Abstract

We measured subject performance as a function of luminance for both detection and discrimination of increment stimuli; some were static, and some were arranged to give two-step apparent motion. Our aim was to examine a prediction for the shape of the psychometric function for motion: an accelerating function due to the presence of a multiplicative nonlinearity contained in many low-level motion models. For the tasks with static stimuli we found psychometric function slopes (of log d versus log luminance plots) between 1.9 and 2.4 in two subjects, as previously reported. For the tasks with apparent motion stimuli in the same range of detectability, however, the slopes are between 1.2 and 1.7. The lower slopes indicate that many low-level motion models are either incorrect or incomplete as currently specified, and changes in nonlinearities and noise placement are discussed.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  47. B. L. Gros, T. E. Cohn, D. R. Pope, “Direction discrimination efficiency on a small scale,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1270 (1994).

1998

G. L. Martinsen, B. L. Gros, T. E. Cohn, “Monochromatic stimuli that are independently processed by the magnocellular and parvocellular pathways,” Invest. Ophthalmol. Visual Sci. Suppl. 39, 163 (1998).

1997

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Quadrature subunits in directionally selective simple cells: spatiotemporal interactions,” Visual Neurosci. 14, 357–371 (1997).
[CrossRef]

1996

M. E. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

B. L. Gros, D. R. Pope, T. E. Cohn, “Relative efficiency for the detection of apparent motion,” Vision Res. 36, 2297–2302 (1996).
[CrossRef] [PubMed]

1995

D. R. Pope, E. P. Hornstein, B. L. Gros, T. E. Cohn, “Sources of visual noise in human observers at low scotopic light levels,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 905 (1995).

J. Allik, A. Pulver, “Contrast response of a movement-encoding system,” J. Opt. Soc. Am. A 12, 1185–1197 (1995).
[CrossRef]

1994

B. L. Gros, T. E. Cohn, D. R. Pope, “Direction discrimination efficiency on a small scale,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1270 (1994).

1993

D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
[PubMed]

1992

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

1990

G. Mather, “Computational modeling of motion detectors: responses to two-frame displays,” Spatial Vision 5, 1–14 (1990).
[CrossRef]

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

L. T. Maloney, “Confidence intervals for the parameters of psychometric functions,” Percept. Psychophys. 47, 127–134 (1990).
[CrossRef] [PubMed]

1989

1987

1986

T. Cohn, D. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

1985

1984

1983

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

1982

1981

D. H. Foster, J. Thorson, J. T. McIlwain, M. Biederman-Thorson, “The fine-grain movement illusion: a perceptual probe of neuronal connectivity in the human visual system,” Vision Res. 21, 1123–1128 (1981).
[CrossRef] [PubMed]

D. J. Lasley, T. E. Cohn, “Why luminance distribution may be better than detection,” Vision Res. 21, 273–278 (1981).
[CrossRef]

1980

O. J. Braddick, “Low-level and high-level processes in apparent motion,” Philos. Trans. R. Soc. London Ser. B 290, 137–151 (1980).
[CrossRef]

H. Wilson, “A transducer function for threshold and suprathreshold spatial vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef]

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

1975

T. E. Cohn, D. J. Lasley, “Spatial summation of foveal increments and decrements,” Vision Res. 15, 389–399 (1975).
[CrossRef] [PubMed]

1974

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

T. E. Cohn, L. N. Thibos, R. N. Kleinstein, “Detectability of a luminance increment,” J. Opt. Soc. Am. 64, 1321–1327 (1974).
[CrossRef] [PubMed]

1970

1969

J. Thorson, G. D. Lange, M. Biederman-Thorson, “Objective measure of the dynamics of a visual movement illusion,” Science 164, 1087–1088 (1969).
[CrossRef] [PubMed]

1961

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[CrossRef]

1957

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discriminations,” J. Physiol. (London) 136, 469–488 (1957).

