Abstract

Gibson [ J. Exp. Psychol. 16, 1 (1993) ] observed that during prolonged viewing, a line perceptually rotates toward the nearest vertical or horizontal meridian (the normalization effect), and moreover, the perceived orientation of a subsequently presented line depends on the orientation of the adapting one (the tilt after-effect). The mechanisms of both phenomena remain poorly understood. According to our experimental results, the adapting line perceptually rotates to the nearest of three orientations: vertical, horizontal, and diagonal. We propose a simple neuronal model of orientation detectors whose responses are determined by the cardinal detectors. It is shown that both normalization and tilt after-effect may be explained by adaptation of these cardinal detectors.

© 2009 Optical Society of America

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    [CrossRef]
  2. J. J. Gibson, “Adaptation, after-effect and simultaneous contrast and real restriction of the after-effect,” J. Exp. Psychol. 20, 186-196 (1937).
    [CrossRef]
  3. J. J. Gibson and M. Radner, “Adaptation, after-effect and contrast in the perception of tilted lines. I. Quantitative studies,” J. Exp. Psychol. 20, 453-467 (1937).
    [CrossRef]
  4. W. Köhler and H. Wallach, “Figural after-effects: an investigation of visual processes,” Proc. Am. Philos. Soc. 88, 269-375 (1944).
  5. F. W. Campbell and L. Maffei, “The tilt after-effect: a fresh look,” Vision Res. 11, 833-840 (1971).
    [CrossRef] [PubMed]
  6. D. E. Mitchell and D. W. Muir, “Does the tilt after-effect occur in the oblique meridian?” Vision Res. 16, 609-614 (1976).
    [CrossRef] [PubMed]
  7. J. A. Bednar and R. Miikkulainen, “Tilt aftereffects in a self-organizing model of the primary visual cortex,” Neural Comput. 12, 1721-1740 (2000).
    [CrossRef] [PubMed]
  8. C. W. G. Clifford, P. Wenderoth, and B. Spehar, “A functional angle on some after-effects in cortical vision,” Proc. R. Soc. London, Ser. B 267, 1705-1710 (2000).
    [CrossRef]
  9. O. Schwartz, A. Hsu, and P. Dayan, “Space and time in visual context,” Nat. Rev. Neurosci. 8, 522-532 (2007).
    [CrossRef] [PubMed]
  10. L. Ganz, “Mechanism of the figural after-effects,” Psychol. Rev. 73, 128-150 (1956).
    [CrossRef]
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    [CrossRef] [PubMed]
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  18. J. McLean and L. A. Palmer, “Plasticity of neuronal response properties in adult cat striate cortex,” Visual Neurosci. 15, 177-196 (1998).
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    [CrossRef] [PubMed]
  37. W. R. Levick and L. Thibos, “Analysis of orientation bias in cat retina,” J. Physiol. (London) 329, 243-261 (1982).
  38. T. Vidyasagar and J. Urbas, “Orientation sensitivity of cat LGN neurones with and without inputs from visual cortical areas 17 and 18,” Exp. Brain Res. 46, 157-169 (1992).
  39. T. D. Shou and A. G. Leventhal, “Organized arrangement of orientation-sensitive relay cells in the cat's dorsal lateral geniculate nucleus,” J. Neurosci. 9, 4287-4302 (1989).
    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  43. O. Creutzfeldt and M. Ito, “Functional synaptic organization of primary visual cortex neurons in the cat,” Exp. Brain Res. 6, 324-352 (1968).
    [CrossRef] [PubMed]
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    [CrossRef]
  45. B. Chapman and T. Bonhoeffer, “Overrepresentation of horizontal and vertical orientation preferences in developing ferret area 17,” Proc. Natl. Acad. Sci. U.S.A. 95, 2609-2614 (1998).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  49. D. Foster and S. Westland, “Orientation contrast vs. orientation in line-target detection,” Vision Res. 35, 733-738 (1995).
    [CrossRef] [PubMed]
  50. D. Foster and S. Westland, “Multiple groups of orientation-selective visual mechanisms underlying rapid orientated-line detection,” Proc. R. Soc. London, Ser. B 265, 1605-1613 (1998).
    [CrossRef]
  51. W. R. Levick, “Receptive fields and trigger features of ganglion cells in the visual streak of the rabbit's retina,” J. Physiol. (London) 188, 285-307 (1967).
  52. M. Carandini, J. A. Movshon, and D. Ferster, “Pattern adaptation and cross-orientation interactions in the primary visual cortex,” Neuropharmacology 37, 501-511 (1998).
    [CrossRef] [PubMed]
  53. J. A. Movshon and P. Lennie, “Pattern selective adaptation in visual cortical neurones,” Nature 278, 850-852 (1979).
    [CrossRef] [PubMed]
  54. I. Ohzawa, G. Sclar, and R. D. Freeman, “Contrast gain control in the cat's visual system,” J. Neurobiol. 54, 651-667 (1985).
  55. F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. (London) 187, 427-436 (1966).
  56. F. W. Campbell and J. J. Kulikowski, “Orientational selectivity of the human visual system,” J. Physiol. (London) 187, 437-445 (1966).
  57. C. W. Clifford, A. M. Wyatt, D. H. Arnold, S. T. Smith, and P. Wenderoth, “Orthogonal adaptation improves orientation discrimination,” Vision Res. 41, 151-159 (2001).
    [CrossRef] [PubMed]
  58. B. G. Cleland and A. W. Freeman, “Visual adaptation is highly localized in the cat's retina,” J. Physiol. (London) 40, 591-611 (1968).
  59. R. L. De Valois, E. W. Yund, and N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531-544 (1982).
    [CrossRef] [PubMed]
  60. K. Sakai and Y. Hirai, “Neural grouping and geometric effect in the determination of apparent orientation,” J. Opt. Soc. Am. A 19, 1049-1062 (2002).
    [CrossRef]
  61. C. Blakemore and E. A. Tobin, “Lateral inhibition between orientation detectors in the cat's visual cortex,” Exp. Brain Res. 15, 439-440 (1972).
    [CrossRef] [PubMed]
  62. V. A. F. Lamme, “The neurophysiology visual cortex figure-ground segregation primary,” J. Neurosci. 132, 1605-1615 (1995).
  63. S. Suzuki, “Attention-dependent brief adaptation to contour orientation: a high-level aftereffect for convexity?” Vision Res. 41, 3883-3902 (2001).
    [CrossRef] [PubMed]
  64. H. E. Jones, W. Wang, and A. M. Sillito, “Spatial organization and magnitude of orientation contrast interactions in primate V1,” J. Neurophysiol. 88, 2796-2808 (2002).
    [CrossRef] [PubMed]
  65. H. Ozeki, O. Sadakane, T. Akasaki, T. Naito, S. Shimegi, and H. Sato, “Relationship between excitation and inhibition underlying size tuning and contextual response modulation in the cat primary visual cortex,” J. Neurosci. 24, 1428-1438 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]

