Abstract

Spectral efficiency functions and tests of additivity were obtained with three observers to identify possible chromatic contributions to spatially induced blackness. Stimuli consisted of a series of monochromatic (400–700 nm; 10-nm steps), 52-arcmin circular test lights surrounded by broadband (x=0.31, y=0.37), 63–138-arcmin annuli of fixed retinal illuminance. The stimuli were imaged on the fovea in Maxwellian view as 500-ms flashes with 10-s interstimulus intervals. Observers decreased the intensity of the test center until it was first perceived as completely black. Action spectra determined for two surround levels [2.5 and 3.5 log trolands] had three sensitivity peaks (at approximately 440, 540, and 600 nm). However, when monochromatic surrounds were adjusted to induce blackness in a broadband center, action spectra were unimodal and identical to functions obtained by heterochromatic flicker photometry. Tests of additivity revealed that when blackness is induced by a broadband surround into a bichromatic center, there is an additivity failure of the cancellation type. This additivity failure indicates that blackness induction is influenced, in part, by signals from opponent-chromatic pathways. A quantitative model is presented to account for these data. This model assumes that blackness induction is determined by the ratio of responses to the stimulus center and the annulus, and while signals from the annulus are based only on achromatic information, responses from the center are based on both chromatic and achromatic properties of the stimulus.

© 1997 Optical Society of America

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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef]
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    [PubMed]
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  56. In their model L-, M-, and S-cone sensitivities are normalized to unity at each λmax. Thus 4L+2M in their equation is close to L+M in this paper’s equation given the use of Smith and Pokorny’s normalization. (Ref. 33).

1996 (1)

L. Spillmann, J. S. Werner, “Long-range interactions in visual perception,” Trends Neurosci. 19, 428–434 (1996).
[PubMed]

1994 (1)

1993 (2)

R. L. DeValois, K. K. DeValois, “A multi-stage color model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef]

P. Heggelund, “Simultaneous luminance contrast with chromatic colors,” Vision Res. 33, 1709–1722 (1993).
[CrossRef] [PubMed]

1992 (4)

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

D. J. Heeger, “Half-squaring in responses of cat striate cells,” Visual Neurosci. 9, 427–443 (1992).
[PubMed]

K. Shinomori, Y. Nakano, K. Uchikawa, “The measurement of blackness on chromatic central field induced by achromatic surround field,” Kagaku (Tokyo) 21, 303–310 (1992).

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

1991 (3)

O. D. Creutzfeldt, J. M. Crook, S. Kastner, C-Y Li, X. Pei, “The neurophysiological correlates of colour and brightness contrast in lateral geniculate neurons,” Exp. Brain Res. 87, 3–21 (1991).

W. S. Geisler, D. G. Albrecht, R. J. Salvi, S. S. Saunders, “Discrimination performance of single neurons: rate and temporal-pattern information,” J. Neurophysiol. 66, 334–361 (1991).
[PubMed]

H. G. Sperling, A. A. Wright, S. L. Mills, “Color vision following intense green light exposure: data and model,” Vision Res. 31, 1797–1812 (1991).
[CrossRef]

1990 (1)

1989 (1)

1988 (2)

Y. Nakano, M. Ikeda, P. K. Kaiser, “Contributions of the opponent mechanisms to brightness and nonlinear models,” Vision Res. 28, 799–810 (1988).
[CrossRef] [PubMed]

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” CRC Critical Rev. Neurobiol. 3, 333–340 (1988).
[PubMed]

1986 (4)

C. M. Cicerone, V. J. Volbrecht, S. K. Donnelly, J. S. Werner, “Perception of blackness,” J. Opt. Soc. Am. A 3, 432–436 (1986).
[CrossRef] [PubMed]

K. Fuld, T. A. Otto, C. W. Slade, “Spectral responsivity of the white–black channel,” J. Opt. Soc. Am. A 3, 1182–1188 (1986).
[CrossRef] [PubMed]

M. Ikeda, Y. Nakano, “The Stiles summation index applied to heterochromatic brightness matching,” Perception 15, 765–776 (1986).
[PubMed]

L. O. Harvey, “Efficient estimation of sensory thresholds,” Behav. Res. Methods Instrum. Comput. 18, 623–632 (1986).

1985 (2)

