Abstract

Retinal images evolve continuously over time owing to self-motions and to movements in the world. Such an evolving image, also known as optic flow, if arising from natural scenes can be locally decomposed in a Bayesian manner into several elementary components, including translation, expansion, and rotation. To take advantage of this decomposition, the brain has neurons tuned to these types of motions. However, these neurons typically have large receptive fields, often spanning tens of degrees of visual angle. Can neurons such as these compute elementary optic-flow components sufficiently locally to achieve a reasonable decomposition? We show that human discrimination of angular velocity is local. Local discrimination of angular velocity requires an accurate estimation of the center of rotation within the optic-flow field. Inaccuracies in estimating the center of rotation result in a predictable systematic error when one is estimating local angular velocity. Our results show that humans make the predicted errors. We discuss how the brain might estimate the elementary components of the optic flow locally by using large receptive fields.

© 2003 Optical Society of America

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References

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  7. P. J. Bex, W. Makous, “Radial motion looks faster,” Vision Res. 37, 3399–3405 (1997).
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  16. A. Tanaka, H. Saito, “Analysis of motion of the visual field by direction, expansion/contraction, and rotation cells clustered in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 626–641 (1989).
  17. A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).
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  24. J. F. Barraza, N. M. Grzywacz, “Fine discrimination of angular velocity despite poor localization of center of rotation,” presented at Vision Sciences Society 2nd Annual Meeting, Sarasota, Florida, May 10–15, 2002.
  25. M. E. Goldberg, H. M. Eggers, P. Gouras. “The ocular motor system,” in Principles of Neural Science, E. R. Kandel, J. H. Schwartz, T. M. Jessell, eds. (Appleton & Lange, Norwalk, Conn., 1991), pp. 660–677.
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  28. D. Ascher, N. M. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427–3434 (2000).
    [CrossRef] [PubMed]
  29. S. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995).
    [PubMed]
  30. E. Simoncelli, D. Heeger, “A model of neural responses in visual area MT,” Vision Res. 38, 743–761 (1998).
    [CrossRef] [PubMed]
  31. N. M. Grzywacz, A. L. Yuille, “A model for the estimate of local image velocity by cells in the visual cortex,” Proc. R. Soc. London Ser. B 239, 129–161 (1990).
    [CrossRef]
  32. J. A. Perrone, “Model for the computation of self-motion in biological systems,” J. Opt. Soc. Am. A9, 177–194 (1992).
    [CrossRef]
  33. B. P. Dyre, G. J. Andersen, “Image velocity and perception of heading,” J. Exp. Psychol. Hum. Percept. Perform. 23, 546–565 (1997).
    [CrossRef] [PubMed]
  34. J. A. Perrone, A. Thiele, “Speed skills: measuring the visual speed analyzing properties of primate MT neurons,” Nat. Neurosci. 4, 526–532 (2001).
    [PubMed]
  35. S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
    [CrossRef] [PubMed]
  36. D. C. Hoagling, F. Mosteller, J. W. Tukey, “Introduction to more refined estimators,” in Understanding Robust and Exploratory Data Analysis, D. C. Hoagling, F. Mosteller, J. W. Tukey, eds. (Wiley, New York, 1983), pp. 283–296.
  37. A. L. Yuille, N. M. Grzywacz, “A mathematical analysis of the motion coherence theory,” Int. J. Comput. Vision 3, 155–175 (1989).
    [CrossRef]

2002 (2)

J. F. Barraza, N. M. Grzywacz, “Measurement of angular velocity in the perception of rotation,” Vision Res. 42, 2457–2462 (2002).
[CrossRef] [PubMed]

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

2001 (1)

J. A. Perrone, A. Thiele, “Speed skills: measuring the visual speed analyzing properties of primate MT neurons,” Nat. Neurosci. 4, 526–532 (2001).
[PubMed]

2000 (1)

