Abstract

We investigate the conditions under which stimuli in apparent (sampled) motion are indistinguishable from those in smooth motion and compare this discrimination with the precision achieved by the visual system in interpolating apparent motion. In an initial experiment, observers were required to discriminate smooth from apparent motion, at variable step sizes, contrasts, velocities, and stimulus types (broadband line or bar stimuli and grating patches of different spatial frequency). Thresholds for discriminating smooth from sampled motion were ∼40 arc min under optimal conditions, corresponding to the diameter of foveal photoreceptors. The tolerated step size between stations increased with velocity, more so for low- than for high-spatial-frequency stimuli. Tolerated step size decreased with presentation duration and with stimulus contrast. A separate experiment examined precision of interpolation. Vernier offsets were produced through temporal delays along the trajectory of an apparent motion, and thresholds for the discrimination of direction of offset were measured as a function of speed of motion and of distance between stations of apparent motion. Perfect interpolation was achieved for distances between stations of ∼2 arc min. A model based on spatiotemporal filtering at an early stage of processing accounts well for the results of both types of experiments.

© 2001 Optical Society of America

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  1. D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London 211, 321–339 (1981).
    [CrossRef]
  2. D. C. Burr, “Human vision in space and time,” in Proceedings of the International Union of Physiological Sciences (IUPS/American Physiological Society, Bethesda, Md., 1983), Vol. XV, p. 510.04.
  3. M. Fahle, T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
    [CrossRef]
  4. D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
    [CrossRef]
  5. D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
    [CrossRef] [PubMed]
  6. D. C. Burr, J. Ross, “Visual processing of motion,” Trends Neurosci. 9, 304–307 (1986).
    [CrossRef]
  7. D. C. Burr, J. Ross, “How does binocular delay give information about depth?” Vision Res. 19, 523–532 (1979).
    [CrossRef] [PubMed]
  8. M. J. Morgan, R. J. Watt, “On the failure of spatiotemporal interpolation: a filtering model,” Vision Res. 23, 997–1004 (1983).
    [CrossRef] [PubMed]
  9. W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
    [PubMed]
  10. A. B. Watson, A. J. Ahumada, J. E. Farrell, “Window of visibility: a psychophysical theory of fidelity in time-sampled visual motion display,” J. Opt. Soc. Am. A 3, 300–307 (1986).
    [CrossRef]
  11. M. Bach, “The Freiburg Visual Acuity Test—automatic measurement of the visual acuity,” Optom. Vision Sci. 73, 49–53 (1996).
    [CrossRef]
  12. M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
    [CrossRef] [PubMed]
  13. E. De Luca, M. Fahle, “Learning of interpolation in 2 and 3 dimensions,” Vision Res. 39, 2051–2062 (1999).
    [CrossRef] [PubMed]
  14. M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability function,” J. Acoust. Soc. Am. 41, 782–787 (1967).
    [CrossRef]
  15. S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
    [CrossRef] [PubMed]

1999

E. De Luca, M. Fahle, “Learning of interpolation in 2 and 3 dimensions,” Vision Res. 39, 2051–2062 (1999).
[CrossRef] [PubMed]

1996

M. Bach, “The Freiburg Visual Acuity Test—automatic measurement of the visual acuity,” Optom. Vision Sci. 73, 49–53 (1996).
[CrossRef]

1995

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

1986

A. B. Watson, A. J. Ahumada, J. E. Farrell, “Window of visibility: a psychophysical theory of fidelity in time-sampled visual motion display,” J. Opt. Soc. Am. A 3, 300–307 (1986).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
[CrossRef] [PubMed]

D. C. Burr, J. Ross, “Visual processing of motion,” Trends Neurosci. 9, 304–307 (1986).
[CrossRef]

W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
[PubMed]

1985

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

1983

M. J. Morgan, R. J. Watt, “On the failure of spatiotemporal interpolation: a filtering model,” Vision Res. 23, 997–1004 (1983).
[CrossRef] [PubMed]

1981

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London 211, 321–339 (1981).
[CrossRef]

M. Fahle, T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[CrossRef]

1979

D. C. Burr, J. Ross, “How does binocular delay give information about depth?” Vision Res. 19, 523–532 (1979).
[CrossRef] [PubMed]

1967

M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability function,” J. Acoust. Soc. Am. 41, 782–787 (1967).
[CrossRef]

Ahumada, A. J.

Anderson, S. J.

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

Bach, M.

