Abstract

The optic flow arising in the eyes of an observer during self-motion is influenced by the occurrence of eye movements. The determination of heading during eye movements may be based on the pattern of retinal image motion (the retinal flow) or on an additional use of an extraretinal eye-movement signal. Previous research has presented support for either of these hypotheses, depending on the movement geometry and the layout of the visual scene. A special situation in which all previous studies unequivocally have agreed that an extraretinal signal is required occurs when the visual scene consists of a single frontoparallel plane. In this situation eye movements shift the center of expansion on the retina to a location that does not correspond to the direction of self-movement. Without extraretinal input, human observers confuse the center of expansion with their heading and show a systematical heading estimation error. We reexamined and further investigated this situation. We presented retinal flow stimuli on a large projection screen in the absence of extraretinal input and varied stimulus size, presentation duration, and orientation of the plane. In contrast to previous studies we found that in the case of a perpendicular approach toward the plane, heading judgments can be accurate. Accurate judgments were observed when the field of view was large (90°×90°) and the stimulus duration was short (⩽0.5 s). For a small field of view or a prolonged stimulus presentation, a systematic and previously described error appeared that is related to the radial structure of the flow field and the location of the center of expansion. An oblique approach toward the plane results in an ambiguous flow field with two mathematically possible solutions for heading. In this situation, when the stimulus duration was short, subjects reported a perceived heading midway between these two solutions. For longer flow sequences, subjects again chose the center of expansion. Our results suggest a dynamical change in the analysis or interpretation of retinal flow during heading perception.

© 1999 Optical Society of America

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References

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  26. J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psych. Gen. 113, 198–216 (1984).
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  27. D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
    [CrossRef] [PubMed]
  28. W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
    [CrossRef] [PubMed]
  29. I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
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  30. D. Regan, K. I. Beverley, “How do we avoid confounding the direction we are looking and the direction we are moving?” Science 215, 194–196 (1982).
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  31. A. V. van den Berg, “Judgements of heading,” Vision Res. 36, 2337–2350 (1996).
    [CrossRef] [PubMed]
  32. T. Haarmeier, M. Thier, P. ans Repnow, D. Petersen, “False perception of motion in a patient who cannot compensate for eye movements,” Nature (London) 389, 849–852 (1997).
    [CrossRef]
  33. A. H. Wertheim, “Retinal and extraretinal information in movement perception: how to invert the Filehne illusion,” Perception 16, 299–308 (1987).
    [CrossRef] [PubMed]
  34. D. Solomon, B. Cohen, “Stabilization of gaze during circular locomotion in light. I. Compensatory head and eye nystagmus in the running monkey,” J. Neurophysiol. 67, 1146–1157 (1992).
    [PubMed]
  35. M. F. Land, “Predictable eye-head coordination during driving,” Nature (London) 359, 318–320 (1992).
    [CrossRef]
  36. M. Lappe, M. Pekel, K.-P. Hoffmann, “Optokinetic eye movements elicited by radial optic flow in the macaque monkey,” J. Neurophysiol. 79, 1461–1480 (1998).
    [PubMed]
  37. T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
    [CrossRef] [PubMed]

1999 (1)

T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
[CrossRef] [PubMed]

1998 (3)

A. Grigo, M. Lappe, “Interaction of stereo vision and optic flow processing revealed by an illusory stimulus,” Vision Res. 38, 281–290 (1998).
[CrossRef] [PubMed]

S. F. T. te Pas, A. M. L. Kappers, J. J. Koenderink, “Locating the singular point in first-order optical flow fields,” J. Exp. Psychol. Hum. Percept. Perform. 24, 1415–1430 (1998).
[CrossRef]

M. Lappe, M. Pekel, K.-P. Hoffmann, “Optokinetic eye movements elicited by radial optic flow in the macaque monkey,” J. Neurophysiol. 79, 1461–1480 (1998).
[PubMed]

1997 (2)

T. Haarmeier, M. Thier, P. ans Repnow, D. Petersen, “False perception of motion in a patient who cannot compensate for eye movements,” Nature (London) 389, 849–852 (1997).
[CrossRef]