D. Ascher, N. M. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427–3434 (2000).
[CrossRef] [PubMed]

1999 (2)

A. Johnston, C. P. Benton, N. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination using the method of single stimuli,” Vision Res. 39, 3849–3854 (1999).
[CrossRef]

C. W. G. Clifford, S. A. Beardsley, L. M. Vaina, “The perception and discrimination of speed in complex motion,” Vision Res. 39, 2213–2227 (1999).
[CrossRef] [PubMed]

1998 (4)

B. J. Geesaman, N. Qian, “The effect of complex motion pattern on speed perception,” Vision Res. 38, 1223–1231 (1998).
[CrossRef] [PubMed]

E. Simoncelli, D. Heeger, “A model of neural responses in visual area MT,” Vision Res. 38, 743–761 (1998).
[CrossRef] [PubMed]

D. R. W. Wylie, W. F. Bischof, B. J. Frost, “Common reference frame for neural coding of translational and rotational optic flow,” Nature 392, 278–282 (1998).
[CrossRef] [PubMed]

P. R. Schrater, E. P. Simoncelli, “Local velocity representation: evidence from motion adaptation,” Vision Res. 38, 3899–3912 (1998).
[CrossRef]

1997 (3)

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

B. P. Dyre, G. J. Andersen, “Image velocity and perception of heading,” J. Exp. Psychol. Hum. Percept. Perform. 23, 546–565 (1997).
[CrossRef] [PubMed]

P. J. Bex, W. Makous, “Radial motion looks faster,” Vision Res. 37, 3399–3405 (1997).
[CrossRef]

1996 (2)

B. J. Geesaman, N. Qian, “A novel speed illusion involving expansion and rotation patterns,” Vision Res. 36, 3281–3292 (1996).
[CrossRef] [PubMed]

S. F. te Pas, A. M. L. Kappers, J. J. Koenderink, “Detection of first-order structure in optic flow fields,” Vision Res. 36, 259–270 (1996).
[CrossRef] [PubMed]

1995 (2)

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. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995).
[PubMed]

1994 (1)

M. S. A. Graziano, R. A. Andersen, R. J. Snowden, “Tuning of MST neurons to spiral motions,” J. Neurosci. 14, 54–67 (1994).
[PubMed]

1992 (3)

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

J. A. Perrone, “Model for the computation of self-motion in biological systems,” J. Opt. Soc. Am. A9, 177–194 (1992).
[CrossRef]

T. A. C. Freeman, M. G. Harris, “Human sensitivity to expanding and rotating motion: effects of complementary masking and directional structure,” Vision Res. 32, 81–87 (1992).
[CrossRef] [PubMed]

1991 (2)

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. I. A continuum of response selectivity to large-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. II. Mechanisms of response selectivity revealed by small-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

1990 (1)

N. M. Grzywacz, A. L. Yuille, “A model for the estimate of local image velocity by cells in the visual cortex,” Proc. R. Soc. London Ser. B 239, 129–161 (1990).
[CrossRef]

1989 (3)

A. L. Yuille, N. M. Grzywacz, “A mathematical analysis of the motion coherence theory,” Int. J. Comput. Vision 3, 155–175 (1989).
[CrossRef]

A. Tanaka, H. Saito, “Analysis of motion of the visual field by direction, expansion/contraction, and rotation cells clustered in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 626–641 (1989).

A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).

1986 (1)

A. Movshon, E. Adelson, M. Gizzi, W. Newsome, “The analysis of moving visual patterns,” Exp. Brain Res. 11, 117–152 (1986).
[CrossRef]

1985 (1)

1983 (1)

J. H. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I: selectivity for stimulus direction, speed, and orientation,” J. Neurophys. 49, 1127–1147 (1983).

1981 (1)

S. P. McKee, “A local mechanism for differential velocity detection,” Vision Res. 21, 491–500 (1981).
[CrossRef] [PubMed]

1976 (1)

Adelson, E.

