Abstract

We investigated the simulated real-world optic flow motion aftereffect (MAE) (illusory sense of moving backward following adaptation to expansive optic flow). In Experiment 1, adaptation duration was either 30, 120, 240, or 480s. Results: duration of the MAE grew with increasing adaptation duration. In Experiment 2, the MAE was measured across different combinations of values of global optical flow rate and optical edge rate. Results: the aftereffect was selective for global optical flow rate, suggesting that the aftereffect reflects gain changes at processing levels where a sense of self-motion is generated. Results were used in a computational model of this MAE, which was a modified framework by van de Grind et al. [Vision Res. 44, 2269 (2004)] .

© 2009 Optical Society of America

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  1. W. D. Ross, The Works of Aristotle. Vol. 3, Parva Naturalia De Somniis. Transl. J. I. Beare (Clarendon, 1931).
  2. G. Mather, F. Verstraten, and S. Anstis, The Motion Aftereffect: a Modern Perspective (MIT, 1998).
  3. V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
    [CrossRef] [PubMed]
  4. P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
    [CrossRef] [PubMed]
  5. M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
    [CrossRef] [PubMed]
  6. W. H. Warren, Jr., The State of Flow (MIT, 1998).
  7. H. C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. London, Ser. B 208, 385-397 (1980).
    [CrossRef]
  8. J. H. Rieger and T. D. Lawton, “Processing differential image motion,” J. Opt. Soc. Am. A 2, 354-360 (1985).
    [CrossRef] [PubMed]
  9. D. Regan and K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194-196 (1982).
    [CrossRef] [PubMed]
  10. In a control experiment, four observers viewed our SRW optic flow display and a display showing a moving spiral pattern (both displays had the same dimensions, similar to our optic flow display in the main experiment). Five trials were collected for each display, presented in random order. Observers rated each display on a scale of 0 to 10, with 0 indicating no sense of self-motion and 10 indicating a very strong sense of self-motion. Average rating of our optic flow display was 8 (S.E.=0.4); average rating of the spiral display was 2 (S.E.=0.5). Our optic flow display generates a much greater sense of self-motion than a spiral display.
  11. W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
    [CrossRef] [PubMed]
  12. W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
    [CrossRef] [PubMed]
  13. Because the poles were of constant distal size in the simulation (in meters), their proximal angular size varied in the display in continuous fashion, from closest to farthest, because the poles were seen in perspective view.
  14. J. W. Forrester, Industrial Dynamics (Pegasus, 1961).
  15. J. W. Forrester, Principles of Systems (Pegasus, 1968).
  16. J. D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (McGraw-Hill, 2000).
  17. A. Grunewald, “A model of transparent motion and non-transparent motion aftereffects,” in Proceedings of the 8th Conference on Advanced Neural Information Processing Systems (1996), Vol. 8, pp. 837-843.
  18. A. Grunewald and M. J. M. Lankheet, “Orthogonal motion after-effect illusion predicted by a model of cortical motion processing,” Nature 384, 358-360 (1996).
    [CrossRef] [PubMed]
  19. C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
    [CrossRef] [PubMed]
  20. M. Hershenson, “Duration, time constant, and decay of the linear motion aftereffect as a function of inspection duration,” Percept. Psychophys. 45, 251-257 (1989).
    [CrossRef] [PubMed]
  21. Adaptation speeds used in the main study ranged from 50to400 m/s, which corresponded to 112.5-900 mph, respectively. While these speeds were excessive relative to highway speeds, our altitude of 5 m made the global optical flow rate (e.g., 20 eyeheights/s) comparable to that encountered at highway speeds (e.g., 45 mph) when individuals travel sitting in a car at an altitude of about 1 m. To control for this, we had four observers, at an altitude of 1 m, adapt to our SRW optic flow for a duration of 2 min or 8 min, at speeds of 20 m/s(45 mph) or 40 m/s(90 mph); thus global optical flow rate was 20 or 40 eyeheights/s, respectively, as in the main study. Results: for adapt duration of 2 min, average MAE duration was 18.8 s and 22.6 s for the 20 m/s and 40 m/s adapt speeds, respectively; for adapt duration of 8 min, average MAE duration was 39.8 s and 52.3 s for the 20 m/s and 40 m/s adapt speeds, respectively. Thus, our results from the main study generalize to more terrestrial speeds typically encountered in the real world.
  22. F. Bremmer, “Navigation in space--the role of the macaque ventral intraparietal area,” J. Physiol. (London) 566, 29-35 (2005).
    [CrossRef]
  23. F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
    [CrossRef] [PubMed]
  24. F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.
  25. We considered adding multiple leaky integrators in serial order with a group of local mechanisms converging onto a head-centric unit at a higher (global) level of processing, the latter of which would adapt with a longer time constant. We rejected this scheme in favor of multiple parallel mechanisms at each processing level because showed that local MAEs can be very long, and this study showed that global MAEs can also be very long; thus both local and global levels require parallel mechanisms with a range of time constants.
  26. R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
    [CrossRef] [PubMed]

