Abstract

We measured the detectability of moving signal dots in dynamic noise to determine whether local motion signals are preferentially combined along an axis parallel to the direction of motion. Observers were asked to detect a signal composed of three dots moving in a linear trajectory among dynamic noise dots. The signal dots were collinear and equally spaced in a configuration that was either parallel to or perpendicular to their trajectory. The probability of detecting the signal was measured as a function of noise density, over a range of signal dot spacings from 0.5° to 5.0°. At any given noise density, the signal in the parallel configuration was more detectable than that in the perpendicular configuration. Our four observers could tolerate 1.5–2.5 times more noise in the parallel configuration. This improvement is not due merely to temporal summation between consecutive dots in the parallel trajectory. Temporal summation functions measured on our observers indicate that the benefit from spatial coincidence of the dots lasts for no more than 50 ms, whereas the increased detectability of the parallel configuration is observed up to the largest temporal separations tested (210 ms). These results demonstrate that dots arranged parallel to the signal trajectory are more easily detected than those arranged perpendicularly. Moreover, this enhancement points to the existence of visual mechanisms that preferentially organize motion information parallel to the direction of motion.

© 2000 Optical Society of America

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  1. D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
    [CrossRef] [PubMed]
  2. I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
    [CrossRef] [PubMed]
  3. U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
    [CrossRef] [PubMed]
  4. U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
    [CrossRef] [PubMed]
  5. V. S. Ramachandran, S. M. Anstis, “Extrapolation of motion path in human visual perception,” Vision Res. 23, 83–85 (1983).
    [CrossRef] [PubMed]
  6. K. Nakayama, G. H. Silverman, “Temporal and spatial characteristics of the upper displacement limit for motion in random dots,” Vision Res. 24, 293–299 (1984).
    [CrossRef] [PubMed]
  7. A. J. van Doorn, J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
    [CrossRef] [PubMed]
  8. S. P. McKee, L. Welch, “Sequential recruitment in the discrimination of velocity,” J. Opt. Soc. Am. A 2, 243–251 (1985).
    [CrossRef] [PubMed]
  9. S. M. Anstis, V. S. Ramachandran, “Visual inertia in apparent motion,” Vision Res. 27, 755–764 (1987).
    [CrossRef] [PubMed]
  10. R. J. Snowden, O. J. Braddick, “The combination of motion signals over time,” Vision Res. 29, 1621–1630 (1989).
    [CrossRef] [PubMed]
  11. P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
    [CrossRef] [PubMed]
  12. S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
    [CrossRef] [PubMed]
  13. N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
    [CrossRef] [PubMed]
  14. P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
    [CrossRef] [PubMed]
  15. R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
    [CrossRef] [PubMed]
  16. S. M. Anderson, D. C. Burr, “Spatial summation properties of directionally selective mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1330–1339 (1991).
    [CrossRef] [PubMed]
  17. K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
    [CrossRef] [PubMed]
  18. P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
    [CrossRef] [PubMed]
  19. Z-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
    [CrossRef] [PubMed]
  20. J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
    [CrossRef] [PubMed]
  21. E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 8, 284–299 (1985).
    [CrossRef]
  22. J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
    [PubMed]
  23. S. M. 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]
  24. R. S. Hubbard, J. A. Marshall, “Self-organizing neural network model of the visual inertia phenomenon in motion perception,” (Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, N. Car., 1994).
  25. P-Y. Burgi, A. L. Yuille, N. M. Grzywacz, “Probabilistic motion estimation based on temporal coherence,” Neural Comput. (to be published).
  26. Since the trajectory passes so close to the fixation point, it is detected almost perfectly if we set the number of possible directions to two, as in Fredericksen et al. (Ref. 15). This is true even at the highest noise density that we used. Setting the number of directions to eight considerably increases the uncertainty of the signal trajectory.
  27. J. Nachmias, R. V. Sansbury, “Grating contrast: Discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  28. A. B. Watson, J. Nachmias, “Patterns of temporal interaction in the detection of gratings,” Vision Res. 17, 893–902 (1977).
    [CrossRef] [PubMed]
  29. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  30. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  31. The d′additivity equation assumes an underlying Gaussian probability distribution, which is not unreasonable. Alternatively, one could calculate probability summation using a high-threshold model, P3=1-(1-P1)3,where P3and P1are the true probabilities of detecting three- and one-dot trajectories, respectively. The high-threshold model yields slightly higher predictions for probability summation, but the error bars on our data roughly span this difference, so it is hard to differentiate between the high-threshold and the d′additivity versions of probability summation.
  32. M. C. Morrone, D. C. Burr, L. M. Vaina, “Two stages of visual processing for radial and circular motion,” Nature 376, 507–509 (1995).
    [CrossRef] [PubMed]
  33. L. Santoro, D. C. Burr, “Temporal integration of optic flow,” Perception (Suppl.) 28, 90 (1999).
  34. W. S. Geisler, “Motion streaks provide a spatial code for motion direction,” Nature (London) 400, 65–69 (1999).
    [CrossRef]
  35. M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
    [CrossRef] [PubMed]
  36. R. Nijhawan, “Motion extrapolation in catching,” Nature 370, 256–257 (1994).
    [CrossRef] [PubMed]