A. Movshon, E. Adelson, M. Gizzi, W. Newsome, “The analysis of moving visual patterns,” Exp. Brain Res. 11, 117–152 (1986).
[CrossRef]

Andersen, G. J.

B. P. Dyre, G. J. Andersen, “Image velocity and perception of heading,” J. Exp. Psychol. Hum. Percept. Perform. 23, 546–565 (1997).
[CrossRef] [PubMed]

Andersen, R. A.

M. S. A. Graziano, R. A. Andersen, R. J. Snowden, “Tuning of MST neurons to spiral motions,” J. Neurosci. 14, 54–67 (1994).
[PubMed]

Ascher, D.

D. Ascher, N. M. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427–3434 (2000).
[CrossRef] [PubMed]

Barraza, J. F.

J. F. Barraza, N. M. Grzywacz, “Measurement of angular velocity in the perception of rotation,” Vision Res. 42, 2457–2462 (2002).
[CrossRef] [PubMed]

J. F. Barraza, N. M. Grzywacz, “Fine discrimination of angular velocity despite poor localization of center of rotation,” presented at Vision Sciences Society 2nd Annual Meeting, Sarasota, Florida, May 10–15, 2002.

Beardsley, S. A.

C. W. G. Clifford, S. A. Beardsley, L. M. Vaina, “The perception and discrimination of speed in complex motion,” Vision Res. 39, 2213–2227 (1999).
[CrossRef] [PubMed]

Beberley, K. J.

Benton, C. P.

A. Johnston, C. P. Benton, N. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination using the method of single stimuli,” Vision Res. 39, 3849–3854 (1999).
[CrossRef]

Bex, P. J.

P. J. Bex, W. Makous, “Radial motion looks faster,” Vision Res. 37, 3399–3405 (1997).
[CrossRef]

Bischof, W. F.

D. R. W. Wylie, W. F. Bischof, B. J. Frost, “Common reference frame for neural coding of translational and rotational optic flow,” Nature 392, 278–282 (1998).
[CrossRef] [PubMed]

Burr, D. C.

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]

Clifford, C. W. G.

C. W. G. Clifford, S. A. Beardsley, L. M. Vaina, “The perception and discrimination of speed in complex motion,” Vision Res. 39, 2213–2227 (1999).
[CrossRef] [PubMed]

Duffy, C. J.

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. I. A continuum of response selectivity to large-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. II. Mechanisms of response selectivity revealed by small-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

Dyre, B. P.

B. P. Dyre, G. J. Andersen, “Image velocity and perception of heading,” J. Exp. Psychol. Hum. Percept. Perform. 23, 546–565 (1997).
[CrossRef] [PubMed]

Egelhaaf, M.

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

Eggers, H. M.

M. E. Goldberg, H. M. Eggers, P. Gouras. “The ocular motor system,” in Principles of Neural Science, E. R. Kandel, J. H. Schwartz, T. M. Jessell, eds. (Appleton & Lange, Norwalk, Conn., 1991), pp. 660–677.

Freeman, T. A. C.

T. A. C. Freeman, M. G. Harris, “Human sensitivity to expanding and rotating motion: effects of complementary masking and directional structure,” Vision Res. 32, 81–87 (1992).
[CrossRef] [PubMed]

Frost, B. J.

D. R. W. Wylie, W. F. Bischof, B. J. Frost, “Common reference frame for neural coding of translational and rotational optic flow,” Nature 392, 278–282 (1998).
[CrossRef] [PubMed]

Fukuda, Y.

A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).

Geesaman, B. J.

B. J. Geesaman, N. Qian, “The effect of complex motion pattern on speed perception,” Vision Res. 38, 1223–1231 (1998).
[CrossRef] [PubMed]

B. J. Geesaman, N. Qian, “A novel speed illusion involving expansion and rotation patterns,” Vision Res. 36, 3281–3292 (1996).
[CrossRef] [PubMed]

Gibson, J. J.

