Abstract

We report the results of psychophysical experiments on color contrast induction. In earlier work [ Vision Res. 34, 3111 ( 1994)], we showed that modulating the spatial contrast of an annulus in time induces an apparent modulation of the contrast of a central disk, at isoluminance. Here we vary the chromatic properties of disk and annulus systematically in a study of the interactions among the luminance and the color-opponent channels. Results show that induced contrast depends linearly on both disk and annulus contrast, at low and moderate contrast levels. This dependence leads us to propose a bilinear model for color contrast gain control. The model predicts the magnitude and the chromatic properties of induced contrast. In agreement with experimental results, the model displays chromatic selectivity in contrast gain control and a negligible effect of contrast modulation at isoluminance on the appearance of achromatic contrast. We show that the bilinear model for chromatic selectivity may be realized as a feed-forward multiplicative gain control. Data collected at high contrast levels are fit by embellishing the model with saturating nonlinearities in the contrast gain control of each color channel.

© 1995 Optical Society of America

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  1. A. Kirschmann, “Ueber die quantitativen Verhältnisse des simultanen Helligkeits- und Farben-Contrastes,” Philos. Studien 6, 391–417 (1890).
  2. D. Jameson, L. M. Hurvich, “Opponent chromatic induction: experimental evaluation and theoretical account,” J. Opt. Soc. Am. 51, 46–53 (1961).
    [CrossRef] [PubMed]
  3. B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
    [CrossRef] [PubMed]
  4. E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. (USA) 80, 5163–5169 (1983).
    [CrossRef]
  5. J. J. McCann, “The role of simple nonlinear operations in modelling human lightness and color sensations,” in Human Vision, Visual Processing and Digital Display, B. E. Rogowitz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1077, 355–363 (1989).
    [CrossRef]
  6. R. O. Brown, D. I. A. MacLeod, “Saturation and color constancy,” in Advances in Color Vision, Vol. 4 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 110–111.
  7. K.-H. Bäuml, “Color appearance: the effect of illuminant changes on different surface collections,” J. Opt. Soc. Am. A 11, 531–542 (1994).
    [CrossRef]
  8. J. W. Jenness, S. K. Shevell, “Color appearance with sparse chromatic context,” Vision Res. (to be published).
    [PubMed]
  9. C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. (USA) 86, 9631–9635 (1989).
    [CrossRef]
  10. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [CrossRef] [PubMed]
  11. D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
    [CrossRef] [PubMed]
  12. J. Krauskopf, D. R. Williams, D. M. Heeley, “The cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
    [CrossRef]
  13. J. Krauskopf, Q. Zaidi, M. B. Mandler, “Mechanisms of simultaneous color induction,” J. Opt. Soc. Am. A 3, 1752–1757 (1986).
    [CrossRef] [PubMed]
  14. J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2683 (1993).
    [CrossRef] [PubMed]
  15. M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
    [CrossRef]
  16. M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on colour appearance,” Vision Res. 34, 1993–2020 (1994).
    [CrossRef] [PubMed]
  17. M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: inhibitory effects among grating patterns of different spatial frequencies, spatial positions and orientations,” Vision Res. 31, 1985–1998 (1991).
    [CrossRef] [PubMed]
  18. D. H. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 171–186.
  19. C. M. Cicerone, D. H. Krantz, J. Larimer, “Opponent-process additivity—III. Effect of moderate chromatic adaptation,” Vision Res. 15, 1125–1135 (1975).
    [CrossRef]
  20. J. Wei, S. K. Shevell, “Color appearance under chromatic adaptation varied along theoretically significant directions in color space,” J. Opt. Soc. Am. A 12, 36–46 (1995).
    [CrossRef]
  21. D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef] [PubMed]
  22. M. D’Zmura, “Color constancy: surface color from changing illumination,” J. Opt. Soc. Am. A 9, 490–493 (1992).
    [CrossRef]
  23. M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
    [CrossRef]
  24. M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
    [CrossRef]
  25. M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
    [CrossRef]
  26. G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
    [CrossRef]
  27. D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
    [CrossRef]
  28. B. Singer, M. D’Zmura, G. Iverson, D. J. Lewis, L. Dinh, “A bilinear model for color contrast induction,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).
  29. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).
  30. S. Ishihara, The Series of Plates Designed as a Test for Colour-Blindness (Kanehara, Tokyo, 1986).
  31. W. H. Greub, Multilinear Algebra (Springer, New York, 1967).
    [CrossRef]
  32. J. von Kries, “Influence of adaptation on the effects produced by luminous stimuli,” in Handbuch der Physiologie de Menschen (1905), Vol. 3, pp. 109–282;in Sources of Color Vision, D. L. MacAdam, ed. (MIT Press, Cambridge, Mass., 1970).
  33. M. D’Zmura, “Color in visual search,” Vision Res. 31, 951–966 (1991).
    [CrossRef]
  34. J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher-order color mechanisms,” Vision Res. 26, 23–32 (1986).
    [CrossRef]
  35. M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
    [CrossRef]
  36. P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
    [PubMed]
  37. J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color processing?” Vision Res. 33, 123–129 (1993).
    [CrossRef] [PubMed]
  38. Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
    [PubMed]
  39. J. G. Robson, “Linear and non-linear operations in the visual system,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 117 (1988).
  40. M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).
  41. K. R. Gegenfurtner, “praxis: Brent’s algorithm for function minimization,” Behav. Res. Meth. Instrum. Comput. 24, 560–564 (1993).
    [CrossRef]

