Abstract

We have shown previously that random dots with an interocular time delay (ITD), the time difference of the onset of dots between the two eyes, yield both apparent depth and motion, although depth and velocity are covariant and, thus, ITD is inherently ambiguous. The depth of random dots with ITD was proportional to ITD, suggesting that the visual system assumes a constant velocity of the dots and determines depth on the basis of this constant velocity. We performed psychophysical experiments to investigate whether subjects perceive a constant velocity with a variety of ITDs in random dots aligned along a single vertical line that ensures neither apparent motion nor accidental disparity between the dots. The results showed that subjects perceive a constant velocity for a variety of ITDs with simultaneous perception of depth in proportion to ITD, indicating the priority of depth over velocity in ambiguous binocular perception derived from ITD.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  27. K. Sakai and H. Nishimura, “Surrounding suppression and facilitation in the determination of border ownership,” J. Cogn. Neurosci. 18, 562–579 (2006).
    [CrossRef] [PubMed]

2009

B. Rokers, L. K. Cormack, and A. C. Huk, “Disparity- and velocity-based signals for three-dimensional motion perception in human MT+,” Nat. Neurosci. 12, 1050–1055 (2009).
[CrossRef] [PubMed]

2007

X. Huang, T. D. Albright, and G. R. Stoner, “Adaptive surround modulation in cortical area MT,” Neuron 53, 761–770 (2007).
[CrossRef] [PubMed]

K. Sakai and S. Katsumata, “Simultaneous determination of depth and motion in early vision,” Neurocomputing 70, 1819–1823 (2007).
[CrossRef]

2006

K. Sakai and H. Nishimura, “Surrounding suppression and facilitation in the determination of border ownership,” J. Cogn. Neurosci. 18, 562–579 (2006).
[CrossRef] [PubMed]

2005

J. C. Read and B. G. Cumming, “The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth,” J. Vision 5, 417–434 (2005).
[CrossRef]

J. C. Read and B. G. Cumming, “Effect of interocular delay on disparity-selective V1 neurons: relationship to stereoacuity and the Pulfrich effect,” J. Neurophysiol. 94, 1541–1553 (2005).
[CrossRef] [PubMed]

J. C. Read and B. G. Cumming, “All Pulfrich-like illusions can be explained without joint encoding of motion and disparity,” J. Vision 5, 901–927 (2005).
[CrossRef]

K. Sakai, M. Ogiya, and Y. Hirai, “Perception of depth and motion from ambiguous binocular information,” Vision Res. 45, 2471–2480 (2005).
[CrossRef] [PubMed]

2004

K. Sakai and M. Ogiya, “Perception of depth and motion from ambiguous binocular information,” J. Vision 4, 459a (2004) (Abstract).
[CrossRef]

2003

T. Uka and G. C. DeAngelis, “Contribution of middle temporal area to coarse depth discrimination: comparison of neuronal and psychophysical sensitivity,” J. Neurosci. 23, 3515–3530(2003).
[PubMed]

C. C. Pack, R. T. Born, and M. S. Livingstone, “Two-dimensional substructure of stereo and motion interactions in macaque visual cortex,” Neuron 37, 525–535 (2003).
[CrossRef] [PubMed]

2001

A. Anzai, I. Ohzawa, and R. D. Freeman, “Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect,” Nat. Neurosci. 4, 513–518 (2001).
[CrossRef] [PubMed]

1999

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

A. Anzai, I. Ohzawa, and R. D. Freeman, “Neural mechanisms for processing binocular information I. Simple cells,” J. Neurophysiol. 82, 891–908 (1999).
[PubMed]

1998

D. C. Bradley, G. C. Chang, and R. A. Andersen, “Encoding of three-dimensional structure-from-motion by primate area MT neurons,” Nature 392, 714–717 (1998).
[CrossRef] [PubMed]

1997

N. Qian and R. A. Andersen, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

1990

K. Nakayama and S. Shimojo, “da Vinci stereopsis: depth and subjective occluding contours from unpaired image points,” Vision Res. 30, 1811–25 (1990).
[CrossRef] [PubMed]