2005 (1)

F. Bremmer, “Navigation in space--the role of the macaque ventral intraparietal area,” J. Physiol. (London) 566, 29-35 (2005).
[CrossRef]

2004 (1)

W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
[CrossRef] [PubMed]

2003 (1)

W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
[CrossRef] [PubMed]

2002 (1)

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

2001 (1)

P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
[CrossRef] [PubMed]

1999 (1)

M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
[CrossRef] [PubMed]

1996 (2)

A. Grunewald and M. J. M. Lankheet, “Orthogonal motion after-effect illusion predicted by a model of cortical motion processing,” Nature 384, 358-360 (1996).
[CrossRef] [PubMed]

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

1994 (2)

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
[CrossRef] [PubMed]

1989 (1)

M. Hershenson, “Duration, time constant, and decay of the linear motion aftereffect as a function of inspection duration,” Percept. Psychophys. 45, 251-257 (1989).
[CrossRef] [PubMed]

1985 (1)

1982 (1)

D. Regan and K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194-196 (1982).
[CrossRef] [PubMed]

1980 (1)

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

Angilletta, M.

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Anstis, S.

G. Mather, F. Verstraten, and S. Anstis, The Motion Aftereffect: a Modern Perspective (MIT, 1998).

Barton-Howard, W.

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Ben Hamed, S.

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.

Beverley, K. I.

D. Regan and K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194-196 (1982).
[CrossRef] [PubMed]

Blake, R.

V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
[CrossRef] [PubMed]

Bowd, C.

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Bremmer, F.

F. Bremmer, “Navigation in space--the role of the macaque ventral intraparietal area,” J. Physiol. (London) 566, 29-35 (2005).
[CrossRef]

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
[CrossRef] [PubMed]

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.

Duhamel, J.-R.

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.

Forrester, J. W.

J. W. Forrester, Industrial Dynamics (Pegasus, 1961).

J. W. Forrester, Principles of Systems (Pegasus, 1968).

Graf, W.

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.

Grunewald, A.

A. Grunewald and M. J. M. Lankheet, “Orthogonal motion after-effect illusion predicted by a model of cortical motion processing,” Nature 384, 358-360 (1996).
[CrossRef] [PubMed]

A. Grunewald, “A model of transparent motion and non-transparent motion aftereffects,” in Proceedings of the 8th Conference on Advanced Neural Information Processing Systems (1996), Vol. 8, pp. 837-843.

Hershenson, M.

M. Hershenson, “Duration, time constant, and decay of the linear motion aftereffect as a function of inspection duration,” Percept. Psychophys. 45, 251-257 (1989).
[CrossRef] [PubMed]

Knill, D. C.

P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
[CrossRef] [PubMed]

Lankheet, M. J. M.

W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
[CrossRef] [PubMed]

A. Grunewald and M. J. M. Lankheet, “Orthogonal motion after-effect illusion predicted by a model of cortical motion processing,” Nature 384, 358-360 (1996).
[CrossRef] [PubMed]

Lappe, M.

M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
[CrossRef] [PubMed]

Lawton, T. D.

Longuet-Higgins, H. C.

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

Mather, G.

G. Mather, F. Verstraten, and S. Anstis, The Motion Aftereffect: a Modern Perspective (MIT, 1998).

Patterson, R.

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Phinney, R.

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Pohndorf, R.

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Prazdny, K.

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

Regan, D.

D. Regan and K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194-196 (1982).
[CrossRef] [PubMed]

Rieger, J. H.

