Abstract

We investigate the spatiotemporal dynamics of depth filling in on an illusory surface by measuring the temporal asynchrony of perceived depth between an illusory neon-colored surface and real contours. We temporally modulated the horizontal disparity at vertical edges of the illusory surface and measured the perceptual delay for the interpolated surface’s depth under two different boundary conditions: disparity given at both sides, or disparity given at one side and a free boundary at the other side. The results showed that the amount of the delay depends on the spatial distance between the measured point and the edges where disparity was physically given. Importantly, the observed delay as a function of spatial distance was clearly different under the two boundary conditions. We found that this difference can be fairly well explained by a model based on a diffusion equation under different boundary conditions. These results support the existence of locally represented depth information and an interpolation process based on mutual interaction of this information.

© 2007 Optical Society of America

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References

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  1. B. Julesz, Foundations of Cyclopean Perception (U. of Chicago Press, 197l).
  2. M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
    [CrossRef] [PubMed]
  3. M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991).
    [CrossRef] [PubMed]
  4. S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985).
    [CrossRef] [PubMed]
  5. K. F. Arrington, "The temporal dynamics of brightness filling-in," Vision Res. 34, 3371-3387 (1994).
    [CrossRef] [PubMed]
  6. R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
    [CrossRef] [PubMed]
  7. A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996).
    [CrossRef] [PubMed]
  8. S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
    [CrossRef] [PubMed]
  9. S. Nishina and M. Kawato, "A computational model of spatio-temporal dynamics in depth filling-in," Neural Networks 17, 159-163 (2004).
    [CrossRef] [PubMed]
  10. G. Kanizsa, "Margini quasi-percettivi in campi con stimulazione omogenea," Rivista di psicologia 49, 7-30 (1955).
  11. Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004).
    [CrossRef] [PubMed]
  12. H. F. v. Tuijl, "A new visual illusion: neonlike color spreading and complementary color induction between subjective contours," Appl. Phys. (Berlin) 39, 441-445 (1975).
  13. K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
    [CrossRef] [PubMed]

2004

S. Nishina and M. Kawato, "A computational model of spatio-temporal dynamics in depth filling-in," Neural Networks 17, 159-163 (2004).
[CrossRef] [PubMed]

Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004).
[CrossRef] [PubMed]

2003

S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
[CrossRef] [PubMed]

1998

M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
[CrossRef] [PubMed]

1996

A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996).
[CrossRef] [PubMed]

1994

K. F. Arrington, "The temporal dynamics of brightness filling-in," Vision Res. 34, 3371-3387 (1994).
[CrossRef] [PubMed]

1991

M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991).
[CrossRef] [PubMed]

1990

K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

1986

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

1985

S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985).
[CrossRef] [PubMed]

1975

H. F. v. Tuijl, "A new visual illusion: neonlike color spreading and complementary color induction between subjective contours," Appl. Phys. (Berlin) 39, 441-445 (1975).

1955

G. Kanizsa, "Margini quasi-percettivi in campi con stimulazione omogenea," Rivista di psicologia 49, 7-30 (1955).

Arrington, K. F.

K. F. Arrington, "The temporal dynamics of brightness filling-in," Vision Res. 34, 3371-3387 (1994).
[CrossRef] [PubMed]

Davey, M. P.

M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
[CrossRef] [PubMed]

De Valois, K. K.

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

De Valois, R. L.

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

Grossberg, S.

S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985).
[CrossRef] [PubMed]

Julesz, B.

B. Julesz, Foundations of Cyclopean Perception (U. of Chicago Press, 197l).

Kanizsa, G.

G. Kanizsa, "Margini quasi-percettivi in campi con stimulazione omogenea," Rivista di psicologia 49, 7-30 (1955).

Kawato, M.

S. Nishina and M. Kawato, "A computational model of spatio-temporal dynamics in depth filling-in," Neural Networks 17, 159-163 (2004).
[CrossRef] [PubMed]

S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
[CrossRef] [PubMed]

Lingelbach, B.

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

Maddess, T.

M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
[CrossRef] [PubMed]

Mingolla, E.

S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985).
[CrossRef] [PubMed]

Nakayama, K.

M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991).
[CrossRef] [PubMed]

K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Nishina, S.

S. Nishina and M. Kawato, "A computational model of spatio-temporal dynamics in depth filling-in," Neural Networks 17, 159-163 (2004).
[CrossRef] [PubMed]

S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
[CrossRef] [PubMed]

Okada, M.

S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
[CrossRef] [PubMed]

Paradiso, M. A.

A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996).
[CrossRef] [PubMed]

M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991).
[CrossRef] [PubMed]

Ramachandran, V. S.

K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Rossi, A. F.

A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996).
[CrossRef] [PubMed]

Sasaki, Y.

Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004).
[CrossRef] [PubMed]

Shimojo, S.

K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Srinivasan, M. V.

M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
[CrossRef] [PubMed]

Tuijl, H. F. v.

H. F. v. Tuijl, "A new visual illusion: neonlike color spreading and complementary color induction between subjective contours," Appl. Phys. (Berlin) 39, 441-445 (1975).

Watanabe, T.

Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004).
[CrossRef] [PubMed]

Webster, M. A.

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

Appl. Phys. (Berlin)

H. F. v. Tuijl, "A new visual illusion: neonlike color spreading and complementary color induction between subjective contours," Appl. Phys. (Berlin) 39, 441-445 (1975).