1980

D. S. Falk and R. Williams, “Dynamic visual noise and the stereophenomenon: Interocular time delays, depth, and coherent velocities,” Percept. Psychophys. 28, 19–27 (1980).
[CrossRef] [PubMed]

1979

M. J. Morgan, “Perception of continuity in stroboscopic motion: a temporal frequency analysis,” Vision Res. 19, 491–500(1979).
[CrossRef] [PubMed]

1978

M. Kaye, “Stereoposis without binocular correlation,” Vision Res. 18, 1013–1022 (1978).
[CrossRef] [PubMed]

1977

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
[CrossRef] [PubMed]

C. W. Tyler, “Stereomovement from interocular delay in dynamic visual noise: a random spatial disparity hypothesis,” Am. J. Optom. Physiol. Opt. 54, 374–386 (1977).
[PubMed]

1976

J. Ross, “The resources of binocular perception,” Sci. Am. 234, 80–86 (1976).
[CrossRef] [PubMed]

1974

C. W. Tyler, “Stereopsis in dynamic visual noise,” Nature 250, 781–782 (1974).
[CrossRef] [PubMed]

J. Ross, “Stereopsis by binocular delay,” Nature 248, 363–364(1974).
[CrossRef] [PubMed]

J. Ross and J. H. Hogben, “Short-term memory in stereopsis,” Vision Res. 14, 1195–1201 (1974).
[CrossRef] [PubMed]

Albright, T. D.

X. Huang, T. D. Albright, and G. R. Stoner, “Adaptive surround modulation in cortical area MT,” Neuron 53, 761–770 (2007).
[CrossRef] [PubMed]

Andersen, R. A.

D. C. Bradley, G. C. Chang, and R. A. Andersen, “Encoding of three-dimensional structure-from-motion by primate area MT neurons,” Nature 392, 714–717 (1998).
[CrossRef] [PubMed]

N. Qian and R. A. Andersen, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

Anzai, A.

A. Anzai, I. Ohzawa, and R. D. Freeman, “Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect,” Nat. Neurosci. 4, 513–518 (2001).
[CrossRef] [PubMed]

A. Anzai, I. Ohzawa, and R. D. Freeman, “Neural mechanisms for processing binocular information I. Simple cells,” J. Neurophysiol. 82, 891–908 (1999).
[PubMed]

Born, R. T.

C. C. Pack, R. T. Born, and M. S. Livingstone, “Two-dimensional substructure of stereo and motion interactions in macaque visual cortex,” Neuron 37, 525–535 (2003).
[CrossRef] [PubMed]

Bradley, D. C.

D. C. Bradley, G. C. Chang, and R. A. Andersen, “Encoding of three-dimensional structure-from-motion by primate area MT neurons,” Nature 392, 714–717 (1998).
[CrossRef] [PubMed]

Carello, C.

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
[CrossRef] [PubMed]

Chang, G. C.

D. C. Bradley, G. C. Chang, and R. A. Andersen, “Encoding of three-dimensional structure-from-motion by primate area MT neurons,” Nature 392, 714–717 (1998).
[CrossRef] [PubMed]

Cormack, L. K.

B. Rokers, L. K. Cormack, and A. C. Huk, “Disparity- and velocity-based signals for three-dimensional motion perception in human MT+,” Nat. Neurosci. 12, 1050–1055 (2009).
[CrossRef] [PubMed]

Cumming, B. G.

J. C. Read and B. G. Cumming, “The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth,” J. Vision 5, 417–434 (2005).
[CrossRef]

J. C. Read and B. G. Cumming, “Effect of interocular delay on disparity-selective V1 neurons: relationship to stereoacuity and the Pulfrich effect,” J. Neurophysiol. 94, 1541–1553 (2005).
[CrossRef] [PubMed]

J. C. Read and B. G. Cumming, “All Pulfrich-like illusions can be explained without joint encoding of motion and disparity,” J. Vision 5, 901–927 (2005).
[CrossRef]

DeAngelis, G. C.