2000 (1)

J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
[CrossRef] [PubMed]

1999 (4)

P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

L. Santoro, D. C. Burr, “Temporal integration of optic flow,” Perception (Suppl.) 28, 90 (1999).

W. S. Geisler, “Motion streaks provide a spatial code for motion direction,” Nature (London) 400, 65–69 (1999).
[CrossRef]

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

1998 (1)

Z-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

1995 (4)

M. C. Morrone, D. C. Burr, L. M. Vaina, “Two stages of visual processing for radial and circular motion,” Nature 376, 507–509 (1995).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
[CrossRef] [PubMed]

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
[CrossRef] [PubMed]

1994 (3)

R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
[CrossRef] [PubMed]

R. Nijhawan, “Motion extrapolation in catching,” Nature 370, 256–257 (1994).
[CrossRef] [PubMed]

1993 (3)

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
[CrossRef] [PubMed]

1991 (2)

1990 (1)

P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
[CrossRef] [PubMed]

1989 (1)

R. J. Snowden, O. J. Braddick, “The combination of motion signals over time,” Vision Res. 29, 1621–1630 (1989).
[CrossRef] [PubMed]

1987 (2)

S. M. Anstis, V. S. Ramachandran, “Visual inertia in apparent motion,” Vision Res. 27, 755–764 (1987).
[CrossRef] [PubMed]

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

1985 (3)

S. P. McKee, L. Welch, “Sequential recruitment in the discrimination of velocity,” J. Opt. Soc. Am. A 2, 243–251 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 8, 284–299 (1985).
[CrossRef]

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

1984 (2)

K. Nakayama, G. H. Silverman, “Temporal and spatial characteristics of the upper displacement limit for motion in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef] [PubMed]

A. J. van Doorn, J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

1983 (1)

V. S. Ramachandran, S. M. Anstis, “Extrapolation of motion path in human visual perception,” Vision Res. 23, 83–85 (1983).
[CrossRef] [PubMed]

1980 (1)

1977 (1)

A. B. Watson, J. Nachmias, “Patterns of temporal interaction in the detection of gratings,” Vision Res. 17, 893–902 (1977).
[CrossRef] [PubMed]

1974 (1)

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

Adelson, E. H.

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 8, 284–299 (1985).
[CrossRef]

Anderson, S. M.

Anstis, S. M.

S. M. Anstis, V. S. Ramachandran, “Visual inertia in apparent motion,” Vision Res. 27, 755–764 (1987).
[CrossRef] [PubMed]

V. S. Ramachandran, S. M. Anstis, “Extrapolation of motion path in human visual perception,” Vision Res. 23, 83–85 (1983).
[CrossRef] [PubMed]

Bergen, J. R.

E. H. Adelson, J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 8, 284–299 (1985).
[CrossRef]

Berry, M. J.

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

Braddick, O. J.

R. J. Snowden, O. J. Braddick, “The combination of motion signals over time,” Vision Res. 29, 1621–1630 (1989).
[CrossRef] [PubMed]

Brivanlou, I. H.

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

Burgi, P-Y.

P-Y. Burgi, A. L. Yuille, N. M. Grzywacz, “Probabilistic motion estimation based on temporal coherence,” Neural Comput. (to be published).

Burr, D. C.

Dosher, B. A.

Z-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

Field, D. J.

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Foley, J. M.