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

Gizzi, M.

A. Movshon, E. Adelson, M. Gizzi, W. Newsome, “The analysis of moving visual patterns,” Exp. Brain Res. 11, 117–152 (1986).
[CrossRef]

Goldberg, M. E.

M. E. Goldberg, H. M. Eggers, P. Gouras. “The ocular motor system,” in Principles of Neural Science, E. R. Kandel, J. H. Schwartz, T. M. Jessell, eds. (Appleton & Lange, Norwalk, Conn., 1991), pp. 660–677.

Gouras, P.

M. E. Goldberg, H. M. Eggers, P. Gouras. “The ocular motor system,” in Principles of Neural Science, E. R. Kandel, J. H. Schwartz, T. M. Jessell, eds. (Appleton & Lange, Norwalk, Conn., 1991), pp. 660–677.

Graziano, M. S. A.

M. S. A. Graziano, R. A. Andersen, R. J. Snowden, “Tuning of MST neurons to spiral motions,” J. Neurosci. 14, 54–67 (1994).
[PubMed]

Grzywacz, N. M.

J. F. Barraza, N. M. Grzywacz, “Measurement of angular velocity in the perception of rotation,” Vision Res. 42, 2457–2462 (2002).
[CrossRef] [PubMed]

D. Ascher, N. M. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427–3434 (2000).
[CrossRef] [PubMed]

N. M. Grzywacz, A. L. Yuille, “A model for the estimate of local image velocity by cells in the visual cortex,” Proc. R. Soc. London Ser. B 239, 129–161 (1990).
[CrossRef]

A. L. Yuille, N. M. Grzywacz, “A mathematical analysis of the motion coherence theory,” Int. J. Comput. Vision 3, 155–175 (1989).
[CrossRef]

J. F. Barraza, N. M. Grzywacz, “Fine discrimination of angular velocity despite poor localization of center of rotation,” presented at Vision Sciences Society 2nd Annual Meeting, Sarasota, Florida, May 10–15, 2002.

A. L. Yuille, N. M. Grzywacz, “A theoretical framework for visual motion,” in High-Level Motion Processing—Computational, Neurobiological, and Psychophysical Perspectives, T. Watanabe, ed. (MIT Press, Cambridge, Mass., 1998), pp. 187–211.

Harris, M. G.

T. A. C. Freeman, M. G. Harris, “Human sensitivity to expanding and rotating motion: effects of complementary masking and directional structure,” Vision Res. 32, 81–87 (1992).
[CrossRef] [PubMed]

Heeger, D.

E. Simoncelli, D. Heeger, “A model of neural responses in visual area MT,” Vision Res. 38, 743–761 (1998).
[CrossRef] [PubMed]

Hoagling, D. C.

D. C. Hoagling, F. Mosteller, J. W. Tukey, “Introduction to more refined estimators,” in Understanding Robust and Exploratory Data Analysis, D. C. Hoagling, F. Mosteller, J. W. Tukey, eds. (Wiley, New York, 1983), pp. 283–296.

Johnston, A.

A. Johnston, C. P. Benton, N. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination using the method of single stimuli,” Vision Res. 39, 3849–3854 (1999).
[CrossRef]

Kappers, A. M. L.

S. F. te Pas, A. M. L. Kappers, J. J. Koenderink, “Detection of first-order structure in optic flow fields,” Vision Res. 36, 259–270 (1996).
[CrossRef] [PubMed]

Kern, R.

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

Koenderink, J. J.

S. F. te Pas, A. M. L. Kappers, J. J. Koenderink, “Detection of first-order structure in optic flow fields,” Vision Res. 36, 259–270 (1996).
[CrossRef] [PubMed]

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

Krapp, H. G.

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

Kretzberg, J.

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

Lagae, L.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Maes, H.

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Makous, W.