1995 (1)

1994 (6)

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on colour appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

K.-H. Bäuml, “Color appearance: the effect of illuminant changes on different surface collections,” J. Opt. Soc. Am. A 11, 531–542 (1994).
[CrossRef]

M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
[CrossRef]

B. Singer, M. D’Zmura, G. Iverson, D. J. Lewis, L. Dinh, “A bilinear model for color contrast induction,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).

1993 (6)

K. R. Gegenfurtner, “praxis: Brent’s algorithm for function minimization,” Behav. Res. Meth. Instrum. Comput. 24, 560–564 (1993).
[CrossRef]

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color processing?” Vision Res. 33, 123–129 (1993).
[CrossRef] [PubMed]

Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
[PubMed]

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2683 (1993).
[CrossRef] [PubMed]

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[CrossRef]

M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
[CrossRef]

1992 (3)

1991 (3)

M. D’Zmura, “Color in visual search,” Vision Res. 31, 951–966 (1991).
[CrossRef]

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
[CrossRef]

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: inhibitory effects among grating patterns of different spatial frequencies, spatial positions and orientations,” Vision Res. 31, 1985–1998 (1991).
[CrossRef] [PubMed]

1990 (1)

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

1989 (2)

G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
[CrossRef]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. (USA) 86, 9631–9635 (1989).
[CrossRef]

1988 (1)

J. G. Robson, “Linear and non-linear operations in the visual system,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 117 (1988).

1986 (3)

1984 (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

1983 (1)

E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. (USA) 80, 5163–5169 (1983).
[CrossRef]

1982 (1)

J. Krauskopf, D. R. Williams, D. M. Heeley, “The cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

1979 (1)

1975 (2)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

C. M. Cicerone, D. H. Krantz, J. Larimer, “Opponent-process additivity—III. Effect of moderate chromatic adaptation,” Vision Res. 15, 1125–1135 (1975).
[CrossRef]

1961 (1)

1905 (1)

J. von Kries, “Influence of adaptation on the effects produced by luminous stimuli,” in Handbuch der Physiologie de Menschen (1905), Vol. 3, pp. 109–282;in Sources of Color Vision, D. L. MacAdam, ed. (MIT Press, Cambridge, Mass., 1970).

1890 (1)

A. Kirschmann, “Ueber die quantitativen Verhältnisse des simultanen Helligkeits- und Farben-Contrastes,” Philos. Studien 6, 391–417 (1890).

Atick, J. J.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color processing?” Vision Res. 33, 123–129 (1993).
[CrossRef] [PubMed]

Bäuml, K.-H.

Boynton, R. M.

Brainard, D. H.

D. H. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 171–186.

Brown, A. M.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher-order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef]

Brown, R. O.

R. O. Brown, D. I. A. MacLeod, “Saturation and color constancy,” in Advances in Color Vision, Vol. 4 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 110–111.

Cannon, M. W.

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: inhibitory effects among grating patterns of different spatial frequencies, spatial positions and orientations,” Vision Res. 31, 1985–1998 (1991).
[CrossRef] [PubMed]

Chubb, C.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2683 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. (USA) 86, 9631–9635 (1989).
[CrossRef]

Cicerone, C. M.

