Abstract

While an observer is moving forward, his retinal image of the outside world contains a flow field. This optical flow field carries information both about external objects and about where the observer is going relative to these objects. Mathematically, the flow pattern can be analyzed into elements that include the curl of local velocity (i.e., vorticity), and it has been suggested that the visual pathway might contain independent neural mechanisms sensitive to these mathematical elements [ H. C. Longuet-Higgins and K. Prazdny, Proc. R. Soc. London Ser. B 208, 385– 397 ( 1980)]. To test this suggestion we compared visual responses to two circular areas of random dots, A and B. These two stimuli were identical in that all dots oscillated along a straight line in one of two possible directions. However, the relative phases of dot oscillations were different for A and B, causing A to have a rotary component of motion that B did not have. We found that rotary motion thresholds for a rotary test stimulus were more elevated after adapting to A than after adapting to B, a difference that cannot be explained in terms of visual responses to linear motion, since linear motion components were the same for A and B. This finding is consistent with the idea of a neural mechanism sensitive to the curl of velocity (i.e., vorticity). Adding this to previous evidence for a mechanism specifically sensitive to the divergence of velocity (i.e., dilatation), we suggest that one role of these postulated mechanisms might be to parallel vector calculus by analyzing each small patch of the visual flow field into neural representations of the mathematically independent quantities curl and divergence of velocity.

© 1985 Optical Society of America

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References

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  1. J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, (1950).
  2. D. E. Rutherford, Vector Methods (Oliver and Boyd, London, 1954).
  3. J. J. Koenderink, A. J. van Doorn, “Local structure of movement parallax of the plane,”J. Opt. Soc. Am. 66, 717–723 (1976).
    [CrossRef]
  4. H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. Lond. B 208, 385–397 (1980).
    [CrossRef] [PubMed]
  5. D. Regan, K. I. Beverley, “Looming detectors in the human visual pathway,” Vision Res. 18, 415–421 (1978).
    [CrossRef] [PubMed]
  6. D. Regan, K. I. Beverley, “Visual responses to changing size and to sideways motion for different directions of motion in depth: linearization of visual responses,”J. Opt. Soc. Am. 70, 1289–1296 (1980).
    [CrossRef] [PubMed]
  7. D. Regan, K. I. Beverley, “Visually guided locomotion: psychophysical evidence for a neural mechanism sensitive to flow patterns,” Science 205, 311–313 (1979).
    [CrossRef] [PubMed]
  8. In principle, a difference between the effects of stimuli A and B might be affected by interactions between vorticity and linear motion mechanisms as well as by the properties of a vorticity mechanism. However, this does not detract from our main point, namely, that any difference between the effects of A and B cannot be explained in terms of responses to linear motion.
  9. Adapting stimulus B had finite div V along the joins of the four quadrants, whereas div V was zero at all points on adapting stimulus A. However, because div V was zero at all points on the test stimulus, we assume that divergence can be ignored.
  10. R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.
  11. B. Julesz, R. I. Hesse, “Inability to perceive the direction of rotation of line segments,” Nature 225, 243–244 (1970).
    [CrossRef] [PubMed]
  12. D. Regan, “Visual information channeling in normal and disordered vision,” Psychol. Rev. 89, 407–444 (1982).
    [CrossRef] [PubMed]
  13. O. Braddick, F. W. Campbell, J. Atkinson, “Channels in vision: basic aspects,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.
  14. N. Graham, “Psychophysics of spatial frequency channels,” in Perceptual Organization, M. Kubovy, J. R. Pomerantz, eds. (Erlbaum, Hillsdale, N.J., 1981), pp. 1–25.
  15. H. H. Bell, J. S. Lappin, “The detection of rotation in random dot patterns,” Percep. Psychophys. 26, 415–417 (1979).
    [CrossRef]
  16. S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
    [CrossRef] [PubMed]
  17. D. Regan, H. Spekreijse, “Electrophysiological correlate of binocular depth perception in man,” Nature 225, 92–94 (1970).
    [CrossRef] [PubMed]
  18. O. Braddick, “A short range process in apparent motion,” Vision Res. 14, 519–527 (1974).
    [CrossRef] [PubMed]
  19. W. R. Uttal, An Autocorrelation Theory of Form Detection (Erlbaum, Hillsdale, N. J., 1975).
  20. J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 18, 161–168 (1976).
    [CrossRef]

1982 (1)

D. Regan, “Visual information channeling in normal and disordered vision,” Psychol. Rev. 89, 407–444 (1982).
[CrossRef] [PubMed]

1980 (2)

1979 (2)

D. Regan, K. I. Beverley, “Visually guided locomotion: psychophysical evidence for a neural mechanism sensitive to flow patterns,” Science 205, 311–313 (1979).
[CrossRef] [PubMed]