1956

W. P. Tanner, “Theory of recognition,” J. Opt. Soc. Am. 28, 882–888 (1956).

1954

W. P. Tanner, J. A. Swets, “A decision making theory of visual detection,” Psychol. Rev. 61, 401–409 (1954).
[CrossRef] [PubMed]

1948

Adelson, E. H.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Quadrature subunits in directionally selective simple cells: spatiotemporal interactions,” Visual Neurosci. 14, 357–371 (1997).
[CrossRef]

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

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

Ahumada, A. J.

Allik, J.

Badcock, D. R.

M. E. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Baker, C. L.

C. L. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).
[CrossRef] [PubMed]

Barlow, H. B.

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discriminations,” J. Physiol. (London) 136, 469–488 (1957).

Bergen, J. R.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Quadrature subunits in directionally selective simple cells: spatiotemporal interactions,” Visual Neurosci. 14, 357–371 (1997).
[CrossRef]

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

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

Biederman-Thorson, M.

D. H. Foster, J. Thorson, J. T. McIlwain, M. Biederman-Thorson, “The fine-grain movement illusion: a perceptual probe of neuronal connectivity in the human visual system,” Vision Res. 21, 1123–1128 (1981).
[CrossRef] [PubMed]

J. Thorson, G. D. Lange, M. Biederman-Thorson, “Objective measure of the dynamics of a visual movement illusion,” Science 164, 1087–1088 (1969).
[CrossRef] [PubMed]

Borst, A.

Braddick, O. J.

C. L. Baker, O. J. Braddick, “Temporal properties of the short-range process in apparent motion,” Perception 14, 181–192 (1985).
[CrossRef] [PubMed]

O. J. Braddick, “Low-level and high-level processes in apparent motion,” Philos. Trans. R. Soc. London Ser. B 290, 137–151 (1980).
[CrossRef]

Breton, M. E.

Burgess, A. E.

Cohn, T.

T. Cohn, D. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

Cohn, T. E.

G. L. Martinsen, B. L. Gros, T. E. Cohn, “Monochromatic stimuli that are independently processed by the magnocellular and parvocellular pathways,” Invest. Ophthalmol. Visual Sci. Suppl. 39, 163 (1998).

B. L. Gros, D. R. Pope, T. E. Cohn, “Relative efficiency for the detection of apparent motion,” Vision Res. 36, 2297–2302 (1996).
[CrossRef] [PubMed]

D. R. Pope, E. P. Hornstein, B. L. Gros, T. E. Cohn, “Sources of visual noise in human observers at low scotopic light levels,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 905 (1995).

B. L. Gros, T. E. Cohn, D. R. Pope, “Direction discrimination efficiency on a small scale,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1270 (1994).

T. E. Cohn, D. J. Lasley, “Site of the accelerating nonlinearity underlying luminance change detection,” J. Opt. Soc. Am. A 2, 202–205 (1985).
[CrossRef] [PubMed]

D. J. Lasley, T. E. Cohn, “Why luminance distribution may be better than detection,” Vision Res. 21, 273–278 (1981).
[CrossRef]

T. E. Cohn, D. J. Lasley, “Spatial summation of foveal increments and decrements,” Vision Res. 15, 389–399 (1975).
[CrossRef] [PubMed]

T. E. Cohn, L. N. Thibos, R. N. Kleinstein, “Detectability of a luminance increment,” J. Opt. Soc. Am. 64, 1321–1327 (1974).
[CrossRef] [PubMed]

Creelman, C. D.

N. A. Macmillan, C. D. Creelman, Detection Theory: A Users’ Guide (Cambridge University, Cambridge, UK, 1991).

Edwards, M. E.

M. E. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Egelhaaf, M.

Emerson, R. C.

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Quadrature subunits in directionally selective simple cells: spatiotemporal interactions,” Visual Neurosci. 14, 357–371 (1997).
[CrossRef]

R. C. Emerson, J. R. Bergen, E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
[CrossRef] [PubMed]

Foley, J. M.

Foster, D. H.