C. M. Cicerone, D. H. Krantz, J. Larimer, “Opponent-process additivity—III. Effect of moderate chromatic adaptation,” Vision Res. 15, 1125–1135 (1975).
[CrossRef]

D’Zmura, M.

Derrington, A. M.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Din, L.

M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).

Dinh, L.

B. Singer, M. D’Zmura, G. Iverson, D. J. Lewis, L. Dinh, “A bilinear model for color contrast induction,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

Fullenkamp, S. C.

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: inhibitory effects among grating patterns of different spatial frequencies, spatial positions and orientations,” Vision Res. 31, 1985–1998 (1991).
[CrossRef] [PubMed]

Gegenfurtner, K. R.

K. R. Gegenfurtner, “praxis: Brent’s algorithm for function minimization,” Behav. Res. Meth. Instrum. Comput. 24, 560–564 (1993).
[CrossRef]

Greub, W. H.

W. H. Greub, Multilinear Algebra (Springer, New York, 1967).
[CrossRef]

Heeger, D. J.

D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
[CrossRef]

Heeley, D. M.

J. Krauskopf, D. R. Williams, D. M. Heeley, “The cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

Hurvich, L. M.

Ishihara, S.

S. Ishihara, The Series of Plates Designed as a Test for Colour-Blindness (Kanehara, Tokyo, 1986).

Iverson, G.

Jameson, D.

Jenness, J. W.

J. W. Jenness, S. K. Shevell, “Color appearance with sparse chromatic context,” Vision Res. (to be published).
[PubMed]

Kim, J.

M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).

Kirschmann, A.

A. Kirschmann, “Ueber die quantitativen Verhältnisse des simultanen Helligkeits- und Farben-Contrastes,” Philos. Studien 6, 391–417 (1890).

Krantz, D. H.

C. M. Cicerone, D. H. Krantz, J. Larimer, “Opponent-process additivity—III. Effect of moderate chromatic adaptation,” Vision Res. 15, 1125–1135 (1975).
[CrossRef]

Krauskopf, J.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

J. Krauskopf, Q. Zaidi, M. B. Mandler, “Mechanisms of simultaneous color induction,” J. Opt. Soc. Am. A 3, 1752–1757 (1986).
[CrossRef] [PubMed]

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher-order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef]

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

J. Krauskopf, D. R. Williams, D. M. Heeley, “The cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

Land, E. H.

E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. (USA) 80, 5163–5169 (1983).
[CrossRef]

Larimer, J.

C. M. Cicerone, D. H. Krantz, J. Larimer, “Opponent-process additivity—III. Effect of moderate chromatic adaptation,” Vision Res. 15, 1125–1135 (1975).
[CrossRef]

Lennie, P.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
[CrossRef]

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Lewis, D. J.

B. Singer, M. D’Zmura, G. Iverson, D. J. Lewis, L. Dinh, “A bilinear model for color contrast induction,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

Lewis, J.

M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).

Li, Z.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color processing?” Vision Res. 33, 123–129 (1993).
[CrossRef] [PubMed]

MacLeod, D. I. A.

D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
[CrossRef] [PubMed]

R. O. Brown, D. I. A. MacLeod, “Saturation and color constancy,” in Advances in Color Vision, Vol. 4 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 110–111.

Mandler, M. B.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher-order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef]

J. Krauskopf, Q. Zaidi, M. B. Mandler, “Mechanisms of simultaneous color induction,” J. Opt. Soc. Am. A 3, 1752–1757 (1986).
[CrossRef] [PubMed]

Marimont, D. H.

McCann, J. J.

J. J. McCann, “The role of simple nonlinear operations in modelling human lightness and color sensations,” in Human Vision, Visual Processing and Digital Display, B. E. Rogowitz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1077, 355–363 (1989).
[CrossRef]

Mollon, J. D.

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on colour appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
[CrossRef]

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Redlich, A. N.

J. J. Atick, Z. Li, A. N. Redlich, “What does post-adaptation color appearance reveal about cortical color processing?” Vision Res. 33, 123–129 (1993).
[CrossRef] [PubMed]

Robson, J. G.

J. G. Robson, “Linear and non-linear operations in the visual system,” Invest. Ophthalmol. Vis. Sci. Suppl. 29, 117 (1988).

Sclar, G.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

Shapiro, A. G.

Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
[PubMed]

Shevell, S. K.