L. S. Stone, J. A. Perrone, “Human heading estimation during visually simulated curvilinear motion,” Vision Res. 37, 573–590 (1997).
[CrossRef] [PubMed]

1996 (3)

D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
[CrossRef] [PubMed]

A. V. van den Berg, “Judgements of heading,” Vision Res. 36, 2337–2350 (1996).
[CrossRef] [PubMed]

M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
[CrossRef] [PubMed]

1995 (1)

T. S. Meese, M. G. Harris, T. C. A. Freeman, “Speed gradients and the perception of surface slant: analysis is two-dimensional not one-dimensional,” Vision Res. 35, 2879–2888 (1995).
[CrossRef] [PubMed]

1994 (4)

A. V. van den Berg, E. Brenner, “Humans combine the optic flow with static depth cues for robust perception of heading,” Vision Res. 34, 2153–2167 (1994).
[CrossRef] [PubMed]

A. V. van den Berg, E. Brenner, “Why two eyes are better than one for judgements of heading,” Nature (London) 371, 700–702 (1994).
[CrossRef]

C. S. Royden, J. A. Crowell, M. S. Banks, “Estimating heading during eye movements,” Vision Res. 34, 3197–3214 (1994).
[CrossRef] [PubMed]

C. S. Royden, “Analysis of misperceived observer motion during simulated eye rotations,” Vision Res. 34, 3215–3222 (1994).
[CrossRef] [PubMed]

1993 (1)

A. V. van den Berg, “Perception of heading,” Nature (London) 365, 497–498 (1993).
[CrossRef]

1992 (3)

C. S. Royden, M. S. Banks, J. A. Crowell, “The perception of heading during eye movements,” Nature (London) 360, 583–585 (1992).
[CrossRef]

D. Solomon, B. Cohen, “Stabilization of gaze during circular locomotion in light. I. Compensatory head and eye nystagmus in the running monkey,” J. Neurophysiol. 67, 1146–1157 (1992).
[PubMed]

M. F. Land, “Predictable eye-head coordination during driving,” Nature (London) 359, 318–320 (1992).
[CrossRef]

1991 (1)

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
[CrossRef] [PubMed]

1990 (2)

J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

W. H. Warren, D. J. Hannon, “Eye movements and optical flow,” J. Opt. Soc. Am. A 7, 160–169 (1990).
[CrossRef] [PubMed]

1988 (1)

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 14, 646–660 (1988).
[CrossRef] [PubMed]

1987 (2)

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[CrossRef] [PubMed]

A. H. Wertheim, “Retinal and extraretinal information in movement perception: how to invert the Filehne illusion,” Perception 16, 299–308 (1987).
[CrossRef] [PubMed]

1985 (2)

J. H. Rieger, D. T. Lawton, “Processing differential image motion,” J. Opt. Soc. Am. A 2, 354–360 (1985).
[CrossRef] [PubMed]

J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3-D rotations,” Biol. Cybern. 52, 377–381 (1985).
[CrossRef] [PubMed]

1984 (2)

H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. R. Soc. London, Ser. B 223, 165–175 (1984).
[CrossRef]

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psych. Gen. 113, 198–216 (1984).
[CrossRef]

1982 (1)

D. Regan, 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]

1981 (1)

1980 (1)

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

1976 (1)

1975 (1)

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

1973 (1)

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[CrossRef] [PubMed]

ans Repnow, P.

T. Haarmeier, M. Thier, P. ans Repnow, D. Petersen, “False perception of motion in a patient who cannot compensate for eye movements,” Nature (London) 389, 849–852 (1997).
[CrossRef]

Backus, B. T.

M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
[CrossRef] [PubMed]

Banks, M. S.

M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
[CrossRef] [PubMed]

C. S. Royden, J. A. Crowell, M. S. Banks, “Estimating heading during eye movements,” Vision Res. 34, 3197–3214 (1994).
[CrossRef] [PubMed]

C. S. Royden, M. S. Banks, J. A. Crowell, “The perception of heading during eye movements,” Nature (London) 360, 583–585 (1992).
[CrossRef]

J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

Beverley, K. I.

