 1 Nakayama Silverman υ 75 = β g 1 ( m ) g 1 ( m ) sin ( θ ) = α G N ( M ) sin ( θ ) .

Metrics