2008

2007

O. Schwartz, A. Hsu, and P. Dayan, “Space and time in visual context,” Nat. Rev. Neurosci. 8, 522-532 (2007).
[CrossRef] [PubMed]

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

D. Z. Jin, V. Dragoi, M. Sur, and H. S. Seung, “Tilt aftereffect and adaptation-induced changes in orientation tuning in visual cortex,” J. Neurophysiol. 94, 4038-4050 (2005).
[CrossRef] [PubMed]

2004

H. Ozeki, O. Sadakane, T. Akasaki, T. Naito, S. Shimegi, and H. Sato, “Relationship between excitation and inhibition underlying size tuning and contextual response modulation in the cat primary visual cortex,” J. Neurosci. 24, 1428-1438 (2004).
[CrossRef] [PubMed]

2003

V. Dragoi, J. Sharma, and M. Sur, “Response plasticity in primary visual cortex and its role in vision and visuomotor behaviour: bottom-up and top-down influences,” Institute of Electronics and Telecommunication Engineers (India) Journal of Research 49, 1-9 (2003).

M. J. McMahon and D. I. MacLeod, “The origin of the oblique effect examined with pattern adaptation and masking,” J. Vision 3, 230-239 (2003).
[CrossRef]

2002

K. Sakai and Y. Hirai, “Neural grouping and geometric effect in the determination of apparent orientation,” J. Opt. Soc. Am. A 19, 1049-1062 (2002).
[CrossRef]

H. E. Jones, W. Wang, and A. M. Sillito, “Spatial organization and magnitude of orientation contrast interactions in primate V1,” J. Neurophysiol. 88, 2796-2808 (2002).
[CrossRef] [PubMed]