D. Regan, 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]

Blackwell, A. W.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
[CrossRef] [PubMed]

Blake, A.

D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
[CrossRef] [PubMed]

Brenner, E.

A. V. van den Berg, E. Brenner, “Why two eyes are better than one for judgements of heading,” Nature (London) 371, 700–702 (1994).
[CrossRef]

A. V. van den Berg, E. Brenner, “Humans combine the optic flow with static depth cues for robust perception of heading,” Vision Res. 34, 2153–2167 (1994).
[CrossRef] [PubMed]

Buckley, D.

D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
[CrossRef] [PubMed]

Büscher, A.

T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
[CrossRef] [PubMed]

Cohen, B.

D. Solomon, B. Cohen, “Stabilization of gaze during circular locomotion in light. I. Compensatory head and eye nystagmus in the running monkey,” J. Neurophysiol. 67, 1146–1157 (1992).
[PubMed]

Crowell, J. A.

M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
[CrossRef] [PubMed]

C. S. Royden, J. A. Crowell, M. S. Banks, “Estimating heading during eye movements,” Vision Res. 34, 3197–3214 (1994).
[CrossRef] [PubMed]

C. S. Royden, M. S. Banks, J. A. Crowell, “The perception of heading during eye movements,” Nature (London) 360, 583–585 (1992).
[CrossRef]

J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

Cumming, R. W.

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[CrossRef] [PubMed]

Cutting, J.

J. Cutting, Perception with an Eye for Motion (Massachusetts Institute of Technology, Cambridge, Mass., 1986).

Cutting, J. E.

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psych. Gen. 113, 198–216 (1984).
[CrossRef]

Ehrlich, S. M.

M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
[CrossRef] [PubMed]

Freeman, T. C. A.

T. S. Meese, M. G. Harris, T. C. A. Freeman, “Speed gradients and the perception of surface slant: analysis is two-dimensional not one-dimensional,” Vision Res. 35, 2879–2888 (1995).
[CrossRef] [PubMed]

Frisby, J. P.

D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
[CrossRef] [PubMed]

Gibson, J. J.

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

J. J. Gibson, The Senses Considered As Perceptual Systems (Houghton Mifflin, Boston, Mass., 1966).

Grigo, A.

A. Grigo, M. Lappe, “Interaction of stereo vision and optic flow processing revealed by an illusory stimulus,” Vision Res. 38, 281–290 (1998).
[CrossRef] [PubMed]

Haarmeier, T.

T. Haarmeier, M. Thier, P. ans Repnow, D. Petersen, “False perception of motion in a patient who cannot compensate for eye movements,” Nature (London) 389, 849–852 (1997).
[CrossRef]

Hannon, D. J.

Harris, M. G.

T. S. Meese, M. G. Harris, T. C. A. Freeman, “Speed gradients and the perception of surface slant: analysis is two-dimensional not one-dimensional,” Vision Res. 35, 2879–2888 (1995).
[CrossRef] [PubMed]

Hoffmann, K.-P.

T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
[CrossRef] [PubMed]

M. Lappe, M. Pekel, K.-P. Hoffmann, “Optokinetic eye movements elicited by radial optic flow in the macaque monkey,” J. Neurophysiol. 79, 1461–1480 (1998).
[PubMed]

Johnston, I. R.

I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
[CrossRef] [PubMed]

Kalish, M.

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 14, 646–660 (1988).
[CrossRef] [PubMed]

Kappers, A. M. L.

S. F. T. te Pas, A. M. L. Kappers, J. J. Koenderink, “Locating the singular point in first-order optical flow fields,” J. Exp. Psychol. Hum. Percept. Perform. 24, 1415–1430 (1998).
[CrossRef]

Koenderink, J. J.