M. Bach, “The Freiburg Visual Acuity Test—automatic measurement of the visual acuity,” Optom. Vision Sci. 73, 49–53 (1996).
[CrossRef]

Burr, D. C.

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
[CrossRef]

D. C. Burr, J. Ross, “Visual processing of motion,” Trends Neurosci. 9, 304–307 (1986).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
[CrossRef] [PubMed]

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London 211, 321–339 (1981).
[CrossRef]

D. C. Burr, J. Ross, “How does binocular delay give information about depth?” Vision Res. 19, 523–532 (1979).
[CrossRef] [PubMed]

D. C. Burr, “Human vision in space and time,” in Proceedings of the International Union of Physiological Sciences (IUPS/American Physiological Society, Bethesda, Md., 1983), Vol. XV, p. 510.04.

Creelman, C. D.

M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability function,” J. Acoust. Soc. Am. 41, 782–787 (1967).
[CrossRef]

De Luca, E.

E. De Luca, M. Fahle, “Learning of interpolation in 2 and 3 dimensions,” Vision Res. 39, 2051–2062 (1999).
[CrossRef] [PubMed]

Edelman, S.

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

Fahle, M.

E. De Luca, M. Fahle, “Learning of interpolation in 2 and 3 dimensions,” Vision Res. 39, 2051–2062 (1999).
[CrossRef] [PubMed]

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

M. Fahle, T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[CrossRef]

Farrell, J. E.

Mikami, A.

W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
[PubMed]

Morgan, M. J.

M. J. Morgan, R. J. Watt, “On the failure of spatiotemporal interpolation: a filtering model,” Vision Res. 23, 997–1004 (1983).
[CrossRef] [PubMed]

Morrone, M. C.

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
[CrossRef] [PubMed]

Newsome, W. T.

W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
[PubMed]

Poggio, T.

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

M. Fahle, T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[CrossRef]

Ross, J.

D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
[CrossRef] [PubMed]

D. C. Burr, J. Ross, “Visual processing of motion,” Trends Neurosci. 9, 304–307 (1986).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
[CrossRef]

D. C. Burr, J. Ross, “How does binocular delay give information about depth?” Vision Res. 19, 523–532 (1979).
[CrossRef] [PubMed]

Taylor, M. M.

M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability function,” J. Acoust. Soc. Am. 41, 782–787 (1967).
[CrossRef]

Watson, A. B.

Watt, R. J.

M. J. Morgan, R. J. Watt, “On the failure of spatiotemporal interpolation: a filtering model,” Vision Res. 23, 997–1004 (1983).
[CrossRef] [PubMed]

Wurtz, R. H.

W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
[PubMed]

J. Acoust. Soc. Am.

M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability function,” J. Acoust. Soc. Am. 41, 782–787 (1967).
[CrossRef]

J. Neurophysiol.

W. T. Newsome, A. Mikami, R. H. Wurtz, “Motion selectivity in macaque visual cortex. III. Psychophysics and physiology of apparent motion,” J. Neurophysiol. 55, 1340–1351 (1986).
[PubMed]

J. Opt. Soc. Am. A

Optom. Vision Sci.

M. Bach, “The Freiburg Visual Acuity Test—automatic measurement of the visual acuity,” Optom. Vision Sci. 73, 49–53 (1996).
[CrossRef]

Proc. R. Soc. London

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London 211, 321–339 (1981).
[CrossRef]

D. C. Burr, J. Ross, M. C. Morrone, “Seeing objects in motion,” Proc. R. Soc. London 227, 249–265 (1986).
[CrossRef]

Proc. R. Soc. London Ser. B

M. Fahle, T. Poggio, “Visual hyperacuity: spatio-temporal interpolation in human vision,” Proc. R. Soc. London Ser. B 213, 451–477 (1981).
[CrossRef]

Trends Neurosci.

D. C. Burr, J. Ross, “Visual processing of motion,” Trends Neurosci. 9, 304–307 (1986).
[CrossRef]

Vision Res.