Rose, D.

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
[CrossRef] [PubMed]

Ross, W. D.

W. D. Ross, The Works of Aristotle. Vol. 3, Parva Naturalia De Somniis. Transl. J. I. Beare (Clarendon, 1931).

Schrater, P. R.

P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
[CrossRef] [PubMed]

Simoncelli, E. P.

P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
[CrossRef] [PubMed]

Steiner, V.

V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
[CrossRef] [PubMed]

Sterman, J. D.

J. D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (McGraw-Hill, 2000).

Tao, R.

W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
[CrossRef] [PubMed]

van de Grind, W. A.

W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
[CrossRef] [PubMed]

W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
[CrossRef] [PubMed]

van den Berg, A. V.

M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
[CrossRef] [PubMed]

van der Smagt, M. J.

W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
[CrossRef] [PubMed]

Verstraten, F.

G. Mather, F. Verstraten, and S. Anstis, The Motion Aftereffect: a Modern Perspective (MIT, 1998).

Verstraten, F. A. J.

W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
[CrossRef] [PubMed]

Warren, W. H.

W. H. Warren, Jr., The State of Flow (MIT, 1998).

Eur. J. Neurosci. (1)

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “Heading encoding in the macaque ventral intraparietal area (VIP),” Eur. J. Neurosci. 16, 1554-1568 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Physiol. (London) (1)

F. Bremmer, “Navigation in space--the role of the macaque ventral intraparietal area,” J. Physiol. (London) 566, 29-35 (2005).
[CrossRef]

Nature (2)

P. R. Schrater, D. C. Knill, and E. P. Simoncelli, “Perceiving visual expansion without optic flow,” Nature 410, 816-819 (2001).
[CrossRef] [PubMed]

A. Grunewald and M. J. M. Lankheet, “Orthogonal motion after-effect illusion predicted by a model of cortical motion processing,” Nature 384, 358-360 (1996).
[CrossRef] [PubMed]

Percept. Psychophys. (1)

M. Hershenson, “Duration, time constant, and decay of the linear motion aftereffect as a function of inspection duration,” Percept. Psychophys. 45, 251-257 (1989).
[CrossRef] [PubMed]

Perception (1)

V. Steiner, R. Blake, and D. Rose, “Interocular transfer of expansion, rotation, and translation motion aftereffects,” Perception 23, 1197-1202 (1994).
[CrossRef] [PubMed]

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

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

Science (1)

D. Regan and K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194-196 (1982).
[CrossRef] [PubMed]

Trends Cogn. Sci. (1)

M. Lappe, F. Bremmer, and A. V. van den Berg, “Perception of self-motion from visual flow,” Trends Cogn. Sci. 3, 329-336 (1999).
[CrossRef] [PubMed]

Vision Res. (4)

C. Bowd, D. Rose, R. Phinney, and R. Patterson, “Enduring stereoscopic motion aftereffects induced by prolonged adaptation,” Vision Res. 36, 3655-3660 (1996).
[CrossRef] [PubMed]

W. A. van de Grind, M. J. M. Lankheet, and R. Tao, “A gain-control model relating nulling results to the duration of dynamic motion aftereffects,” Vision Res. 43, 117-133 (2003).
[CrossRef] [PubMed]

W. A. van de Grind, M. J. van der Smagt, and F. A. J. Verstraten, “Storage for free: a surprising property of a simple gain-control model of motion aftereffects,” Vision Res. 44, 2269-2284 (2004).
[CrossRef] [PubMed]

R. Patterson, C. Bowd, R. Phinney, R. Pohndorf, W. Barton-Howard, and M. Angilletta, “Properties of stereoscopic motion aftereffects,” Vision Res. 34, 1139-1147 (1994).
[CrossRef] [PubMed]

Other (12)

F. Bremmer, J.-R. Duhamel, S. Ben Hamed, and W. Graf, “The representation of movement in near extra-personal space in the macaque ventral intraparietal area (VIP),” in Parietal Lobe Contributions to Orientation in 3D Space, P.Thier and H.-O.Karnath, eds. (Springer-Verlag, 1997), pp. 619-630.