S. F. T. te Pas, A. M. L. Kappers, J. J. Koenderink, “Locating the singular point in first-order optical flow fields,” J. Exp. Psychol. Hum. Percept. Perform. 24, 1415–1430 (1998).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Exterospecific component of the motion parallax field,” J. Opt. Soc. Am. 71, 953–957 (1981).
[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]

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

Land, M. F.

M. F. Land, “Predictable eye-head coordination during driving,” Nature (London) 359, 318–320 (1992).
[CrossRef]

Lappe, M.

T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
[CrossRef] [PubMed]

M. Lappe, M. Pekel, K.-P. Hoffmann, “Optokinetic eye movements elicited by radial optic flow in the macaque monkey,” J. Neurophysiol. 79, 1461–1480 (1998).
[PubMed]

A. Grigo, M. Lappe, “Interaction of stereo vision and optic flow processing revealed by an illusory stimulus,” Vision Res. 38, 281–290 (1998).
[CrossRef] [PubMed]

Lawton, D. T.

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, “The visual ambiguity of a moving plane,” Proc. R. Soc. London, Ser. B 223, 165–175 (1984).
[CrossRef]

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

Meese, T. S.

T. S. Meese, M. G. Harris, T. C. A. Freeman, “Speed gradients and the perception of surface slant: analysis is two-dimensional not one-dimensional,” Vision Res. 35, 2879–2888 (1995).
[CrossRef] [PubMed]

Mestre, D. R.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
[CrossRef] [PubMed]

Millard, R. T.

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psych. Gen. 113, 198–216 (1984).
[CrossRef]

Morris, M. W.

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
[CrossRef] [PubMed]

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 14, 646–660 (1988).
[CrossRef] [PubMed]

Niemann, T.

T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
[CrossRef] [PubMed]

Pekel, M.

M. Lappe, M. Pekel, K.-P. Hoffmann, “Optokinetic eye movements elicited by radial optic flow in the macaque monkey,” J. Neurophysiol. 79, 1461–1480 (1998).
[PubMed]

Perrone, J. A.

L. S. Stone, J. A. Perrone, “Human heading estimation during visually simulated curvilinear motion,” Vision Res. 37, 573–590 (1997).
[CrossRef] [PubMed]

Petersen, D.

T. Haarmeier, M. Thier, P. ans Repnow, D. Petersen, “False perception of motion in a patient who cannot compensate for eye movements,” Nature (London) 389, 849–852 (1997).
[CrossRef]

Prazdny, K.

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

Regan, D.

D. Regan, 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.

J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3-D rotations,” Biol. Cybern. 52, 377–381 (1985).
[CrossRef] [PubMed]

J. H. Rieger, D. T. Lawton, “Processing differential image motion,” J. Opt. Soc. Am. A 2, 354–360 (1985).
[CrossRef] [PubMed]

Royden, C. S.

C. S. Royden, J. A. Crowell, M. S. Banks, “Estimating heading during eye movements,” Vision Res. 34, 3197–3214 (1994).
[CrossRef] [PubMed]

C. S. Royden, “Analysis of misperceived observer motion during simulated eye rotations,” Vision Res. 34, 3215–3222 (1994).
[CrossRef] [PubMed]

C. S. Royden, M. S. Banks, J. A. Crowell, “The perception of heading during eye movements,” Nature (London) 360, 583–585 (1992).
[CrossRef]

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Sekuler, A. B.

J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

Solomon, D.

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J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

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J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
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W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
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A. H. Wertheim, “Retinal and extraretinal information in movement perception: how to invert the Filehne illusion,” Perception 16, 299–308 (1987).
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I. R. Johnston, G. R. White, R. W. Cumming, “The role of optical expansion patterns in locomotor control,” Am. J. Psychol. 86, 311–324 (1973).
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J. J. Koenderink, A. J. van Doorn, “Facts on optic flow,” Biol. Cybern. 56, 247–254 (1987).
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J. H. Rieger, L. Toet, “Human visual navigation in the presence of 3-D rotations,” Biol. Cybern. 52, 377–381 (1985).
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Invest. Ophthalmol. Visual Sci. Suppl. (1)

J. A. Crowell, C. S. Royden, M. S. Banks, K. H. Swenson, A. B. Sekuler, “Optic flow and heading judgements,” Invest. Ophthalmol. Visual Sci. Suppl. 31, 522 (1990).