2001

S. Suzuki, “Attention-dependent brief adaptation to contour orientation: a high-level aftereffect for convexity?” Vision Res. 41, 3883-3902 (2001).
[CrossRef] [PubMed]

C. W. Clifford, A. M. Wyatt, D. H. Arnold, S. T. Smith, and P. Wenderoth, “Orthogonal adaptation improves orientation discrimination,” Vision Res. 41, 151-159 (2001).
[CrossRef] [PubMed]

A. Hyvarinen and P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413-2423 (2001).
[CrossRef] [PubMed]

2000

V. Dragoi, J. Sharma, and M. Sur, “Adaptation-induced plasticity of orientation tuning in adult visual cortex,” Neuron 28, 287-298 (2000).
[CrossRef] [PubMed]

J. A. Bednar and R. Miikkulainen, “Tilt aftereffects in a self-organizing model of the primary visual cortex,” Neural Comput. 12, 1721-1740 (2000).
[CrossRef] [PubMed]

C. W. G. Clifford, P. Wenderoth, and B. Spehar, “A functional angle on some after-effects in cortical vision,” Proc. R. Soc. London, Ser. B 267, 1705-1710 (2000).
[CrossRef]

P. O. Hoyer and A. Hyvarinen, “Independent component analysis applied to feature extraction from colour and stereo images,” Network Comput. Neural Syst. 11, 191-210 (2000).
[CrossRef]

1998

D. Foster and S. Westland, “Multiple groups of orientation-selective visual mechanisms underlying rapid orientated-line detection,” Proc. R. Soc. London, Ser. B 265, 1605-1613 (1998).
[CrossRef]

M. Carandini, J. A. Movshon, and D. Ferster, “Pattern adaptation and cross-orientation interactions in the primary visual cortex,” Neuropharmacology 37, 501-511 (1998).
[CrossRef] [PubMed]

B. Chapman and T. Bonhoeffer, “Overrepresentation of horizontal and vertical orientation preferences in developing ferret area 17,” Proc. Natl. Acad. Sci. U.S.A. 95, 2609-2614 (1998).
[CrossRef] [PubMed]

D. M. Coppola, L. E. White, D. Fitzpatrick, and D. Purves, “Unequal representation of cardinal and oblique contours in ferret visual cortex,” Proc. Natl. Acad. Sci. U.S.A. 95, 2621-2623 (1998).
[CrossRef] [PubMed]

J. H. van Hateren and A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London, Ser. B 265, 359-366 (1998).
[CrossRef]

J. H. van Hateren and D. L. Ruderman, “Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex,” Proc. R. Soc. London, Ser. B 265, 2315-2320 (1998).
[CrossRef]

J. McLean and L. A. Palmer, “Plasticity of neuronal response properties in adult cat striate cortex,” Visual Neurosci. 15, 177-196 (1998).
[CrossRef]

1997

B. A. Olshausen and D. J. Field, “Sparse coding with an over complete basis set: a strategy employed by V1?” Vision Res. 37, 3311-3325 (1997).
[CrossRef]

1996

R. Baddelay, “An efficient code in VI,” Nature 381, 560-561 (1996).
[CrossRef]

B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607-609 (1996).
[CrossRef] [PubMed]

B. A. Olshausen and D. J. Field, “Natural image statistics and efficient coding,” Network Comput. Neural Syst. 7, 333-339 (1996).
[CrossRef]

H. Barlow, “Intraneuronal information processing, directional selectivity and memory for spatio-temporal sequences,” Network Comput. Neural Syst. 7, 7251-7259 (1996).
[CrossRef]

T. Vidyasagar, P. Xing, and M. Volgushev, “Multiple mechanisms underlying the orientation selectivity of visual cortical neurons,” Trends Neurosci. 19, 272-277 (1996).
[CrossRef] [PubMed]

1995

D. Foster and S. Westland, “Orientation contrast vs. orientation in line-target detection,” Vision Res. 35, 733-738 (1995).
[CrossRef] [PubMed]

V. A. F. Lamme, “The neurophysiology visual cortex figure-ground segregation primary,” J. Neurosci. 132, 1605-1615 (1995).

1994

D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559-601 (1994).
[CrossRef]

1992

T. Vidyasagar and J. Urbas, “Orientation sensitivity of cat LGN neurones with and without inputs from visual cortical areas 17 and 18,” Exp. Brain Res. 46, 157-169 (1992).