D. H. Foster, J. Thorson, J. T. McIlwain, M. Biederman-Thorson, “The fine-grain movement illusion: a perceptual probe of neuronal connectivity in the human visual system,” Vision Res. 21, 1123–1128 (1981).
[CrossRef] [PubMed]

Geisler, W. S.

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, California, 1966).

Gros, B. L.

G. L. Martinsen, B. L. Gros, T. E. Cohn, “Monochromatic stimuli that are independently processed by the magnocellular and parvocellular pathways,” Invest. Ophthalmol. Visual Sci. Suppl. 39, 163 (1998).

B. L. Gros, D. R. Pope, T. E. Cohn, “Relative efficiency for the detection of apparent motion,” Vision Res. 36, 2297–2302 (1996).
[CrossRef] [PubMed]

D. R. Pope, E. P. Hornstein, B. L. Gros, T. E. Cohn, “Sources of visual noise in human observers at low scotopic light levels,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 905 (1995).

B. L. Gros, T. E. Cohn, D. R. Pope, “Direction discrimination efficiency on a small scale,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1270 (1994).

Heeger, D. J.

D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
[PubMed]

Hornstein, E. P.

D. R. Pope, E. P. Hornstein, B. L. Gros, T. E. Cohn, “Sources of visual noise in human observers at low scotopic light levels,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 905 (1995).

Johnston, A.

A. Johnston, M. J. Wright, “Lower thresholds of motion for gratings as a function of eccentricity and contrast,” Vision Res. 25, 179–185 (1985).
[CrossRef] [PubMed]

Kersten, D.

Kleinstein, R. N.

Kocher, E. C.

Lange, G. D.

J. Thorson, G. D. Lange, M. Biederman-Thorson, “Objective measure of the dynamics of a visual movement illusion,” Science 164, 1087–1088 (1969).
[CrossRef] [PubMed]

Lasley, D.

T. Cohn, D. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

Lasley, D. J.

T. E. Cohn, D. J. Lasley, “Site of the accelerating nonlinearity underlying luminance change detection,” J. Opt. Soc. Am. A 2, 202–205 (1985).
[CrossRef] [PubMed]

D. J. Lasley, T. E. Cohn, “Why luminance distribution may be better than detection,” Vision Res. 21, 273–278 (1981).
[CrossRef]

T. E. Cohn, D. J. Lasley, “Spatial summation of foveal increments and decrements,” Vision Res. 15, 389–399 (1975).
[CrossRef] [PubMed]

Legge, G.

Legge, G. E.

G. E. Legge, “Binocular contrast summation—I. detection and discrimination,” Vision Res. 24, 373–383 (1984).
[CrossRef]

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

Lennie, P.

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

Macmillan, N. A.

N. A. Macmillan, C. D. Creelman, Detection Theory: A Users’ Guide (Cambridge University, Cambridge, UK, 1991).

Maloney, L. T.

L. T. Maloney, “Confidence intervals for the parameters of psychometric functions,” Percept. Psychophys. 47, 127–134 (1990).
[CrossRef] [PubMed]

Martinsen, G. L.

G. L. Martinsen, B. L. Gros, T. E. Cohn, “Monochromatic stimuli that are independently processed by the magnocellular and parvocellular pathways,” Invest. Ophthalmol. Visual Sci. Suppl. 39, 163 (1998).

Mather, G.

G. Mather, “Computational modeling of motion detectors: responses to two-frame displays,” Spatial Vision 5, 1–14 (1990).
[CrossRef]

Maunsell, J. H. R.

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

McGill, W. J.

McIlwain, J. T.

D. H. Foster, J. Thorson, J. T. McIlwain, M. Biederman-Thorson, “The fine-grain movement illusion: a perceptual probe of neuronal connectivity in the human visual system,” Vision Res. 21, 1123–1128 (1981).
[CrossRef] [PubMed]

Nachmias, J.

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

J. Nachmias, E. C. Kocher, “Visual detection and discrimination of luminance increment,” J. Opt. Soc. Am. 60, 382–389 (1970).
[CrossRef] [PubMed]

Nakayama, K.

Nishida, S.