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S. F. T. te Pas, A. M. L. Kappers, J. J. Koenderink, “Locating the singular point in first-order optical flow fields,” J. Exp. Psychol. Hum. Percept. Perform. 24, 1415–1430 (1998).
[CrossRef]

W. H. Warren, D. R. Mestre, A. W. Blackwell, M. W. Morris, “Perception of circular heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 17, 28–43 (1991).
[CrossRef] [PubMed]

W. H. Warren, M. W. Morris, M. Kalish, “Perception of translational heading from optical flow,” J. Exp. Psychol. Hum. Percept. Perform. 14, 646–660 (1988).
[CrossRef] [PubMed]

J. Neurophysiol. (2)

D. Solomon, B. Cohen, “Stabilization of gaze during circular locomotion in light. I. Compensatory head and eye nystagmus in the running monkey,” J. Neurophysiol. 67, 1146–1157 (1992).
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M. F. Land, “Predictable eye-head coordination during driving,” Nature (London) 359, 318–320 (1992).
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A. V. van den Berg, E. Brenner, “Why two eyes are better than one for judgements of heading,” Nature (London) 371, 700–702 (1994).
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C. S. Royden, M. S. Banks, J. A. Crowell, “The perception of heading during eye movements,” Nature (London) 360, 583–585 (1992).
[CrossRef]

A. V. van den Berg, “Perception of heading,” Nature (London) 365, 497–498 (1993).
[CrossRef]

Opt. Acta (1)

J. J. Koenderink, A. J. van Doorn, “Invariant properties of the motion parallax field due to the movement of rigid bodies relative to an observer,” Opt. Acta 22, 773–791 (1975).
[CrossRef]

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A. H. Wertheim, “Retinal and extraretinal information in movement perception: how to invert the Filehne illusion,” Perception 16, 299–308 (1987).
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Vision Res. (10)

A. V. van den Berg, “Judgements of heading,” Vision Res. 36, 2337–2350 (1996).
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T. Niemann, M. Lappe, A. Büscher, K.-P. Hoffmann, “Ocular responses to radial optic flow and single accelerated targets in humans,” Vision Res. 39, 1359–1371 (1999).
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C. S. Royden, “Analysis of misperceived observer motion during simulated eye rotations,” Vision Res. 34, 3215–3222 (1994).
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L. S. Stone, J. A. Perrone, “Human heading estimation during visually simulated curvilinear motion,” Vision Res. 37, 573–590 (1997).
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D. Buckley, J. P. Frisby, A. Blake, “Does the human visual system implement an ideal observer theory of slant from texture,” Vision Res. 36, 1163–1176 (1996).
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C. S. Royden, J. A. Crowell, M. S. Banks, “Estimating heading during eye movements,” Vision Res. 34, 3197–3214 (1994).
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M. S. Banks, S. M. Ehrlich, B. T. Backus, J. A. Crowell, “Estimating heading during real and simulated eye movements,” Vision Res. 36, 431–443 (1996).
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J. Cutting, Perception with an Eye for Motion (Massachusetts Institute of Technology, Cambridge, Mass., 1986).

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

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Figures (11)

Fig. 1
Fig. 1

Retinal flow patterns resulting from different observer motions with respect to a frontoparallel plane. Triangles, heading; circles, direction of gaze; arrows, motions of points as they are projected on the screen. (A) Retinal flow caused by a pure forward translation along the plane normal. The flow consists of a radial motion pattern with the center of expansion located in the direction of self-movement. (B) Retinal flow pattern caused by an eye rotation. The magnitude of this eye rotation is such that gaze follows the motion of the point on the plane that is projected on the fovea. (C) Forward motion during a smooth pursuit eye movement (A+B) results in an approximately radial flow pattern with its center in the direction of gaze. This motion pattern somewhat resembles the motion seen during pure forward translation in the direction of gaze. (D) Retinal flow caused by a linear forward motion when the direction of gaze coincides with the direction of translation. (E) The differences between the flow patterns in (C) and (D). They are largest in the periphery of the field of view (here 90°×90°).