D. C. Burr, J. Ross, “How does binocular delay give information about depth?” Vision Res. 19, 523–532 (1979).
[CrossRef] [PubMed]

M. J. Morgan, R. J. Watt, “On the failure of spatiotemporal interpolation: a filtering model,” Vision Res. 23, 997–1004 (1983).
[CrossRef] [PubMed]

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

D. C. Burr, J. Ross, M. C. Morrone, “Smooth and sampled motion,” Vision Res. 26, 643–652 (1986).
[CrossRef] [PubMed]

M. Fahle, S. Edelman, T. Poggio, “Fast perceptual learning in hyperacuity,” Vision Res. 35, 3003–3013 (1995).
[CrossRef] [PubMed]

E. De Luca, M. Fahle, “Learning of interpolation in 2 and 3 dimensions,” Vision Res. 39, 2051–2062 (1999).
[CrossRef] [PubMed]

Other

D. C. Burr, “Human vision in space and time,” in Proceedings of the International Union of Physiological Sciences (IUPS/American Physiological Society, Bethesda, Md., 1983), Vol. XV, p. 510.04.

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Figures (8)

Fig. 1
Fig. 1

Fourier contents in the domain of temporal (ft) and spatial frequencies (fx) of a grating patch (see inset) moving (a) continuously and (b) discontinuously. The solid parts of the oblique lines represent the visible parts of the spectrum. The sidebands created by discontinuous sampling are situated at distances corresponding to 1/Δx and 1/Δt along the abscissa and the ordinate, respectively; Δx is the spatial and Δt the temporal distance between subsequent presentations of the discontinuous motion (after Fahle and Poggio3). (c) A vernier offset is presented through purely temporal information: The lower segment of the vernier is presented shortly (δt) after the upper segment at each station of the apparent motion. The sidebands are replicated along the fx axis. (d) Schematic description of the vernier offset created by temporal delays between vernier elements moving in apparent motion.

Fig. 2
Fig. 2

Spatial distance between adjacent stations of the apparent motion at which this typical observer yielded 75% correct discriminations between apparent and continuous motion as a function of (apparent) velocity of motion for three different durations of the motion sequence (100 ms, 250 ms, and 625 ms). Spatial frequency was (a) 1 c/deg, (b) 8 c/deg, (c) 20 c/deg, and (d) broadband. Results of observer AS, who deviated most of all observers from the means shown in Fig. 3.

Fig. 3
Fig. 3

Same as Fig. 2; means over all six observers ± standard errors.

Fig. 4
Fig. 4

Same as Fig. 2, but only one duration of the motion sequence, namely 250 ms. While contrast in all other experiments was always maximal (95%), this figure compares results for maximal contrast with those for near-threshold contrast (6–8%). No data were collected for the broadband stimulus. Observer AS, as in Fig. 2.

Fig. 5
Fig. 5

(a)–(c) Same empirical thresholds as Fig. 4, but these are means over all six observers ± standard errors. (d)–(f) Empirical results (symbols) as well as model fits (lines) for thresholds of the grating patch of (d) 1, (e) 8, and (f) 20 c/deg and contrasts of 95% (high) and 6–8% (low).

Fig. 6
Fig. 6

(a), (b) Spatial and temporal selectivity of the four filters of Eq. (2) corresponding to P=0.25, 1, 4, and 16 c/deg, on a logarithmic scale. The temporal-frequency cross section is taken at the peak spatial frequency of each filter. (c), (d) Contour plots of amplitude spectra of the filter with (c) P=4 c/deg and (d) P=16 c/deg. The solid lines are the amplitude spectra of a delta function in smooth motion with a velocity of 1 deg/s. The dashed lines indicate the amplitude spectra of the spurious bands introduced by temporal sampling at a frequency of 35 Hz.

Fig. 7
Fig. 7

Threshold for the discrimination of the direction of offset in vernier offsets created by spatiotemporal interpolation as a function of apparent velocity of motion. Five different spatial offsets between adjacent stations. (a)–(f) Results of six individual observers and (g) their means ± standard errors. Presentation time, 250 ms.

Fig. 8
Fig. 8

Vernier discrimination thresholds for interpolative verniers in apparent motion at distances between stations of 0.5, 2, 10, 20, and 40 arc min. Empirical results [solid symbols, from Fig. 7(g)] and model fits (lines). The model selects the highest-spatial-frequency filter that responds reliably to the line in smooth motion. It determines the offset using Eq. (4) with the constant K equal to 0.0694 deg or, equivalently, to 250 arc sec.

Equations (4)

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

L(x)=Lmin+Lpp/2 exp(-x2/s2)[1+ph cos(2fx)],
G(ft, fx)=exp(-ft2/2σt2)exp{-[ln(fx/P)]2/2σx2},
F(fx, fy, ft)=H(fy)cos(dxfx-ft/v)·nδ(fx-ft/v+n/Δx),
V=K/P,

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