P. J. Bex, W. Makous, “Radial motion looks faster,” Vision Res. 37, 3399–3405 (1997).
[CrossRef]

Marcar, V. L.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

Maunsell, J. H. R.

J. H. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I: selectivity for stimulus direction, speed, and orientation,” J. Neurophys. 49, 1127–1147 (1983).

McKee, S. P.

S. P. McKee, “A local mechanism for differential velocity detection,” Vision Res. 21, 491–500 (1981).
[CrossRef] [PubMed]

Morgan, N. J.

A. Johnston, C. P. Benton, N. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination using the method of single stimuli,” Vision Res. 39, 3849–3854 (1999).
[CrossRef]

Morrone, M. C.

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]

Mosteller, F.

D. C. Hoagling, F. Mosteller, J. W. Tukey, “Introduction to more refined estimators,” in Understanding Robust and Exploratory Data Analysis, D. C. Hoagling, F. Mosteller, J. W. Tukey, eds. (Wiley, New York, 1983), pp. 283–296.

Movshon, A.

A. Movshon, E. Adelson, M. Gizzi, W. Newsome, “The analysis of moving visual patterns,” Exp. Brain Res. 11, 117–152 (1986).
[CrossRef]

Newsome, W.

A. Movshon, E. Adelson, M. Gizzi, W. Newsome, “The analysis of moving visual patterns,” Exp. Brain Res. 11, 117–152 (1986).
[CrossRef]

Nowlan, S. J.

S. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995).
[PubMed]

Orban, G. A.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Perrone, J. A.

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[PubMed]

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[CrossRef]

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B. J. Geesaman, N. Qian, “The effect of complex motion pattern on speed perception,” Vision Res. 38, 1223–1231 (1998).
[CrossRef] [PubMed]

B. J. Geesaman, N. Qian, “A novel speed illusion involving expansion and rotation patterns,” Vision Res. 36, 3281–3292 (1996).
[CrossRef] [PubMed]

Raiguel, S.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Regan, D.

Saito, H.

A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).

A. Tanaka, H. Saito, “Analysis of motion of the visual field by direction, expansion/contraction, and rotation cells clustered in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 626–641 (1989).

Schrater, P. R.

P. R. Schrater, E. P. Simoncelli, “Local velocity representation: evidence from motion adaptation,” Vision Res. 38, 3899–3912 (1998).
[CrossRef]

Sejnowski, T. J.

S. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995).
[PubMed]

Simoncelli, E.

E. Simoncelli, D. Heeger, “A model of neural responses in visual area MT,” Vision Res. 38, 743–761 (1998).
[CrossRef] [PubMed]

Simoncelli, E. P.

P. R. Schrater, E. P. Simoncelli, “Local velocity representation: evidence from motion adaptation,” Vision Res. 38, 3899–3912 (1998).
[CrossRef]

Snowden, R. J.

M. S. A. Graziano, R. A. Andersen, R. J. Snowden, “Tuning of MST neurons to spiral motions,” J. Neurosci. 14, 54–67 (1994).
[PubMed]

Tanaka, A.

A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).

A. Tanaka, H. Saito, “Analysis of motion of the visual field by direction, expansion/contraction, and rotation cells clustered in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 626–641 (1989).

te Pas, S. F.

S. F. te Pas, A. M. L. Kappers, J. J. Koenderink, “Detection of first-order structure in optic flow fields,” Vision Res. 36, 259–270 (1996).
[CrossRef] [PubMed]

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J. A. Perrone, A. Thiele, “Speed skills: measuring the visual speed analyzing properties of primate MT neurons,” Nat. Neurosci. 4, 526–532 (2001).
[PubMed]

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G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Tukey, J. W.

D. C. Hoagling, F. Mosteller, J. W. Tukey, “Introduction to more refined estimators,” in Understanding Robust and Exploratory Data Analysis, D. C. Hoagling, F. Mosteller, J. W. Tukey, eds. (Wiley, New York, 1983), pp. 283–296.