M. E. Edwards, D. R. Badcock, S. Nishida, “Contrast sensitivity of the motion system,” Vision Res. 36, 2411–2421 (1996).
[CrossRef] [PubMed]

Petersik, J. T.

J. T. Petersik, “The two-process distinction in apparent motion,” Psychol. Bull. 106, 107–127 (1989).
[CrossRef] [PubMed]

Pope, D. R.

B. L. Gros, D. R. Pope, T. E. Cohn, “Relative efficiency for the detection of apparent motion,” Vision Res. 36, 2297–2302 (1996).
[CrossRef] [PubMed]

D. R. Pope, E. P. Hornstein, B. L. Gros, T. E. Cohn, “Sources of visual noise in human observers at low scotopic light levels,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 905 (1995).

B. L. Gros, T. E. Cohn, D. R. Pope, “Direction discrimination efficiency on a small scale,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1270 (1994).

Prucnal, P. R.

Pulver, A.

Reichardt, W.

M. Egelhaaf, A. Borst, W. Reichardt, “Computational structure of a biological motion-detection system as revealed by local detector analysis in the fly’s nervous system,” J. Opt. Soc. Am. A 6, 1070–1087 (1989).
[CrossRef] [PubMed]

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

Robson, J. G.

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

Rose, A.

Sansbury, R. V.

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

Sclar, G.

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

Silverman, G. H.

Sperling, G.

Swets, J. A.

W. P. Tanner, J. A. Swets, “A decision making theory of visual detection,” Psychol. Rev. 61, 401–409 (1954).
[CrossRef] [PubMed]

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, California, 1966).

Tanner, W. P.

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Figures (9)

Fig. 1
Fig. 1

(a) Temporal and (b) spatial layout of the stimulus. The LED flashes were 10 ms in duration and were separated by ISI’s of either 1 or 10 ms. The LED’s were 3 arc min wide, 9 arc min tall, and 6 arc min apart, center to center. They were viewed at a distance of 114 cm.

Fig. 2
Fig. 2

Schematic diagrams of the six experiments. The schematic is a space–time plot: Time is on the vertical axis, increasing downward. Position in space is shown across the horizontal. The two vertical lines indicate the locations of the two spots in the stimulus, the circles indicate luminance increments of the spots, and the shaded bar indicates the time between the two temporal intervals. The observer’s task was to indicate either which of two temporal intervals contained the stimulus presentation [(a), (c), and (e)] or which of two spatial configurations was presented [(b), (d), and (f)]. (a) Position detection, (b) position discrimination, (c) cued position detection, (d) cued position discrimination, (e) motion detection, and (f) direction discrimination.

Fig. 3
Fig. 3

Psychometric functions for the position detection task shown in Fig. 2. (a) Data for subject BLG, and (b) data for subject DDN.

Fig. 4
Fig. 4

Same as Fig. 3.

Fig. 5
Fig. 5

Psychometric functions for the three detection and three discrimination tasks shown in Fig. 2. (a) Data for subject BLG, and (b) data for subject DDN. Two plots are given for each subject, one for each ISI value used. Each plot shows log d versus log luminance, with the data shown as points and the linear regression line superimposed. The error bars are ±1 standard error.

Fig. 6
Fig. 6

Same as Fig. 5 but for cued position discrimination.

Fig. 7
Fig. 7

Same as Fig. 5 but for motion detection.

Fig. 8
Fig. 8

Same as Fig. 5 but for direction discrimination.

Fig. 9
Fig. 9

Simulated psychometric functions for direction discrimination. (a) Psychometric function for the simulated correlation motion model with Gaussian, uncorrelated noise added after the multiplication stage. As expected, the slope of the function is 2.0, reflecting the accelerating nature of the multiplicative nonlinearity. (b) Psychometric function from the same model, but in this case the noise was added at the inputs, before the multiplication stage. The result is again a function with a slope of 2.0, indicating that there are no constraints to the noise location in this simple model.

Tables (1)

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Table 1 Slopes of Log–Log Psychometric Functions

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