Singer, B.

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

B. Singer, M. D’Zmura, G. Iverson, D. J. Lewis, L. Dinh, “A bilinear model for color contrast induction,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, 1656 (1994).

M. D’Zmura, B. Singer, L. Din, J. Kim, J. Lewis, “Spatial sensitivity of contrast induction mechanisms,” Opt. Photon. News 5, Suppl. 48 (1994).

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Solomon, J. A.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2683 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. (USA) 86, 9631–9635 (1989).
[CrossRef]

Sperling, G.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2683 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. (USA) 86, 9631–9635 (1989).
[CrossRef]

G. Sperling, “Three stages and two systems of visual processing,” Spatial Vision 4, 183–207 (1989).
[CrossRef]

von Kries, J.

J. von Kries, “Influence of adaptation on the effects produced by luminous stimuli,” in Handbuch der Physiologie de Menschen (1905), Vol. 3, pp. 109–282;in Sources of Color Vision, D. L. MacAdam, ed. (MIT Press, Cambridge, Mass., 1970).

Wandell, B. A.

D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
[CrossRef] [PubMed]

D. H. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 171–186.

Webster, M. A.

M. A. Webster, J. D. Mollon, “The influence of contrast adaptation on colour appearance,” Vision Res. 34, 1993–2020 (1994).
[CrossRef] [PubMed]

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
[CrossRef]

Wei, J.

Williams, D. R.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher-order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef]

J. Krauskopf, D. R. Williams, D. M. Heeley, “The cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef]

Zaidi, Q.

Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
[PubMed]

J. Krauskopf, Q. Zaidi, M. B. Mandler, “Mechanisms of simultaneous color induction,” J. Opt. Soc. Am. A 3, 1752–1757 (1986).
[CrossRef] [PubMed]

Behav. Res. Meth. Instrum. Comput. (1)

K. R. Gegenfurtner, “praxis: Brent’s algorithm for function minimization,” Behav. Res. Meth. Instrum. Comput. 24, 560–564 (1993).
[CrossRef]

Biol. Cybern. (1)

Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
[PubMed]

Handbuch der Physiologie de Menschen (1)

J. von Kries, “Influence of adaptation on the effects produced by luminous stimuli,” in Handbuch der Physiologie de Menschen (1905), Vol. 3, pp. 109–282;in Sources of Color Vision, D. L. MacAdam, ed. (MIT Press, Cambridge, Mass., 1970).

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Figures (9)

Fig. 1
Fig. 1

Stimulus spatial properties. A central disk with a diameter of 2 deg of visual angle and an annulus with a diameter of 8 deg were filled with binary noise. The stimulus was centered on a gray rectangular background that was 16 deg high by 20 deg wide. See text for further details.

Fig. 2
Fig. 2

Stimulus chromatic properties. At left is depicted the time-varying contrast modulation of an annulus at 1 Hz (solid curves, Inducing) with mean contrast and contrast modulation along the S-cone axis. The dotted curves (Induced) depict the induced modulation in the appearance of a physically steady central disk, also with chromaticities along the S-cone axis. The dashed curves (Nulling) indicate the physical modulation of disk contrast that is needed to make the disk appear steady.

Fig. 3
Fig. 3

Dependence of contrast induction on annulus contrast modulation. Panels in the left, middle, and right columns describe results with annuli along the achromatic, L&M-cone, and S-cone axes, respectively. Panels in the top, middle, and bottom rows describe results with disks along the achromatic, L&M-cone, and S-cone axes, respectively. Along each horizontal axis varies the amplitude of the annulus contrast modulation. Along each vertical axis varies the amplitude of the disk contrast modulation that is needed to null the induced modulation. Units of measurement are specific to each axis: we use standard contrast units along the achromatic axis, contrast to L cones along the L&M-cone axis, and contrast to S cones along the S-cone axis. Each data point represents results averaged across the three observers JC, JL, and BS; error bars represent estimates of the standard error of the mean. Lines are fitted to the data with slope as the only parameter. Data points marked by open circles are excluded from the fits. See text for details.

Fig. 4
Fig. 4

Dependence of contrast induction on disk mean contrast. The format is like that of Fig. 3; results are for the three observers JC, JL, and BS. Panels in the left, middle, and right columns describe results with disks along the achromatic, L&M-cone, and S-cone axes, respectively. Panels in the top, middle, and bottom rows describe results with annuli along the achromatic, L&M-cone, and S-cone axes, respectively. See text for details.