Vaina, L. M.

C. W. G. Clifford, S. A. Beardsley, L. M. Vaina, “The perception and discrimination of speed in complex motion,” Vision Res. 39, 2213–2227 (1999).
[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]

van Doorn, A. J.

Van Essen, D. C.

J. H. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I: selectivity for stimulus direction, speed, and orientation,” J. Neurophys. 49, 1127–1147 (1983).

Van Hulle, M. M.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

Verri, A.

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Warzecha, A.

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

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C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. II. Mechanisms of response selectivity revealed by small-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. I. A continuum of response selectivity to large-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

Wylie, D. R. W.

D. R. W. Wylie, W. F. Bischof, B. J. Frost, “Common reference frame for neural coding of translational and rotational optic flow,” Nature 392, 278–282 (1998).
[CrossRef] [PubMed]

Xiao, D.

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

Xiao, D. K.

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

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N. M. Grzywacz, A. L. Yuille, “A model for the estimate of local image velocity by cells in the visual cortex,” Proc. R. Soc. London Ser. B 239, 129–161 (1990).
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[CrossRef]

A. L. Yuille, N. M. Grzywacz, “A theoretical framework for visual motion,” in High-Level Motion Processing—Computational, Neurobiological, and Psychophysical Perspectives, T. Watanabe, ed. (MIT Press, Cambridge, Mass., 1998), pp. 187–211.

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A. L. Yuille, N. M. Grzywacz, “A mathematical analysis of the motion coherence theory,” Int. J. Comput. Vision 3, 155–175 (1989).
[CrossRef]

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B. P. Dyre, G. J. Andersen, “Image velocity and perception of heading,” J. Exp. Psychol. Hum. Percept. Perform. 23, 546–565 (1997).
[CrossRef] [PubMed]

J. Neurophys. (5)

J. H. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I: selectivity for stimulus direction, speed, and orientation,” J. Neurophys. 49, 1127–1147 (1983).

A. Tanaka, H. Saito, “Analysis of motion of the visual field by direction, expansion/contraction, and rotation cells clustered in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 626–641 (1989).

A. Tanaka, Y. Fukuda, H. Saito, “Underlying mechanisms of the response specificity of expansion/contraction, and rotation cells, in the dorsal part of the medial superior temporal area of the macaque monkey,” J. Neurophys. 62, 642–656 (1989).

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. I. A continuum of response selectivity to large-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

C. J. Duffy, R. H. Wurtz, “Sensitivity of MST neurons to optic flow stimuli. II. Mechanisms of response selectivity revealed by small-field stimuli,” J. Neurophys. 65, 1346–1359 (1991).

J. Neurosci. (2)

M. S. A. Graziano, R. A. Andersen, R. J. Snowden, “Tuning of MST neurons to spiral motions,” J. Neurosci. 14, 54–67 (1994).
[PubMed]

S. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995).
[PubMed]

J. Opt. Soc. Am. (2)

J. A. Perrone, “Model for the computation of self-motion in biological systems,” J. Opt. Soc. Am. A9, 177–194 (1992).
[CrossRef]

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. Opt. Soc. Am. A (1)

Nat. Neurosci. (1)

J. A. Perrone, A. Thiele, “Speed skills: measuring the visual speed analyzing properties of primate MT neurons,” Nat. Neurosci. 4, 526–532 (2001).
[PubMed]

Nature (2)

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]

D. R. W. Wylie, W. F. Bischof, B. J. Frost, “Common reference frame for neural coding of translational and rotational optic flow,” Nature 392, 278–282 (1998).
[CrossRef] [PubMed]

NeuroReport (1)

S. Raiguel, M. M. Van Hulle, D. K. Xiao, V. L. Marcar, L. Lagae, G. A. Orban, “Size and shape of receptive fields in the medial superior temporal area (MST) of the macaque,” NeuroReport 8, 2803–2800 (1997).
[CrossRef] [PubMed]

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

G. A. Orban, L. Lagae, A. Verri, S. Raiguel, D. Xiao, H. Maes, V. Torre, “First-order analysis of optical flow in monkey brain,” Proc. Natl. Acad. Sci. USA 89, 2595–2599 (1992).