1991

D. H. Foster and P. A. Ward, “Asymmetries in oriented-line detection indicate two orthogonal filters in early vision,” Proc. R. Soc. London, Ser. B 243, 75-81 (1991).
[CrossRef]

D. H. Foster and P. A. Ward, “Horizontal-vertical filters in early vision predict anomalous line-orientation identification frequencies,” Proc. R. Soc. London, Ser. B 243, 83-86 (1991).
[CrossRef]

1990

T. Vidyasagar and G. Henry, “Relationship between preferred orientation and ordinal position in neurons of cat striate cortex,” Visual Neurosci. 5, 565-569 (1990).
[CrossRef]

T. Vidyasagar, “Pattern adaptation in cat visual cortex is a co-operative phenomenon,” Neuroscience 36, 175-179 (1990).
[CrossRef] [PubMed]

1989

T. D. Shou and A. G. Leventhal, “Organized arrangement of orientation-sensitive relay cells in the cat's dorsal lateral geniculate nucleus,” J. Neurosci. 9, 4287-4302 (1989).
[PubMed]

1987

T. Vidyasagar, “A model of striate response properties based on geniculate anisotropies,” Biol. Cybern. 57, 11-23 (1987).
[CrossRef] [PubMed]

1985

I. Ohzawa, G. Sclar, and R. D. Freeman, “Contrast gain control in the cat's visual system,” J. Neurobiol. 54, 651-667 (1985).

1983

H. Vaitkevicius, M. Karalius, A. Meskauskas, J. Sinius, and E. Sokolov, “A model for the monocular line orientation analyzer,” Biol. Cybern. 48, 139-147 (1983).
[CrossRef] [PubMed]

1982

W. R. Levick and L. Thibos, “Analysis of orientation bias in cat retina,” J. Physiol. (London) 329, 243-261 (1982).

R. L. De Valois, E. W. Yund, and N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531-544 (1982).
[CrossRef] [PubMed]

1979

J. A. Movshon and P. Lennie, “Pattern selective adaptation in visual cortical neurones,” Nature 278, 850-852 (1979).
[CrossRef] [PubMed]

1976

D. E. Mitchell and D. W. Muir, “Does the tilt after-effect occur in the oblique meridian?” Vision Res. 16, 609-614 (1976).
[CrossRef] [PubMed]

1974

R. S. Dealy and D. J. Tolhurst, “Is spatial adaptation an after-effect of prolonged inhibition?” J. Physiol. (London) 241, 261-270 (1974).

R. Sekuler and J. Littlejohn, “Tilt aftereffect following very brief exposures,” Vision Res. 14, 151-152 (1974).
[CrossRef] [PubMed]

1972

R. Over, J. Broerse, and B. Crassini, “Orientation illusion and masking in central and peripheral vision,” J. Exp. Psychol. 96, 25-31 (1972).
[CrossRef] [PubMed]

D. J. Tolhurst, “Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. (London) 226, 231-248 (1972).

C. Blakemore and E. A. Tobin, “Lateral inhibition between orientation detectors in the cat's visual cortex,” Exp. Brain Res. 15, 439-440 (1972).
[CrossRef] [PubMed]

1971

C. Blakemore, R. H. S. Carpenter, and M. A. Georgeson, “Lateral thinking about lateral inhibition,” Nature 234, 418-419 (1971).
[CrossRef]

F. W. Campbell and L. Maffei, “The tilt after-effect: a fresh look,” Vision Res. 11, 833-840 (1971).
[CrossRef] [PubMed]

1970

C. Blakemore, R. H. S. Carpenter, and M. A. Georgeson, “Lateral inhibition between orientation detectors in the human visual system,” Nature 228, 37-39 (1970).
[CrossRef] [PubMed]

1968

B. G. Cleland and A. W. Freeman, “Visual adaptation is highly localized in the cat's retina,” J. Physiol. (London) 40, 591-611 (1968).

O. Creutzfeldt and M. Ito, “Functional synaptic organization of primary visual cortex neurons in the cat,” Exp. Brain Res. 6, 324-352 (1968).
[CrossRef] [PubMed]

1967

W. R. Levick, “Receptive fields and trigger features of ganglion cells in the visual streak of the rabbit's retina,” J. Physiol. (London) 188, 285-307 (1967).

1966

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. (London) 187, 427-436 (1966).

F. W. Campbell and J. J. Kulikowski, “Orientational selectivity of the human visual system,” J. Physiol. (London) 187, 437-445 (1966).