Fig. 5
Fig. 5

Results with horizontally oriented sinusoids at 2 cycles/deg (filled bars) and with binary spatial noise (open bars) for observers LD, JH, JL, and BS. A, B, and C show average nulling contrast modulations for achromatic, L&M-cone, and S-cone disks, respectively. The color-space axis of the annulus varies across the bottom of each panel. The numbers in parentheses at the tops of the columns are the scale factors that are needed to turn these nulling modulations, expressed in terms of contrast to appropriate cone mechanisms, into the bilinear model matrix entries of Table 3 (fourth and fifth columns). See text for details.

Fig. 6
Fig. 6

Vector fields of nulling modulations that are predicted by the bilinear model of Eq. (5) specified in the second column of Table 3. Each circle represents a portion of a color plane spanned by two cardinal axes of color space, indicated at the top and at the side of each circle. The circle marks the 40% levels of maximum displayable contrast along each of the panel’s cardinal axes; the tick marks represent 10% steps of maximum displayable contrast. The maximum displayable levels are 100% contrast along the achromatic axis, 8.2% contrast to L cones along the L&M-cone axis, and 86% contrast to S cones along the S-cone axis. Each vector shows the null predicted for the disk, with contrast marked by the base of the vector. The color-space axis of the annulus is indicated either by inward-pointing arrows at the circle circumference, in cases in which the cardinal axis of the annulus lies in the disk plane, or by circles at the center of the diagram, in cases in which the annulus axis is perpendicular to the disk color plane. Predictions are shown in A, B, and C for the effects of achromatic, L&M-cone-, and S-cone-axis modulations, respectively, on disks in the isoluminant plane; D, E, and F for the effects of achromatic, L&M-cone-, and S-cone-axis modulations, respectively, on disks in the plane spanned by achromatic and L&M-cone axes; and in G, H, and I for the effects of achromatic, L&M-cone-, and S-cone-axis modulations, respectively, on disks in the plane spanned by achromatic and S-cone axes. In generating these predictions, we set the annulus mean contrast to 30% and annulus contrast modulation to 20% of the corresponding maximum displayable contrasts. See text for details.

Fig. 7
Fig. 7

Dependence of contrast induction on annulus mean contrast. The format is like that of Fig. 3; results are for the three observers JC, JL, and BS. At the lowest annulus mean contrasts, using achromatic annuli and isoluminant disks (D and G), observer JL obtained nulls far in excess of those for the other two observers. In these conditions observer JL’s data are shown as open symbols in parentheses and are excluded from the fits, whereas the normal, filled data points at 20% annulus mean contrast levels refer to the average results for the other two observers. The dashed lines are the predictions of the bilinear model with parameters taken from the experiment on the effects of annulus contrast modulation (Fig. 3 and Table 3, column 2). The solid curves are the fits to the data of a bilinear model with saturating nonlinearities. See text for details.

Fig. 8
Fig. 8

Feed-forward matrix-multiplicative contrast gain control with saturating nonlinearities. An illustrative first stage (top) includes three cone mechanisms that undergo von Kries adaptation. A linear transformation characterizes the second-stage mechanisms in terms of responses along achromatic (A), L&M cone-, (L&M) and S-cone (S) axis dimensions. These responses d = [d1 d2 d3]T at a central position are multiplied by factors determined by the contrast gain control (bottom) to produce the normalized responses d′. The local contrast in each channel’s response ri(x) is pooled according to a pooling function W(x). Contrast is determined by full-wave rectification of a second-stage mechanism’s response. The local surround’s contrast a = [a1 a2 a3]T is then multiplied by bilinear model matrix entries and fed to each of the color channels, where appropriate sums are taken to form the quantities m = [m1 m2 m3]T of Eq. (14). Saturating nonlinearities N act on the cross-channel connections before summation. We subtract the resulting sum for each channel from 1 to determine the channel’s normalization factor 1 − mj for j = 1, 2, 3. See text for details.

Fig. 9
Fig. 9

Saturating nonlinearities. We use nonlinearities with an initial slope of 1 that are intermediate to the soft exponential 1 − exp(−t) and the hard nonlinearity described by the line segments. The medium nonlinearities that we use splice together a straight-line segment for input values less than or equal to some constant c and a doubly exponential function with an initial slope of 1 for input values greater than c [Eqs. (A3)]. See text and Appendix A for details.