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

N. M. Grzywacz, A. L. Yuille, “A model for the estimate of local image velocity by cells in the visual cortex,” Proc. R. Soc. London Ser. B 239, 129–161 (1990).
[CrossRef]

Trends Neurosci. (1)

M. Egelhaaf, R. Kern, H. G. Krapp, J. Kretzberg, A. Warzecha, “Naural encoding of behaviourally relevant visual-motion information in the fly,” Trends Neurosci. 25, 96–102 (2002).
[CrossRef] [PubMed]

Vision Res. (12)

T. A. C. Freeman, M. G. Harris, “Human sensitivity to expanding and rotating motion: effects of complementary masking and directional structure,” Vision Res. 32, 81–87 (1992).
[CrossRef] [PubMed]

S. P. McKee, “A local mechanism for differential velocity detection,” Vision Res. 21, 491–500 (1981).
[CrossRef] [PubMed]

A. Johnston, C. P. Benton, N. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination using the method of single stimuli,” Vision Res. 39, 3849–3854 (1999).
[CrossRef]

J. F. Barraza, N. M. Grzywacz, “Measurement of angular velocity in the perception of rotation,” Vision Res. 42, 2457–2462 (2002).
[CrossRef] [PubMed]

P. J. Bex, W. Makous, “Radial motion looks faster,” Vision Res. 37, 3399–3405 (1997).
[CrossRef]

B. J. Geesaman, N. Qian, “A novel speed illusion involving expansion and rotation patterns,” Vision Res. 36, 3281–3292 (1996).
[CrossRef] [PubMed]

B. J. Geesaman, N. Qian, “The effect of complex motion pattern on speed perception,” Vision Res. 38, 1223–1231 (1998).
[CrossRef] [PubMed]

C. W. G. Clifford, S. A. Beardsley, L. M. Vaina, “The perception and discrimination of speed in complex motion,” Vision Res. 39, 2213–2227 (1999).
[CrossRef] [PubMed]

S. F. te Pas, A. M. L. Kappers, J. J. Koenderink, “Detection of first-order structure in optic flow fields,” Vision Res. 36, 259–270 (1996).
[CrossRef] [PubMed]

E. Simoncelli, D. Heeger, “A model of neural responses in visual area MT,” Vision Res. 38, 743–761 (1998).
[CrossRef] [PubMed]

P. R. Schrater, E. P. Simoncelli, “Local velocity representation: evidence from motion adaptation,” Vision Res. 38, 3899–3912 (1998).
[CrossRef]

D. Ascher, N. M. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427–3434 (2000).
[CrossRef] [PubMed]

Other (5)

J. F. Barraza, N. M. Grzywacz, “Fine discrimination of angular velocity despite poor localization of center of rotation,” presented at Vision Sciences Society 2nd Annual Meeting, Sarasota, Florida, May 10–15, 2002.

M. E. Goldberg, H. M. Eggers, P. Gouras. “The ocular motor system,” in Principles of Neural Science, E. R. Kandel, J. H. Schwartz, T. M. Jessell, eds. (Appleton & Lange, Norwalk, Conn., 1991), pp. 660–677.

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

D. C. Hoagling, F. Mosteller, J. W. Tukey, “Introduction to more refined estimators,” in Understanding Robust and Exploratory Data Analysis, D. C. Hoagling, F. Mosteller, J. W. Tukey, eds. (Wiley, New York, 1983), pp. 283–296.