T. Uka and G. C. DeAngelis, “Contribution of middle temporal area to coarse depth discrimination: comparison of neuronal and psychophysical sensitivity,” J. Neurosci. 23, 3515–3530(2003).
[PubMed]

Efron, B.

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall/CRC Press, 1993).

Falk, D. S.

D. S. Falk and R. Williams, “Dynamic visual noise and the stereophenomenon: Interocular time delays, depth, and coherent velocities,” Percept. Psychophys. 28, 19–27 (1980).
[CrossRef] [PubMed]

Freeman, R. D.

A. Anzai, I. Ohzawa, and R. D. Freeman, “Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect,” Nat. Neurosci. 4, 513–518 (2001).
[CrossRef] [PubMed]

A. Anzai, I. Ohzawa, and R. D. Freeman, “Neural mechanisms for processing binocular information I. Simple cells,” J. Neurophysiol. 82, 891–908 (1999).
[PubMed]

Gonzalez, F.

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

Hirai, Y.

K. Sakai, M. Ogiya, and Y. Hirai, “Perception of depth and motion from ambiguous binocular information,” Vision Res. 45, 2471–2480 (2005).
[CrossRef] [PubMed]

Hogben, J. H.

J. Ross and J. H. Hogben, “Short-term memory in stereopsis,” Vision Res. 14, 1195–1201 (1974).
[CrossRef] [PubMed]

Huang, X.

X. Huang, T. D. Albright, and G. R. Stoner, “Adaptive surround modulation in cortical area MT,” Neuron 53, 761–770 (2007).
[CrossRef] [PubMed]

Huk, A. C.

B. Rokers, L. K. Cormack, and A. C. Huk, “Disparity- and velocity-based signals for three-dimensional motion perception in human MT+,” Nat. Neurosci. 12, 1050–1055 (2009).
[CrossRef] [PubMed]

Justo, M. S.

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

Katsumata, S.

K. Sakai and S. Katsumata, “Simultaneous determination of depth and motion in early vision,” Neurocomputing 70, 1819–1823 (2007).
[CrossRef]

Kaye, M.

M. Kaye, “Stereoposis without binocular correlation,” Vision Res. 18, 1013–1022 (1978).
[CrossRef] [PubMed]

Livingstone, M. S.

C. C. Pack, R. T. Born, and M. S. Livingstone, “Two-dimensional substructure of stereo and motion interactions in macaque visual cortex,” Neuron 37, 525–535 (2003).
[CrossRef] [PubMed]

Michaels, C. F.

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
[CrossRef] [PubMed]

Morgan, M. J.

M. J. Morgan, “Perception of continuity in stroboscopic motion: a temporal frequency analysis,” Vision Res. 19, 491–500(1979).
[CrossRef] [PubMed]

Nakayama, K.

K. Nakayama and S. Shimojo, “da Vinci stereopsis: depth and subjective occluding contours from unpaired image points,” Vision Res. 30, 1811–25 (1990).
[CrossRef] [PubMed]

Nishimura, H.

K. Sakai and H. Nishimura, “Surrounding suppression and facilitation in the determination of border ownership,” J. Cogn. Neurosci. 18, 562–579 (2006).
[CrossRef] [PubMed]

Ogiya, M.

K. Sakai, M. Ogiya, and Y. Hirai, “Perception of depth and motion from ambiguous binocular information,” Vision Res. 45, 2471–2480 (2005).
[CrossRef] [PubMed]

K. Sakai and M. Ogiya, “Perception of depth and motion from ambiguous binocular information,” J. Vision 4, 459a (2004) (Abstract).
[CrossRef]

Ohzawa, I.

A. Anzai, I. Ohzawa, and R. D. Freeman, “Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect,” Nat. Neurosci. 4, 513–518 (2001).
[CrossRef] [PubMed]

A. Anzai, I. Ohzawa, and R. D. Freeman, “Neural mechanisms for processing binocular information I. Simple cells,” J. Neurophysiol. 82, 891–908 (1999).
[PubMed]

Pack, C. C.