1956

L. Ganz, “Mechanism of the figural after-effects,” Psychol. Rev. 73, 128-150 (1956).
[CrossRef]

1944

W. Köhler and H. Wallach, “Figural after-effects: an investigation of visual processes,” Proc. Am. Philos. Soc. 88, 269-375 (1944).

1937

J. J. Gibson, “Adaptation, after-effect and simultaneous contrast and real restriction of the after-effect,” J. Exp. Psychol. 20, 186-196 (1937).
[CrossRef]

J. J. Gibson and M. Radner, “Adaptation, after-effect and contrast in the perception of tilted lines. I. Quantitative studies,” J. Exp. Psychol. 20, 453-467 (1937).
[CrossRef]

1933

J. J. Gibson, “Adaptation, after-effect and contrast in the perception of curved line,” J. Exp. Psychol. 16, 1-13 (1933).
[CrossRef]

Akasaki, T.

H. Ozeki, O. Sadakane, T. Akasaki, T. Naito, S. Shimegi, and H. Sato, “Relationship between excitation and inhibition underlying size tuning and contextual response modulation in the cat primary visual cortex,” J. Neurosci. 24, 1428-1438 (2004).
[CrossRef] [PubMed]

Arnold, D. H.

C. W. Clifford, A. M. Wyatt, D. H. Arnold, S. T. Smith, and P. Wenderoth, “Orthogonal adaptation improves orientation discrimination,” Vision Res. 41, 151-159 (2001).
[CrossRef] [PubMed]

Baddelay, R.

R. Baddelay, “An efficient code in VI,” Nature 381, 560-561 (1996).
[CrossRef]

Barlow, H.

H. Barlow, “Intraneuronal information processing, directional selectivity and memory for spatio-temporal sequences,” Network Comput. Neural Syst. 7, 7251-7259 (1996).
[CrossRef]

Barlow, H. B.

H. B. Barlow and P. Foldiak, “Adaptation and decorrelation in the cortex,” in The Computing Neuron, R.Durbin, C.Miall, C.Mitchison, eds. (Addison-Wesley, 1989), pp. 54-72.

Bednar, J. A.

J. A. Bednar and R. Miikkulainen, “Tilt aftereffects in a self-organizing model of the primary visual cortex,” Neural Comput. 12, 1721-1740 (2000).
[CrossRef] [PubMed]

Blakemore, C.

C. Blakemore and E. A. Tobin, “Lateral inhibition between orientation detectors in the cat's visual cortex,” Exp. Brain Res. 15, 439-440 (1972).
[CrossRef] [PubMed]

C. Blakemore, R. H. S. Carpenter, and M. A. Georgeson, “Lateral thinking about lateral inhibition,” Nature 234, 418-419 (1971).
[CrossRef]

C. Blakemore, R. H. S. Carpenter, and M. A. Georgeson, “Lateral inhibition between orientation detectors in the human visual system,” Nature 228, 37-39 (1970).
[CrossRef] [PubMed]

Bonhoeffer, T.

B. Chapman and T. Bonhoeffer, “Overrepresentation of horizontal and vertical orientation preferences in developing ferret area 17,” Proc. Natl. Acad. Sci. U.S.A. 95, 2609-2614 (1998).
[CrossRef] [PubMed]

Broerse, J.

R. Over, J. Broerse, and B. Crassini, “Orientation illusion and masking in central and peripheral vision,” J. Exp. Psychol. 96, 25-31 (1972).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell and L. Maffei, “The tilt after-effect: a fresh look,” Vision Res. 11, 833-840 (1971).
[CrossRef] [PubMed]

F. W. Campbell, J. J. Kulikowski, and J. Levinson, “The effect of orientation on the visual resolution of gratings,” J. Physiol. (London) 187, 427-436 (1966).

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Figures (7)

Fig. 1
Fig. 1

Influence of adaptation on the eight spatial orientations. a . The responses of two cardinal detectors versus an orientation ϕ. The absolute values of the cardinal detector responses to the four lines oriented by 0°, 45°, 90°, and 135° are equal (see solid arrows). Four lines oriented by ± 22.5 ° , 67.5°, and 112.5° excite only one of two cardinal detectors (see dashed arrows). The perceived orientations of these eight lines should not change during adaptation. b . Orientations of 0°, 45°, 90°, and 135° are marked with solid lines and orientations of ± 22.5 ° , 67.5°, and 112.5° are marked with dashed lines. The arrows represent the direction of a subjective drift of the orientation during prolonged viewing.