We considered adding multiple leaky integrators in serial order with a group of local mechanisms converging onto a head-centric unit at a higher (global) level of processing, the latter of which would adapt with a longer time constant. We rejected this scheme in favor of multiple parallel mechanisms at each processing level because showed that local MAEs can be very long, and this study showed that global MAEs can also be very long; thus both local and global levels require parallel mechanisms with a range of time constants.

Because the poles were of constant distal size in the simulation (in meters), their proximal angular size varied in the display in continuous fashion, from closest to farthest, because the poles were seen in perspective view.

J. W. Forrester, Industrial Dynamics (Pegasus, 1961).

J. W. Forrester, Principles of Systems (Pegasus, 1968).

J. D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (McGraw-Hill, 2000).

A. Grunewald, “A model of transparent motion and non-transparent motion aftereffects,” in Proceedings of the 8th Conference on Advanced Neural Information Processing Systems (1996), Vol. 8, pp. 837-843.

Adaptation speeds used in the main study ranged from 50to400 m/s, which corresponded to 112.5-900 mph, respectively. While these speeds were excessive relative to highway speeds, our altitude of 5 m made the global optical flow rate (e.g., 20 eyeheights/s) comparable to that encountered at highway speeds (e.g., 45 mph) when individuals travel sitting in a car at an altitude of about 1 m. To control for this, we had four observers, at an altitude of 1 m, adapt to our SRW optic flow for a duration of 2 min or 8 min, at speeds of 20 m/s(45 mph) or 40 m/s(90 mph); thus global optical flow rate was 20 or 40 eyeheights/s, respectively, as in the main study. Results: for adapt duration of 2 min, average MAE duration was 18.8 s and 22.6 s for the 20 m/s and 40 m/s adapt speeds, respectively; for adapt duration of 8 min, average MAE duration was 39.8 s and 52.3 s for the 20 m/s and 40 m/s adapt speeds, respectively. Thus, our results from the main study generalize to more terrestrial speeds typically encountered in the real world.

W. H. Warren, Jr., The State of Flow (MIT, 1998).

W. D. Ross, The Works of Aristotle. Vol. 3, Parva Naturalia De Somniis. Transl. J. I. Beare (Clarendon, 1931).

G. Mather, F. Verstraten, and S. Anstis, The Motion Aftereffect: a Modern Perspective (MIT, 1998).

In a control experiment, four observers viewed our SRW optic flow display and a display showing a moving spiral pattern (both displays had the same dimensions, similar to our optic flow display in the main experiment). Five trials were collected for each display, presented in random order. Observers rated each display on a scale of 0 to 10, with 0 indicating no sense of self-motion and 10 indicating a very strong sense of self-motion. Average rating of our optic flow display was 8 (S.E.=0.4); average rating of the spiral display was 2 (S.E.=0.5). Our optic flow display generates a much greater sense of self-motion than a spiral display.

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Figures (8)

Fig. 1
Fig. 1

Picture of the visual display showing a simulated real-world scene. In the study, the sky was light blue and the ground plane a homogeneous gray.

Fig. 2
Fig. 2

Results of Experiment 1. MAE duration for different durations of adaptation. Each data point is a mean of five observers. Error bars depict plus and minus one standard error of the mean.

Fig. 3
Fig. 3

Results of Experiment 2. MAE duration for different global optical flow rates (upper panel) and for different optical edge rates (lower panel). Each data point is a mean of six observers. Error bars depict plus and minus one standard error of the mean.

Fig. 4
Fig. 4

Schematic of an automatic gain-control model derived from Fig. 2 of van de Grind et al. [12] and from Fig. 3 of van de Grind et al. [11]. This model is simplified by having only two opponent motion-direction channels, an “up” channel and a “down” channel, and therefore two leaky integrators; the up channel is the one being adapted. A lowered gain in the adapted channel will give it a lower output during testing relative to the nonadapted channel, and the nonadapted channel will be most active, producing an illusion of motion (MAE). The MAE ends when the difference between the output of the two channels becomes less than the perceptual threshold criterion θ.