Neural Networks

S. Nishina and M. Kawato, "A computational model of spatio-temporal dynamics in depth filling-in," Neural Networks 17, 159-163 (2004).
[CrossRef] [PubMed]

Perception

K. Nakayama, S. Shimojo, and V. S. Ramachandran, "Transparency: relation to depth, subjective contours, luminance, and neon color spreading," Perception 19, 497-513 (1990).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

Y. Sasaki and T. Watanabe, "The primary visual cortex fills in color," Proc. Natl. Acad. Sci. U.S.A. 101, 18251-18256 (2004).
[CrossRef] [PubMed]

Psychol. Rev.

S. Grossberg and E. Mingolla, "Neural dynamics of form perception: boundary completion, illusory figures, and neon color spreading," Psychol. Rev. 92, 173-211 (1985).
[CrossRef] [PubMed]

Rivista di psicologia

G. Kanizsa, "Margini quasi-percettivi in campi con stimulazione omogenea," Rivista di psicologia 49, 7-30 (1955).

Vision Res.

M. P. Davey, T. Maddess, and M. V. Srinivasan, "The spatiotemporal properties of the Craik-O'Brien-Cornsweet effect are consistent with 'filling-in'," Vision Res. 38, 2037-2046 (1998).
[CrossRef] [PubMed]

M. A. Paradiso and K. Nakayama, "Brightness perception and filling-in," Vision Res. 31, 1221-1236 (1991).
[CrossRef] [PubMed]

K. F. Arrington, "The temporal dynamics of brightness filling-in," Vision Res. 34, 3371-3387 (1994).
[CrossRef] [PubMed]

R. L. De Valois, M. A. Webster, K. K. De Valois, and B. Lingelbach, "Temporal properties of brightness and color induction," Vision Res. 26, 887-897 (1986).
[CrossRef] [PubMed]

A. F. Rossi and M. A. Paradiso, "Temporal limits of brightness induction and mechanisms of brightness perception," Vision Res. 36, 1391-1398 (1996).
[CrossRef] [PubMed]

S. Nishina, M. Okada, and M. Kawato, "Spatio-temporal dynamics of depth propagation on uniform region," Vision Res. 43, 2493-2503 (2003).
[CrossRef] [PubMed]

Other

B. Julesz, Foundations of Cyclopean Perception (U. of Chicago Press, 197l).

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Figures (5)

Fig. 1
Fig. 1

Typical spatial configurations of the stimuli are shown. Gray areas were presented in dark blue in the actual experiment. In the double side condition, (a) four circles with blue sections were presented as inducers at the four corners of the illusory surface. In the single-side condition, (b) only two circles were presented at one side. Small rectangles with blue and white colors were presented as supplementary inducers. The four square dots around the center were fixation dots, and the two vertical lines at the center were comparison stimuli.

Fig. 2
Fig. 2

Static example of the binocular stimulus for cross fusers. Although these two images differ only at the vertical edges in the circle (and the vertical edges at the center), the entire filled-in surface is perceived as popping out in depth.

Fig. 3
Fig. 3

Disparities of the vertical edges in the circles and the probe stimulus were updated at every display frame according to these equations. Both were sinusoidally modulated with the same amplitude and frequency, but they could have different phases.

Fig. 4
Fig. 4

Psychometric curves show the ratio of ahead response as functions of phase difference. The circles, squares, and triangles represent the different horizontal lengths of the stimuli, 4.0 ° , 5.0 ° , and 6.0 ° , respectively. Curves are sigmoid functions fit to the data.

Fig. 5
Fig. 5

Phases at which the filled-in surface and the probe were perceived in phase were shown for each distance between the bar’s ends and the probe. The dots connected with the black solid line represent the double-side condition, and the dots connected with the thick dashed line represent the single-side condition. The dotted curves are the model predictions. The gray lines at the bottom are the result of a control experiment, where no illusory surface was perceived.

Equations (19)

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

τ D t = λ 2 2 D x 2 .
λ 2 τ = v 2 2 ω ,
v = 2 λ 2 ω τ .
D t = v 2 2 ω 2 D x 2 .
D single ( x , t ) = C exp ( ω v x ) sin ( ω t ω v x + θ )
= C exp ( ω v x ) sin { ω ( t x v ) + θ } ,
Φ ω v L .
D double ( x , t ) = D single + ( x , t ) + D single ( x , t ) ,
D single + ( x , t ) = c exp ( ω v x ) sin ( ω t ω v x + θ ) ,
D single ( x , t ) = D + ( x , t ) = c exp ( ω v x ) sin ( ω t + ω v x + θ ) .
D ( 0 , t ) = 2 c sin ( ω t + θ ) ,
D ( L , t ) = D ( L , t )
= c exp ( ω v L ) sin ( ω t ω v L + θ ) + c exp ( ω v L ) sin ( ω t + ω v L + θ )
= A c sin ( ω t + θ Φ ) ,
A ( L )
= exp ( 2 ω v L ) + exp ( 2 ω v L ) + 2 { 1 2 sin 2 ( ω v L ) } ,
Φ = arctan [ { exp ( ω v L ) exp ( ω v L ) } sin ( ω v L ) { exp ( ω v L ) + exp ( ω v L ) } cos ( ω v L ) ] .
A ( L ) 2 + o ( L 2 ) ,
Φ ( ω v L ) 2 .

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