Fig. 2
Fig. 2

Simulated movement geometry seen from the top. The observer moves toward a frontoparallel plane under a certain angle φ with respect to the plane normal n. During the movement gaze is directed to a point fixed on the plane. During the time t the observer moves with speed v to his final position, which is at a distance D from the plane. At the end of the movement the time to collision is τ and the retinal heading angle is νend.

Fig. 3
Fig. 3

Overview of the simulated movement in experiments 1 to 5. The observer moves with speed v along the plane normal. After time t he reaches his final position. To fixate a point on the plane during the movement, the observer’s eyes have to rotate about an angle ε. At the end of the movement the angle between the gaze direction and the direction of self-motion, the retinal heading angle ν, can take five different values, depending on the location of the fixation target on the plane.

Fig. 4
Fig. 4

Results of experiment 1. The perceived retinal heading angle is plotted against the simulated retinal heading angle, which was 0°, ±3°, or ±6°. Circles, mean responses of six subjects averaged over ten repetitions each; vertical lines, standard deviations; horizontal dashed line, direction of gaze, i.e., the location of the fixation point, which was always at 0° at the center of the screen. Correct answers must lie on the diagonal (dotted line). The regression line deviates only slightly from the diagonal, which means that heading estimation is quite accurate.

Fig. 5
Fig. 5

Responses of individual subjects in experiment 1. Individual overestimation and underestimation of heading can be observed, which in all cases is roughly proportional to the simulated retinal heading angle. Only one subject (FB) consistently perceived the fixation point as his direction of self-motion.

Fig. 6
Fig. 6

Mean results for seven subjects for the heading estimation task with high rotation rates. The simulated retinal heading angle was as high as 20°. Nevertheless, subjects on average estimated heading correctly.

Fig. 7
Fig. 7

Results of experiment 3. Shown is the mean perceived heading of nine subjects for trials with a presentation duration of 0.4 s (top) and 3.2 s (bottom). Vertical lines, standard deviations. The deviation of the regression line from the diagonal is much larger for the long presentation time, indicating a decrease in heading estimation performance.

Fig. 8
Fig. 8

Results of experiment 4. The three panels present the three angular differences Δν between the initial and the final retinal heading angles. The final heading angles are 0° and ±6° in all figures. The initial retinal heading angles are accordingly different. Within each figure, the mean results of five subjects for different stimulus durations are shown together with their standard deviations. For less confusion the different means are slightly separated horizontally from one another. Overall, a significant bias toward the direction of gaze can be observed for prolonged stimulus durations.

Fig. 9
Fig. 9

Results of experiment 5, showing the mean perceived heading of four subjects. Vertical lines give the standard deviations. Trials had a total duration of 3.2 s, but the distribution of dots was randomly changed every 0.4 s. Each redistribution resulted in an interruption of the continuous flow but did not change the simulated motion. The deviation of the regression line from the diagonal is much smaller than for a single long presentation (compare Fig. 7).

Fig. 10
Fig. 10

Illustration of the experimental setup in experiment 6. The observer approaches the plane under an angle φ with respect to the plane normal n. During the movement the observer fixates a point to the right or left of the plane normal. This results in a retinal heading angle ν with respect to his direction of gaze.

Fig. 11
Fig. 11

Results of experiment 6. Mean responses of seven subjects are presented for different path angles φ. Dotted diagonal, simulated heading angle; dashed-dotted line parallel to the diagonal, direction of the plane normal. Whereas for perpendicular approaches (φ=0) the subjects’ judgments are correct, for φ0 a systematic offset toward the plane normal can be observed. Note that for φ=20° and for φ=-20° only four data points are available. Because we wanted the magnitude of the retinal heading angle ν to remain below 30°, these conditions could not include trials in which the fixation point deviated by -20° or by 20°, respectively, from the plane normal.

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