Fig. 5
Fig. 5

System dynamics representation of the van de Grind et al. [11, 12] MAE model. Rectangles (stocks) represent integration, solid arrows (flows) represent rates of change or derivatives, dashed arrows represent information connections and feedback, and circles represent variables, constants, or expressions. Information processing flows from left to right. The two solid thick horizontal arrows represent signals in up and down motion-direction channels, respectively. x a and x t are the adaptation stimulus and test stimulus, respectively; w is a weighting constant. Two stocks in the middle of the diagram represent leaky integrators, one integrator for the up channel (“Up Leaky Integrato”) and one integrator for the down channel (“Down Leaky Integrator”). The gain in each channel is denoted by g. k is the inverse of the time constant of the negative feedback loop (e.g., “ k * ULI ”) on each leaky integrator. Computations performed in the simulation are shown above or below their respective icons.

Fig. 6
Fig. 6

Estimated empirical MAE durations for different adaptation durations taken from Bowd et al. [19] and simulated MAE durations computed from the van de Grind et al. model (see Fig. 5; with w = 0.6 , x a = 10 , x t = 1.4 , and θ = 0.7 , and τ = 20 and k = 0.05 , or τ = 40 and k = 0.025 ), and computed from the double RC-circuit mechanism model ( τ 1 = 30 , k 1 = 0.033 , τ 2 = 200 , k 2 = 0.005 , w = 0.125 , x a = 10 , x t = 1.4 , and θ = 0.7 ) and the triple RC-circuit mechanism model (with τ 1 = 30 , k 1 = 0.033 , τ 2 = 100 , k 2 = 0.01 , τ 3 = 800 , k 3 = 0.00125 , w = 0.098 , x a = 10 , x t = 1.4 , and θ = 0.7 ).

Fig. 7
Fig. 7

System dynamics representation of the SRW optic flow MAE model, a multiple-mechanism model based on the modified van de Grind et al. [11, 12] model. The two solid thick horizontal arrows represent signals in the forward and backward self-motion direction channels, respectively. The six stocks in the middle of the diagram represent leaky integrators, three integrators for the forward channel (“Forward Leaky Integrator”) and three integrators for the backward channel (“Backward Leaky Integrator”). k n is the inverse of the time constant of the negative feedback loop (e.g., “ k 1 * FLI 1 ”) on each leaky integrator, where n = 1 , 2, or 3. See caption to Fig. 5 for meaning of the other symbols.

Fig. 8
Fig. 8

Empirical SRW optic flow MAE durations for different adaptation durations taken from Fig. 2 (this paper) and simulated MAE durations for different adaptation durations computed from the triple RC-circuit mechanism model of the optic flow MAE (see Fig. 7; with τ 1 = 30 , k 1 = 0.033 , τ 2 = 100 , k 2 = 0.01 , τ 3 = 800 , k 3 = 0.00125 , w = 0.25 , x a = 10 , x t = 1.4 , and θ = 0.7 ).

Equations (30)

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channel output = y ( t s ) = x ( t s ) ( 1 + u ( t s ) ) ,
adapting charge = w x a ( 1 e k t a ) ,
decay of adapting charge = e k t ,
adapting charge = w x a k ,
testing charge = w x t k ,
decay of adapting or test charge = e k t s ,
adapting charge = w x a ( 1 e k t a ) ( e k t ) ,
testing charge = w x t ( 1 e k t ) ,
adapted channel charge = u u ( t s ) = [ w x a ( 1 e k t a ) ( e k t ) ] + [ w x t ( 1 e k t ) ] .
nonadapted channel charge = u d ( t s ) = w x t ( 1 e k t ) .
adapted channel charge = u u = i = 1 n [ w x a ( 1 e k i t a ) ( e k i t ) + w x t ( 1 e k i t ) ] ,
nonadapted channel charge = u d = i = 1 n [ w x t ( 1 e k i t ) ] ,
d ULI d t = k w x a k ULI , ULI ( 0 ) = 0
d ULI d t = k ( w x a ULI )
d ULI ( w x a ULI ) = k d t
d ULI ( w x a ULI ) = k d t
ln w x a ULI = k t + c 1
ln w x a ULI = k t c 1
e ln w x a ULI = e k t c 1
w x a ULI = e k t e c 1
let C = e c 1 .
w x a ULI = C e k t
w x a ULI = C e k t
ULI = C e k t w x a
ULI = w x a C e k t
0 = w x a C e k ( 0 )
0 = w x a C
C = w x a
ULI = w x a w x a e k t
ULI = w x a ( 1 e k t ) , which is the expression for the RC - circuit response .

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