Fredericksen, R. E.

R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, “Motion streaks provide a spatial code for motion direction,” Nature (London) 400, 65–69 (1999).
[CrossRef]

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Grzywacz, N. M.

S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
[CrossRef] [PubMed]

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

P-Y. Burgi, A. L. Yuille, N. M. Grzywacz, “Probabilistic motion estimation based on temporal coherence,” Neural Comput. (to be published).

Hayes, A.

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Hess, R. F.

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

Hubbard, R. S.

R. S. Hubbard, J. A. Marshall, “Self-organizing neural network model of the visual inertia phenomenon in motion perception,” (Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, N. Car., 1994).

Jones, J. P.

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

Jordan, T. A.

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

Julesz, B.

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

Koenderink, J. J.

P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
[CrossRef] [PubMed]

A. J. van Doorn, J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

Kovacs, I.

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

Legge, G. E.

Lu, Z-L.

Z-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

MacLeod, D. I. A.

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Marshall, J. A.

R. S. Hubbard, J. A. Marshall, “Self-organizing neural network model of the visual inertia phenomenon in motion perception,” (Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, N. Car., 1994).

McKee, S. P.

P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
[CrossRef] [PubMed]

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

S. P. McKee, L. Welch, “Sequential recruitment in the discrimination of velocity,” J. Opt. Soc. Am. A 2, 243–251 (1985).
[CrossRef] [PubMed]

Meister, M.

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

Morrone, M. C.

Mulligan, J.

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Nachmias, J.

A. B. Watson, J. Nachmias, “Patterns of temporal interaction in the detection of gratings,” Vision Res. 17, 893–902 (1977).
[CrossRef] [PubMed]

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

Nakayama, K.

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Temporal and spatial characteristics of the upper displacement limit for motion in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef] [PubMed]

Nijhawan, R.

R. Nijhawan, “Motion extrapolation in catching,” Nature 370, 256–257 (1994).
[CrossRef] [PubMed]

Palmer, J.

J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
[CrossRef] [PubMed]

Palmer, L. A.

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

Pavel, M.

J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
[CrossRef] [PubMed]

Polat, U.

U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
[CrossRef] [PubMed]

U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
[CrossRef] [PubMed]

Ramachandran, V. S.

S. M. Anstis, V. S. Ramachandran, “Visual inertia in apparent motion,” Vision Res. 27, 755–764 (1987).
[CrossRef] [PubMed]

V. S. Ramachandran, S. M. Anstis, “Extrapolation of motion path in human visual perception,” Vision Res. 23, 83–85 (1983).
[CrossRef] [PubMed]

Sagi, D.

U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
[CrossRef] [PubMed]

U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
[CrossRef] [PubMed]

Sansbury, R. V.

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

Santoro, L.

L. Santoro, D. C. Burr, “Temporal integration of optic flow,” Perception (Suppl.) 28, 90 (1999).

Silverman, G. H.

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Temporal and spatial characteristics of the upper displacement limit for motion in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef] [PubMed]

Snippe, H. P.

P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
[CrossRef] [PubMed]

Snowden, R. J.

R. J. Snowden, O. J. Braddick, “The combination of motion signals over time,” Vision Res. 29, 1621–1630 (1989).
[CrossRef] [PubMed]

Stone, L. S.

P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
[CrossRef] [PubMed]

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Vaina, L. M.

M. C. Morrone, D. C. Burr, L. M. Vaina, “Two stages of visual processing for radial and circular motion,” Nature 376, 507–509 (1995).
[CrossRef] [PubMed]

van de Grind, W. A.

R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

van Doorn, A. J.

A. J. van Doorn, J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

Verghese, P.

J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
[CrossRef] [PubMed]

P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
[CrossRef] [PubMed]

Verstraten, F. A. J.

R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

Watamaniuk, S. N. J.

P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
[CrossRef] [PubMed]

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, J. Nachmias, “Patterns of temporal interaction in the detection of gratings,” Vision Res. 17, 893–902 (1977).
[CrossRef] [PubMed]

Welch, L.

Werkhoven, P.

P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
[CrossRef] [PubMed]

Yuille, A. L.

P-Y. Burgi, A. L. Yuille, N. M. Grzywacz, “Probabilistic motion estimation based on temporal coherence,” Neural Comput. (to be published).