Tables (4)

Tables Icon

Table 1 Slopes of Lines Fitted to the Data in Fig. 3 and Goodness of Fit for the Average of the Observers

Tables Icon

Table 2 Slopes of Lines Fitted to the Data in Fig. 4 and Goodness of Fit

Tables Icon

Table 3 Bilinear Model Parametersa

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Table 4 Parameters c and rmax of the Saturating Nonlinearities Used to Fit the Data in Fig. 7

Equations (23)

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D ( x , t ) = w + b D ( x ) [ d + δ sin ( 2 π t ) ] ,
A ( x , t ) = w + b A ( x ) [ a m + α sin ( 2 π t ) ] ,
B ( c 1 d 1 + c 2 d 2 , α ) = c 1 B ( d 1 , α ) + c 2 B ( d 2 , α )
B ( d , e 1 α 1 + e 2 α 2 ) = e 1 B ( d , α 1 ) + e 2 B ( d , α 2 ) ;
ν k = j = 1 3 i = 1 3 d j ( B j ) k i α i for k = 1 , 2 , 3 ,
[ ν 1 ν 2 ν 3 ] = { d 1 [ b 111 b 112 b 113 b 121 b 122 b 123 b 131 b 132 b 133 ] + d 2 [ b 211 b 212 b 213 b 221 b 222 b 223 b 231 b 232 b 233 ] { + d 3 [ b 311 b 312 b 313 b 321 b 322 b 323 b 331 b 332 b 333 ] } [ α 1 α 2 α 3 ] .
[ ν 1 ν 2 ν 3 ] = { d 1 [ b 111 b 112 b 113 0 0 0 0 0 0 ] + d 2 [ 0 0 0 b 221 b 222 b 223 0 0 0 ] { + d 3 [ 0 0 0 0 0 0 b 331 b 332 b 333 ] } [ α 1 α 2 α 3 ] .
ν k = i = 1 3 j = 1 3 α i ( B i ) k j d j for k = 1 , 2 , 3 .
[ ν 1 ν 2 ν 3 ] = { α 1 [ b 111 0 0 0 b 221 0 0 0 b 331 ] + α 2 [ b 112 0 0 0 b 222 0 0 0 b 332 ] { + α 3 [ b 113 0 0 0 b 223 0 0 0 b 333 ] } [ d 1 d 2 d 3 ] ,
a ( t ) = a m + α ( t ) .
ν ( t ) = B [ d , a ( t ) ] = B [ d , a m + α ( t ) ] .
ν ( t ) = B [ d , a m ] + B [ d , α ( t ) ] .
ν ( t ) B [ d , a m ] = B [ d , α ( t ) ] .
ν = ( a 1 B 1 + a 2 B 2 + a 3 B 3 ) d .
d = d ν
d = ( I M ) d ,
m 11 = a 1 b 11 + a 2 b 12 + a 3 b 13 , m 22 = a 1 b 21 + a 2 b 22 + a 3 b 23 , m 33 = a 1 b 31 + a 2 b 32 + a 3 b 33 .
[ d 1 d 2 d 3 ] = [ 1 m 1 0 0 0 1 m 2 0 0 0 1 m 3 ] [ d 1 d 2 d 3 ] .
a i = W ( x ) | r i ( x ) | d x for i = 1 , 2 , 3 .
n j i = N j i ( a i b j i ) for i , j = 1 , 2 , 3 .
m j = i = 1 3 n j i = i = 1 3 N j i ( a i b j i ) for j = 1 , 2 , 3 .
n j i = N j i ( a i b j i ) = a i b j i for a i b j i c j i , n j i = c j i + ( r max , j i c j i ) × ( 1 exp { [ exp ( a i b j i c j i ) 1 ] ( r max , j i c j i ) } ) for a i b j i > c j i .
ν ( a m , α ) = d ( a m ) d ( a m + α ) = ( I M ( a m ) ] d [ I M ( a m + α ) ] d = M ( a m + α ) d M ( a m ) d = { [ m 1 ( a m + α ) 0 0 0 m 2 ( a m + α ) 0 0 0 m 3 ( a m + α ) ] { [ m 1 ( a m ) 0 0 0 m 2 ( a m ) 0 0 0 m 3 ( a m ) ] } d ,

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