C. C. Pack, R. T. Born, and M. S. Livingstone, “Two-dimensional substructure of stereo and motion interactions in macaque visual cortex,” Neuron 37, 525–535 (2003).
[CrossRef] [PubMed]

Perez, R.

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

Qian, N.

N. Qian and R. A. Andersen, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

Read, J. C.

J. C. Read and B. G. Cumming, “Effect of interocular delay on disparity-selective V1 neurons: relationship to stereoacuity and the Pulfrich effect,” J. Neurophysiol. 94, 1541–1553 (2005).
[CrossRef] [PubMed]

J. C. Read and B. G. Cumming, “All Pulfrich-like illusions can be explained without joint encoding of motion and disparity,” J. Vision 5, 901–927 (2005).
[CrossRef]

J. C. Read and B. G. Cumming, “The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth,” J. Vision 5, 417–434 (2005).
[CrossRef]

Rokers, B.

B. Rokers, L. K. Cormack, and A. C. Huk, “Disparity- and velocity-based signals for three-dimensional motion perception in human MT+,” Nat. Neurosci. 12, 1050–1055 (2009).
[CrossRef] [PubMed]

Ross, J.

J. Ross, “The resources of binocular perception,” Sci. Am. 234, 80–86 (1976).
[CrossRef] [PubMed]

J. Ross and J. H. Hogben, “Short-term memory in stereopsis,” Vision Res. 14, 1195–1201 (1974).
[CrossRef] [PubMed]

J. Ross, “Stereopsis by binocular delay,” Nature 248, 363–364(1974).
[CrossRef] [PubMed]

Sakai, K.

K. Sakai and S. Katsumata, “Simultaneous determination of depth and motion in early vision,” Neurocomputing 70, 1819–1823 (2007).
[CrossRef]

K. Sakai and H. Nishimura, “Surrounding suppression and facilitation in the determination of border ownership,” J. Cogn. Neurosci. 18, 562–579 (2006).
[CrossRef] [PubMed]

K. Sakai, M. Ogiya, and Y. Hirai, “Perception of depth and motion from ambiguous binocular information,” Vision Res. 45, 2471–2480 (2005).
[CrossRef] [PubMed]

K. Sakai and M. Ogiya, “Perception of depth and motion from ambiguous binocular information,” J. Vision 4, 459a (2004) (Abstract).
[CrossRef]

Shapiro, B.

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
[CrossRef] [PubMed]

Shimojo, S.

K. Nakayama and S. Shimojo, “da Vinci stereopsis: depth and subjective occluding contours from unpaired image points,” Vision Res. 30, 1811–25 (1990).
[CrossRef] [PubMed]

Steitz, C.

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
[CrossRef] [PubMed]

Stoner, G. R.

X. Huang, T. D. Albright, and G. R. Stoner, “Adaptive surround modulation in cortical area MT,” Neuron 53, 761–770 (2007).
[CrossRef] [PubMed]

Tibshirani, R. J.

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall/CRC Press, 1993).

Tyler, C. W.

C. W. Tyler, “Stereomovement from interocular delay in dynamic visual noise: a random spatial disparity hypothesis,” Am. J. Optom. Physiol. Opt. 54, 374–386 (1977).
[PubMed]

C. W. Tyler, “Stereopsis in dynamic visual noise,” Nature 250, 781–782 (1974).
[CrossRef] [PubMed]

Uka, T.

T. Uka and G. C. DeAngelis, “Contribution of middle temporal area to coarse depth discrimination: comparison of neuronal and psychophysical sensitivity,” J. Neurosci. 23, 3515–3530(2003).
[PubMed]

Ulibarrena, C.

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

Williams, R.

D. S. Falk and R. Williams, “Dynamic visual noise and the stereophenomenon: Interocular time delays, depth, and coherent velocities,” Percept. Psychophys. 28, 19–27 (1980).
[CrossRef] [PubMed]

Am. J. Optom. Physiol. Opt.