J. Neurophysiol. (1)

J. P. Jones, L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Nature (3)

M. J. Berry, I. H. Brivanlou, T. A. Jordan, M. Meister, “Anticipation of moving stimuli by the retina,” Nature 398, 334–338 (1999).
[CrossRef] [PubMed]

R. Nijhawan, “Motion extrapolation in catching,” Nature 370, 256–257 (1994).
[CrossRef] [PubMed]

M. C. Morrone, D. C. Burr, L. M. Vaina, “Two stages of visual processing for radial and circular motion,” Nature 376, 507–509 (1995).
[CrossRef] [PubMed]

Nature (London) (1)

W. S. Geisler, “Motion streaks provide a spatial code for motion direction,” Nature (London) 400, 65–69 (1999).
[CrossRef]

Percept. Psychophys. (1)

P. Werkhoven, H. P. Snippe, J. J. Koenderink, “Effects of element orientation on apparent motion perception,” Percept. Psychophys. 47, 509–525 (1990).
[CrossRef] [PubMed]

Perception (1)

K. Nakayama, G. H. Silverman, D. I. A. MacLeod, J. Mulligan, “Sensitivity to shearing and compressive motion in random dots,” Perception 14, 225–238 (1985).
[CrossRef] [PubMed]

Perception (Suppl.) (1)

L. Santoro, D. C. Burr, “Temporal integration of optic flow,” Perception (Suppl.) 28, 90 (1999).

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

I. Kovacs, B. Julesz, “A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation,” Proc. Natl. Acad. Sci. USA 90, 7495–7497 (1993).
[CrossRef] [PubMed]

Vision Res. (17)

U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
[CrossRef] [PubMed]

U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
[CrossRef] [PubMed]

V. S. Ramachandran, S. M. Anstis, “Extrapolation of motion path in human visual perception,” Vision Res. 23, 83–85 (1983).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Temporal and spatial characteristics of the upper displacement limit for motion in random dots,” Vision Res. 24, 293–299 (1984).
[CrossRef] [PubMed]

A. J. van Doorn, J. J. Koenderink, “Spatiotemporal integration in the detection of coherent motion,” Vision Res. 24, 47–53 (1984).
[CrossRef] [PubMed]

S. M. Anstis, V. S. Ramachandran, “Visual inertia in apparent motion,” Vision Res. 27, 755–764 (1987).
[CrossRef] [PubMed]

R. J. Snowden, O. J. Braddick, “The combination of motion signals over time,” Vision Res. 29, 1621–1630 (1989).
[CrossRef] [PubMed]

P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
[CrossRef] [PubMed]

Z-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

J. Palmer, P. Verghese, M. Pavel, “The psychophysics of visual search,” Vision Res. 40, 1227–1268 (2000).
[CrossRef] [PubMed]

S. N. J. Watamaniuk, S. P. McKee, N. M. Grzywacz, “Detecting a trajectory embedded in random-direction motion noise,” Vision Res. 35, 65–77 (1995).
[CrossRef] [PubMed]

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

P. Verghese, S. N. J. Watamaniuk, S. P. McKee, “Local motion detectors cannot account for the detectability of an extended trajectory in noise,” Vision Res. 39, 19–30 (1999).
[CrossRef] [PubMed]

R. E. Fredericksen, F. A. J. Verstraten, W. A. van de Grind, “Spatial summation and its interaction with the temporal integration mechanism in human motion perception,” Vision Res. 34, 3171–3188 (1994).
[CrossRef] [PubMed]

D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local ‘association field,’ ” Vision Res. 33, 173–193 (1993).
[CrossRef] [PubMed]

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

A. B. Watson, J. Nachmias, “Patterns of temporal interaction in the detection of gratings,” Vision Res. 17, 893–902 (1977).
[CrossRef] [PubMed]

Other (5)

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

The d′additivity equation assumes an underlying Gaussian probability distribution, which is not unreasonable. Alternatively, one could calculate probability summation using a high-threshold model, P3=1-(1-P1)3,where P3and P1are the true probabilities of detecting three- and one-dot trajectories, respectively. The high-threshold model yields slightly higher predictions for probability summation, but the error bars on our data roughly span this difference, so it is hard to differentiate between the high-threshold and the d′additivity versions of probability summation.