A. L. Yuille, N. M. Grzywacz, “A theoretical framework for visual motion,” in High-Level Motion Processing—Computational, Neurobiological, and Psychophysical Perspectives, T. Watanabe, ed. (MIT Press, Cambridge, Mass., 1998), pp. 187–211.

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Figures (9)

Fig. 1
Fig. 1

Schematics of a random-dot pattern undergoing rotation, with the center of rotation (white square) deviated from the center of the stimulus, which coincides with the fixation point (plus sign). The large dashed circle indicates the part of the stimulus covered by the mask.

Fig. 2
Fig. 2

Position estimation of the center of rotation as a function of the mask radius. The two graphs correspond to results from two subjects. Each graph shows the results for three conditions: with no training on the task and with training and either the density or the number of dots constant outside the mask. Even trained subjects could not estimate the center of rotation precisely with this task. Before training, errors were much higher for both subjects (solid circles). Finally, the errors do not increase significantly with the radius of the mask.

Fig. 3
Fig. 3

Ratio between matching (ΩM) and reference (ΩR) angular velocities as a function of the distance from the center of rotation to the fixation point. The two curves correspond to results from two subjects. The plot shows that subjects overestimate angular velocity when the center of rotation is different from the fixation point and that this effect increases with distance.

Fig. 4
Fig. 4

Comparison of perceived angular velocity across three different conditions. Condition A (diamonds and solid curve) corresponds to the center of rotation being deviated from the center of the stimulus, where the fixation point is located. Condition B (solid triangles and dashed curve) corresponds to the center of rotation being deviated from the center of the stimulus and the fixation point being located on the center of rotation. Condition C (open triangles and dotted curve) corresponds to the center of rotation being located on the center of the stimulus and the fixation point being deviated from the center. The two panels show results from two subjects.

Fig. 5
Fig. 5

Effect on the overestimation of angular velocity of masking the portion of the stimulus around the fixation point. The two panels show results from two subjects. Masking reduces the overestimation, and this effect increases with the size of the mask.

Fig. 6
Fig. 6

Schematic of how the first stage of the model works. The actual and the perceived center of rotation (CoR and CoRp, respectively) are in different positions. Consequently, the generated local velocities (νi, solid gray vectors) at positions ri are not compatible with a rotation about the perceived center of rotation. The model seeks local vectors (νi*, solid black vectors) that are as consistent as possible with the measured velocities and with a rotation about the perceived center. These vectors tend to be projections of νi onto lines perpendicular to ri.

Fig. 7
Fig. 7

The model accounts for the experiment in which the effect of mislocating the center of rotation on perceived angular velocity is studied (see Fig. 2).

Fig. 8
Fig. 8

The model accounts for the experiment in which the effect of masking the portion of the stimulus around the fixation point is studied (see Fig. 3).

Fig. 9
Fig. 9

Estimates of perceived center of rotation. (a) Distribution, for two subjects, of actual positions of the center of rotation with respect to the fixation point. The position scale corresponds to the ruler used in the experiment. In degrees, the position could take any value between 0 (the fixation point) and 10 (the border of the display). (b) Estimated position of the center of rotation, for two subjects. There is a shift of the distribution of estimated positions toward zero (fixation point) in comparison with the distribution of actual positions. (c) Bias as a function of the actual position of the center of rotation, computed as the difference between the estimated and the actual positions. The plots show, for both subjects, that in most trials the subject saw the center of rotation biased toward the fixation point. Moreover, the bias has a negative linear correlation with the distance from the fixation point.

Equations (4)

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

Ωl(ri)=argminΩ*,νi*i=1N|νi-νi*|+ki=1N|Ω*(ri)×ri-νi|,
Ω(ri)=argminΩ*i=1Nexp-i22σ2|Ω*(ri)-Ω(ri)|+λr[D(Ω*(r))]2.
Ωl(ri)=argminΩ*i=1N|Ω*(ri)×ri-νi|,
Ω=argminΩ*i-1Nexp-i22σ2|Ω*-Ωl(ri)|,

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