C. W. Tyler, “Stereomovement from interocular delay in dynamic visual noise: a random spatial disparity hypothesis,” Am. J. Optom. Physiol. Opt. 54, 374–386 (1977).
[PubMed]

Eur. J. Neurosci.

R. Perez, F. Gonzalez, M. S. Justo, and C. Ulibarrena, “Interocular temporal delay sensitivity in the visual cortex of the awake monkey,” Eur. J. Neurosci. 11, 2593–2595 (1999).
[CrossRef] [PubMed]

J. Cogn. Neurosci.

K. Sakai and H. Nishimura, “Surrounding suppression and facilitation in the determination of border ownership,” J. Cogn. Neurosci. 18, 562–579 (2006).
[CrossRef] [PubMed]

J. Neurophysiol.

J. C. Read and B. G. Cumming, “Effect of interocular delay on disparity-selective V1 neurons: relationship to stereoacuity and the Pulfrich effect,” J. Neurophysiol. 94, 1541–1553 (2005).
[CrossRef] [PubMed]

A. Anzai, I. Ohzawa, and R. D. Freeman, “Neural mechanisms for processing binocular information I. Simple cells,” J. Neurophysiol. 82, 891–908 (1999).
[PubMed]

J. Neurosci.

T. Uka and G. C. DeAngelis, “Contribution of middle temporal area to coarse depth discrimination: comparison of neuronal and psychophysical sensitivity,” J. Neurosci. 23, 3515–3530(2003).
[PubMed]

J. Vision

K. Sakai and M. Ogiya, “Perception of depth and motion from ambiguous binocular information,” J. Vision 4, 459a (2004) (Abstract).
[CrossRef]

J. C. Read and B. G. Cumming, “All Pulfrich-like illusions can be explained without joint encoding of motion and disparity,” J. Vision 5, 901–927 (2005).
[CrossRef]

J. C. Read and B. G. Cumming, “The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth,” J. Vision 5, 417–434 (2005).
[CrossRef]

Nat. Neurosci.

A. Anzai, I. Ohzawa, and R. D. Freeman, “Joint-encoding of motion and depth by visual cortical neurons: neural basis of the Pulfrich effect,” Nat. Neurosci. 4, 513–518 (2001).
[CrossRef] [PubMed]

B. Rokers, L. K. Cormack, and A. C. Huk, “Disparity- and velocity-based signals for three-dimensional motion perception in human MT+,” Nat. Neurosci. 12, 1050–1055 (2009).
[CrossRef] [PubMed]

Nature

D. C. Bradley, G. C. Chang, and R. A. Andersen, “Encoding of three-dimensional structure-from-motion by primate area MT neurons,” Nature 392, 714–717 (1998).
[CrossRef] [PubMed]

C. W. Tyler, “Stereopsis in dynamic visual noise,” Nature 250, 781–782 (1974).
[CrossRef] [PubMed]

J. Ross, “Stereopsis by binocular delay,” Nature 248, 363–364(1974).
[CrossRef] [PubMed]

Neurocomputing

K. Sakai and S. Katsumata, “Simultaneous determination of depth and motion in early vision,” Neurocomputing 70, 1819–1823 (2007).
[CrossRef]

Neuron

X. Huang, T. D. Albright, and G. R. Stoner, “Adaptive surround modulation in cortical area MT,” Neuron 53, 761–770 (2007).
[CrossRef] [PubMed]

C. C. Pack, R. T. Born, and M. S. Livingstone, “Two-dimensional substructure of stereo and motion interactions in macaque visual cortex,” Neuron 37, 525–535 (2003).
[CrossRef] [PubMed]

Percept. Psychophys.

D. S. Falk and R. Williams, “Dynamic visual noise and the stereophenomenon: Interocular time delays, depth, and coherent velocities,” Percept. Psychophys. 28, 19–27 (1980).
[CrossRef] [PubMed]

Sci. Am.