R. S. Hubbard, J. A. Marshall, “Self-organizing neural network model of the visual inertia phenomenon in motion perception,” (Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, N. Car., 1994).

P-Y. Burgi, A. L. Yuille, N. M. Grzywacz, “Probabilistic motion estimation based on temporal coherence,” Neural Comput. (to be published).

Since the trajectory passes so close to the fixation point, it is detected almost perfectly if we set the number of possible directions to two, as in Fredericksen et al. (Ref. 15). This is true even at the highest noise density that we used. Setting the number of directions to eight considerably increases the uncertainty of the signal trajectory.

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Figures (9)

Fig. 1
Fig. 1

Configuration of signal dots. The signal was a collinear triplet of dots that was arranged along one of eight orientations at 45° intervals. The dots in the triplet moved rigidly along a path that was either perpendicular to or parallel to the triplet configuration, as depicted in (a) and (b), respectively. The dots in the triplet had a uniform center-to-center spacing, which ranged from 0.5° to 5°.

Fig. 2
Fig. 2

Psychometric functions for the parallel and perpendicular configurations. The proportion correct is plotted versus the reciprocal of the number of noise dots. Open and solid symbols plot data for the perpendicular and parallel conditions, respectively. The center-to-center spacing of the dots in both configurations was 1°. Continuous curves are Weibull fits to the data. Thresholds were estimated as the noise level corresponding to 82% correct.

Fig. 3
Fig. 3

Thresholds for the parallel and perpendicular configurations in Brownian noise. Open and solid squares plot the thresholds for the parallel configuration and the perpendicular configuration, respectively, as a function of dot spacing. Horizontal dashed line plots threshold for a single dot. The parallel configuration has much lower thresholds than the perpendicular configuration, over the entire range of dot spacings. Error bars represent ±1 standard deviation of the estimate of threshold.

Fig. 4
Fig. 4

(a) Space–time (xt) plot of the parallel signal triplet. The top row of dots shows the triplet at one instant of time. At a time Δt later, one of the dots in the triplet could be in the same spatial location as a previous dot, and the responses to these two dots could sum. (b) A space–time plot of the configuration to measure temporal summation. Two dots are flashed in the same location, and contrast thresholds are measured as a function of the temporal delay between them.

Fig. 5
Fig. 5

Temporal summation functions for our four observers. Open squares plot summation (the ratio of sensitivity to a pulse pair at a given delay to a single pulse) as a function of the delay between the pulses. Solid squares plot the ratio of sensitivities of the parallel and perpendicular configurations.

Fig. 6
Fig. 6

Open squares plot temporal summation between three pulses as a function of delay. Solid squares plot the ratio of sensitivities of the parallel and perpendicular configurations.

Fig. 7
Fig. 7

Space–time (xt) plot of the parallel configuration at dot spacings of (a) 0.5° and (b) 1.0°, respectively, with a local motion unit superimposed. The size of the motion unit in the x dimension is 0.9°, which is the full width at half-height of the optimal motion unit (see text). The summation duration of 50 ms is based on the temporal summation function of Fig. 5. The dashed outline in (b) represents a summation duration of 100 ms. Each diagonal row of dots represents the displacement of a single dot over time.

Fig. 8
Fig. 8

Psychometric functions for various configurations of the signal. Solid squares plot the probability of detecting a single signal trajectory. The dotted curve is the predicted improvement for the detection of three dots, assuming that the three dots are combined independently. Solid and open triangles plot the probability of detecting the parallel and perpendicular configurations, respectively. Solid curves are Weibull fits to the data. Each data point represents a minimum of 192 trials measured over two blocks. Error bars represent ±1 standard error of the percent correct estimate across blocks of trials.

Fig. 9
Fig. 9

Psychometric functions for the rigid and starburst configurations of three signal trajectories. Solid squares and the dashed curve are replotted from Fig. 8 and are the probabilities of detecting a single signal trajectory and the probability summation prediction for three independent signal trajectories, respectively. Solid and open circles plot the probability of detecting the three signal trajectories in the rigid and starburst configurations, respectively. The solid curves are Weibull fits to the data. Each data point represents a minimum of 192 trials measured over two blocks. Error bars represent ±1 standard error across blocks of trials.  

Equations (2)

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d=ccthreshb
d3=d13,

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