H. H. Bell, J. S. Lappin, “The detection of rotation in random dot patterns,” Percep. Psychophys. 26, 415–417 (1979).
[CrossRef]

1978 (1)

D. Regan, K. I. Beverley, “Looming detectors in the human visual pathway,” Vision Res. 18, 415–421 (1978).
[CrossRef] [PubMed]

1976 (2)

J. J. Koenderink, A. J. van Doorn, “Local structure of movement parallax of the plane,”J. Opt. Soc. Am. 66, 717–723 (1976).
[CrossRef]

J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 18, 161–168 (1976).
[CrossRef]

1974 (1)

O. Braddick, “A short range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

1970 (3)

B. Julesz, R. I. Hesse, “Inability to perceive the direction of rotation of line segments,” Nature 225, 243–244 (1970).
[CrossRef] [PubMed]

S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
[CrossRef] [PubMed]

D. Regan, H. Spekreijse, “Electrophysiological correlate of binocular depth perception in man,” Nature 225, 92–94 (1970).
[CrossRef] [PubMed]

Anstis, S. M.

S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
[CrossRef] [PubMed]

Atkinson, J.

O. Braddick, F. W. Campbell, J. Atkinson, “Channels in vision: basic aspects,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Bell, H. H.

H. H. Bell, J. S. Lappin, “The detection of rotation in random dot patterns,” Percep. Psychophys. 26, 415–417 (1979).
[CrossRef]

J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 18, 161–168 (1976).
[CrossRef]

Beverley, K. I.

D. Regan, K. I. Beverley, “Visual responses to changing size and to sideways motion for different directions of motion in depth: linearization of visual responses,”J. Opt. Soc. Am. 70, 1289–1296 (1980).
[CrossRef] [PubMed]

D. Regan, K. I. Beverley, “Visually guided locomotion: psychophysical evidence for a neural mechanism sensitive to flow patterns,” Science 205, 311–313 (1979).
[CrossRef] [PubMed]

D. Regan, K. I. Beverley, “Looming detectors in the human visual pathway,” Vision Res. 18, 415–421 (1978).
[CrossRef] [PubMed]

Braddick, O.

O. Braddick, “A short range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

O. Braddick, F. W. Campbell, J. Atkinson, “Channels in vision: basic aspects,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Campbell, F. W.

O. Braddick, F. W. Campbell, J. Atkinson, “Channels in vision: basic aspects,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Gibson, J. J.

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, (1950).

Graham, N.

N. Graham, “Psychophysics of spatial frequency channels,” in Perceptual Organization, M. Kubovy, J. R. Pomerantz, eds. (Erlbaum, Hillsdale, N.J., 1981), pp. 1–25.

Hesse, R. I.

B. Julesz, R. I. Hesse, “Inability to perceive the direction of rotation of line segments,” Nature 225, 243–244 (1970).
[CrossRef] [PubMed]

Julesz, B.

B. Julesz, R. I. Hesse, “Inability to perceive the direction of rotation of line segments,” Nature 225, 243–244 (1970).
[CrossRef] [PubMed]

Koenderink, J. J.

Lappin, J. S.

H. H. Bell, J. S. Lappin, “The detection of rotation in random dot patterns,” Percep. Psychophys. 26, 415–417 (1979).
[CrossRef]

J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 18, 161–168 (1976).
[CrossRef]

Levinson, E.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. Lond. B 208, 385–397 (1980).
[CrossRef] [PubMed]

Pantle, A.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Prazdny, K.

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. Lond. B 208, 385–397 (1980).
[CrossRef] [PubMed]

Regan, D.

D. Regan, “Visual information channeling in normal and disordered vision,” Psychol. Rev. 89, 407–444 (1982).
[CrossRef] [PubMed]

D. Regan, K. I. Beverley, “Visual responses to changing size and to sideways motion for different directions of motion in depth: linearization of visual responses,”J. Opt. Soc. Am. 70, 1289–1296 (1980).
[CrossRef] [PubMed]

D. Regan, K. I. Beverley, “Visually guided locomotion: psychophysical evidence for a neural mechanism sensitive to flow patterns,” Science 205, 311–313 (1979).
[CrossRef] [PubMed]

D. Regan, K. I. Beverley, “Looming detectors in the human visual pathway,” Vision Res. 18, 415–421 (1978).
[CrossRef] [PubMed]

D. Regan, H. Spekreijse, “Electrophysiological correlate of binocular depth perception in man,” Nature 225, 92–94 (1970).
[CrossRef] [PubMed]

Rutherford, D. E.

D. E. Rutherford, Vector Methods (Oliver and Boyd, London, 1954).

Sekuler, R.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

Spekreijse, H.