J. Ross, “The resources of binocular perception,” Sci. Am. 234, 80–86 (1976).
[CrossRef] [PubMed]

Vision Res.

J. Ross and J. H. Hogben, “Short-term memory in stereopsis,” Vision Res. 14, 1195–1201 (1974).
[CrossRef] [PubMed]

K. Sakai, M. Ogiya, and Y. Hirai, “Perception of depth and motion from ambiguous binocular information,” Vision Res. 45, 2471–2480 (2005).
[CrossRef] [PubMed]

N. Qian and R. A. Andersen, “A physiological model for motion-stereo integration and a unified explanation of Pulfrich-like phenomena,” Vision Res. 37, 1683–1698 (1997).
[CrossRef] [PubMed]

C. F. Michaels, C. Carello, B. Shapiro, and C. Steitz, “An onset to onset rule for binocular integration in the Mach-Dvorak illusion,” Vision Res. 17, 1107–1113 (1977).
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Figures (4)

Fig. 1
Fig. 1

(a) Stimulus configuration. The stationary dots ( 20 cd / m 2 ) were presented for a short duration ( 6.7 ms ) within a thin vertical line of one pixel width ( 0.0 cd / m 2 ) surrounded by a gray background ( 1.2 cd / m 2 ). An ITD ( 33.5 100.5 ms ) was introduced to the dots that were randomly placed along the line so that it appeared as if they moved horizontally behind a thin slit. (b) Experimental procedure. Subjects were instructed to gaze at the fixation aid (x) at the center of the screen and asked to compare depth or motion of the upper and lower dots. The left panel illustrates an example of the temporal sequence of the dot appearance for the left and right eyes. Note that there is no physical motion and no cue to draw eye movement. (c) An illustration of constant velocity hypothesis (left) and constant depth hypothesis (right). See text for details.

Fig. 2
Fig. 2

Mean correct rates of three subjects in the discrimination of depth (triangle) and velocity (square) as a function of the difference in the ITD ( Δ ITD ) between the dots above and below the fixation aid. The ratio of the perception of leftward motion (circle) is also plotted similarly. Δ ITD was defined as positive if the left-eye image was shown first. The perception is defined as correct if the dots with greater ITD appeared further away and slower for the discrimination of depth and velocity, respectively. See text for details. Error bars indicate the 95% confidence interval. Subjects were able to discriminate depth and the direction of motion but not velocity.

Fig. 3
Fig. 3

(a) Stimulus configuration for the quantitative measurement of apparent velocity and depth using the constant stimuli method. In the velocity measurement, subjects were asked to judge whether the dots or the solid bar moved more quickly. (b) Examples of psychometric functions (solid curves) for subject YT in the velocity measurement. Symbols show the results for different ITDs in milliseconds. Shapes of the psychometric functions were similar for a range of ITDs. (c) Measured velocity of dots as a function of the ITD. A positive ITD indicates that dots for the left eye were presented prior to those for the right eye. Positive velocity indicates motion to the left. Symbols show the results for the different individuals, and error bars indicate the residual standard deviation of the corresponding psychometric function. The subjects observed constant velocities of around 5 and + 5 cm / s for the entire range of negative and positive ITDs, respectively, indicating independence of apparent velocity with respect to ITD. (d) Apparent depth of dots that was obtained similarly to the velocity measurement. Apparent depth is linearly proportional to the | ITD | . These results support constant velocity hypothesis.

Fig. 4
Fig. 4

(a) Apparent velocities for the three stationary ranges of reference velocity (conditions 1, 2, and 3). Symbols show the results for different subjects, with error bars indicating the residual standard deviation of the corresponding psychometric function. The black line represents the results of linear regression. The apparent velocity increases as the mean of the reference velocity increases. (b) Apparent velocities for the two dynamic ranges (shown by gray shading) of reference velocity (conditions 4 and 5). The apparent velocity increased (left panel) or decreased (right panel) in accordance with the mean of the reference velocity (dashed lines), which changed 15 min (220 trials) after onset.

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