Fig. 2
Fig. 2

Stimuli and sequence of their presentation under investigation of the normalization phenomenon. (a) Spatial presentation of three adapting lines L A ( l ϕ a ) and one matching or testing line L M ( l ϕ a ± Δ ϕ ) . For more detail, see the text. (b) Sequence of stimuli presentation: t pr , dark adaptation time; t A 1 , preliminary adapting time ( t A 1 = 1 min ) ; t m , the presentation time of matching or testing line ( t m = 0.2 1     s ) ; t ans , time needed to answer; t rad , readaptation time ( t rad = 10 s ) . In the course of the experiment dealing with the normalization phenomenon, the time of the displaying of the adapting lines is imaged by the shadow rectangle.

Fig. 3
Fig. 3

Assessment of perceived orientation after prolonged viewing of the line tilted by 10 ° from vertical (for clarity all angles between lines are enlarged). (a) l ϕ a , true adapting line; l perc , perceived adapting line. (b) All matching (testing) lines are generated within the range spanned by the heavy dotted lines; continuous line represents the adapting line l ϕ a , which divides the range into two equal sectors (gray and white). Perceived adapting line ( l perc ) is rotated clockwise and is represented by the dotted line, which divides the range into two unequal parts. The counterclockwise sector is larger as compared with the sector oriented clockwise from the l perc line.

Fig. 4
Fig. 4

Number of “rotated clockwise” responses ( R c ) or relative “rotated clockwise” frequency ( f c ) versus adapting line orientation in degrees. Vertical bars, 95 % confidence interval. For more detail, see the text.

Fig. 5
Fig. 5

Maximal value of the TAE in degrees versus the test line orientation for three subjects (indicated by the different patterns). The 99% confidence intervals are designated by the vertical bars.

Fig. 6
Fig. 6

Influence of adaptation on the perception of the orientation of the vertical line which follows the adapting one. The abscissa represents the adapting line orientation (degrees). The ordinate represents the difference between the true vertical test line orientation (0°) and the perceived orientation (degrees) of the vertical line after adaptation. Dashed curve is derived from the vector model. The other two curves represent experimental data obtained by Gibson [1] (continuous curve); Campbell, Maffei [5] (dashed–dotted curve).

Fig. 7
Fig. 7

Cumulative influence of simultaneous interaction and adaptation on the perceived orientation of the testing line. The calculated distortions caused by the simultaneous interaction (lateral inhibition) versus the value of the angle Δ ϕ are shown by the dashed curve . The calculated distortion (or value of theTAE) resulting from the adaptation versus Δ ϕ angle is figured by the dotted–dashed curve. The calculated general distortions of the vertical line orientation versus ( Δ ϕ ) are pictured by the light solid curve. The experimental data for one of subjects are depicted by the heavy solid curve.

Equations (11)

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x 1 ( ϕ ) = cos 2 ( ϕ + 22.5 ° ) and x 2 ( ϕ ) = sin 2 ( ϕ + 22.5 ° )     o r
x 1 ( ϕ ) = cos ( 2 ϕ + 45 ° ) and x 2 ( ϕ ) = sin ( 2 ϕ + 45 ° ) .
z j ( ϕ ) = { i = 1 2 c j i x i ( ϕ ) = p , if p 0 0 , if p 0 } .. .
z j ( ϕ ) = ( C j E ( ϕ ) ) = C j E ( ϕ ) cos [ C j , E ( ϕ ) ] , if z j ( ϕ ) 0 .
x 1 ( ϕ a ) = x 2 ( ϕ a ) ,
x i ( ϕ a ) 0 , then x j ( ϕ a ) = 0 ,
a i j = { B exp ( γ x i ( ϕ a ) t ) if i = j 0 if i j , } ,
B exp ( x i ( ϕ a ) t ) E ( ϕ a ) = λ E ( ϕ a ) ,
cos Δ Ψ = ( 1 + α 2 ) cos 2 ( Δ ϕ ) 2 α 1 2 α cos 2 Δ ϕ + α 2 ,
Δ 12 = E 12 ( ϕ 1 ) , E 21 ( ϕ 2 ) ( ϕ 1 ϕ 2 ) .
z 1 ( ϕ 1 ϕ ) = 1 α cos 2 ( ϕ 1 ϕ ) .

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