D. Regan, H. Spekreijse, “Electrophysiological correlate of binocular depth perception in man,” Nature 225, 92–94 (1970).
[CrossRef] [PubMed]

Uttal, W. R.

W. R. Uttal, An Autocorrelation Theory of Form Detection (Erlbaum, Hillsdale, N. J., 1975).

van Doorn, A. J.

J. Opt. Soc. Am. (2)

Nature (2)

B. Julesz, R. I. Hesse, “Inability to perceive the direction of rotation of line segments,” Nature 225, 243–244 (1970).
[CrossRef] [PubMed]

D. Regan, H. Spekreijse, “Electrophysiological correlate of binocular depth perception in man,” Nature 225, 92–94 (1970).
[CrossRef] [PubMed]

Percep. Psychophys. (1)

H. H. Bell, J. S. Lappin, “The detection of rotation in random dot patterns,” Percep. Psychophys. 26, 415–417 (1979).
[CrossRef]

Proc. R. Soc. Lond. B (1)

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. Lond. B 208, 385–397 (1980).
[CrossRef] [PubMed]

Psychol. Rev. (1)

D. Regan, “Visual information channeling in normal and disordered vision,” Psychol. Rev. 89, 407–444 (1982).
[CrossRef] [PubMed]

Science (1)

D. Regan, K. I. Beverley, “Visually guided locomotion: psychophysical evidence for a neural mechanism sensitive to flow patterns,” Science 205, 311–313 (1979).
[CrossRef] [PubMed]

Vision Res. (4)

D. Regan, K. I. Beverley, “Looming detectors in the human visual pathway,” Vision Res. 18, 415–421 (1978).
[CrossRef] [PubMed]

S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
[CrossRef] [PubMed]

O. Braddick, “A short range process in apparent motion,” Vision Res. 14, 519–527 (1974).
[CrossRef] [PubMed]

J. S. Lappin, H. H. Bell, “The detection of coherence in moving random-dot patterns,” Vision Res. 18, 161–168 (1976).
[CrossRef]

Other (8)

W. R. Uttal, An Autocorrelation Theory of Form Detection (Erlbaum, Hillsdale, N. J., 1975).

O. Braddick, F. W. Campbell, J. Atkinson, “Channels in vision: basic aspects,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

N. Graham, “Psychophysics of spatial frequency channels,” in Perceptual Organization, M. Kubovy, J. R. Pomerantz, eds. (Erlbaum, Hillsdale, N.J., 1981), pp. 1–25.

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, (1950).

D. E. Rutherford, Vector Methods (Oliver and Boyd, London, 1954).

In principle, a difference between the effects of stimuli A and B might be affected by interactions between vorticity and linear motion mechanisms as well as by the properties of a vorticity mechanism. However, this does not detract from our main point, namely, that any difference between the effects of A and B cannot be explained in terms of responses to linear motion.

Adapting stimulus B had finite div V along the joins of the four quadrants, whereas div V was zero at all points on adapting stimulus A. However, because div V was zero at all points on the test stimulus, we assume that divergence can be ignored.

R. Sekuler, A. Pantle, E. Levinson, “Physiological basis of motion perception,” in Handbook of Sensory Physiology, R. Held, H. W. Leibowitz, H.-L. Teuber, eds. (Springer, New York, 1978), Vol. 8.

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Figures (3)

Fig. 1
Fig. 1

Adapting stimuli (A and B) and test stimulus C. In both stimulus A and stimulus B, every dot oscillated sinusoidally along a straight line. Every dot had the same amplitude and frequency of oscillation. In A and B, the stimulus areas were divided into four quadrants. The arrows show how the relative phases of oscillation were arranged so that A had a component of rotation about the center but B bad not. Test stimulus C was an area of dots that rotated sinusoidally to and fro about the center.

Fig. 2
Fig. 2

Baseline visual sensitivity to oscillatory rotation. Ordinates plot just-visible angular amplitude of rotation, and abscissas plot frequency of oscillatory rotation. Test stimulus C was used (Fig. 1C). The dotted line plots a constant-velocity law. Vertical bars show ±1 standard deviations for the 10 to 20 settings per point. Results are shown for two subjects.

Fig. 3
Fig. 3

Threshold elevations for oscillatory rotation caused by adapting to stimulus A (continuous line) and by adapting to stimulus B (broken line). Stimulus A contained a rotary component of motion and B did not, but linear motion components were identical in A and B. Vertical bars show ±1 standard error for the 10 to 20 settings per point. Stimuli A and B both subtended 2-deg diameter, while test stimulus C subtended 1-deg diameter. All stimuli were viewed with their centers at 3-deg eccentricity. Results for two subjects are shown.

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V · d l δ a ,

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