K. Fuld, T. A. Otto, “Colors of monochromatic lights that vary in contrast-induced brightness,” J. Opt. Soc. Am. A 2, 76–83 (1985).
[CrossRef] [PubMed]

C. R. Ingling, E. Martinez-Uriegas, “The spatiotemporal properties of the r–g X-cell channel,” Vision Res. 25, 33–38 (1985).
[CrossRef]

1984 (2)

J. S. Werner, C. M. Cicerone, R. Kliegl, D. DellaRosa, “Spectral efficiency of blackness induction,” J. Opt. Soc. Am. A 1, 981–986 (1984).
[CrossRef] [PubMed]

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

1983 (1)

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

1982 (1)

1980 (1)

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[CrossRef]

1979 (2)

1976 (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]

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. II. Yellow/blue equilibria and nonlinear models,” Vision Res. 15, 723–731 (1975).
[CrossRef] [PubMed]

1974 (1)

D. V. Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef] [PubMed]

1972 (1)

1971 (2)

H. G. Sperling, R. S. Harwerth, “Red–green cone inter-actions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1971).
[CrossRef] [PubMed]

R. L. DeValois, P. L. Pease, “Contours and contrast: responses of monkey lateral geniculate nucleus to luminance and color figures,” Science 171, 694–696 (1971).
[CrossRef]

1969 (2)

R. M. Evans, B. K. Swenholt, “Chromatic strength of colors, III. Chromatic surrounds and discussion,” J. Opt. Soc. Am. 59, 628–634 (1969).
[CrossRef] [PubMed]

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

1968 (2)

1967 (2)

1966 (1)

G. Westheimer, “The Maxwellian view,” Vision Res. 6, 669–682 (1966).
[CrossRef] [PubMed]

1957 (1)

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
[PubMed]

1955 (1)

1930 (1)

G. E. Müller, “Über die Farbenempfindungen,” Z. Psychol. Physiol. Sinnesorgane (Ergänzungsbd. Z. Psychol.) 17, 1–434 (1930).

1874 (2)

E. Hering, “Zur Lehre vom Lichtsinne. II. Über simultanen Lichtcontrast,” Sitzungsber. Kaiserl. Akad. Wiss. Wien Math.-Naturwiss. Kl. Abt. 3 68, 186–201 (1874).

E. Hering, “Zur Lehre vom Lichtsinne. IV. Über die sogenannte Intensität der Lichtempfindung und über die Empfindung des Schwarzen,” Sitzungsberg. Kaiserl. Akad. Wiss. Wien Math.-Naturwiss. Kl. Abt. 3 69, 85–104 (1874).

Abramov, I.

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

Akita, M.

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

Albrecht, D. G.

W. S. Geisler, D. G. Albrecht, R. J. Salvi, S. S. Saunders, “Discrimination performance of single neurons: rate and temporal-pattern information,” J. Neurophysiol. 66, 334–361 (1991).
[PubMed]

Bodinger, D. M.

Boynton, R. M.

Cicerone, C. M.

Comerford, J. P.

Cowey, A.

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

Creutzfeldt, O. D.

O. D. Creutzfeldt, J. M. Crook, S. Kastner, C-Y Li, X. Pei, “The neurophysiological correlates of colour and brightness contrast in lateral geniculate neurons,” Exp. Brain Res. 87, 3–21 (1991).

Crook, J. M.

O. D. Creutzfeldt, J. M. Crook, S. Kastner, C-Y Li, X. Pei, “The neurophysiological correlates of colour and brightness contrast in lateral geniculate neurons,” Exp. Brain Res. 87, 3–21 (1991).

D’Zmura, M.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” CRC Critical Rev. Neurobiol. 3, 333–340 (1988).
[PubMed]

Dean, A. F.

D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

DellaRosa, D.

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).

DeValois, K. K.

R. L. DeValois, K. K. DeValois, “A multi-stage color model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef]

DeValois, R. L.

R. L. DeValois, K. K. DeValois, “A multi-stage color model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef]

R. L. DeValois, P. L. Pease, “Contours and contrast: responses of monkey lateral geniculate nucleus to luminance and color figures,” Science 171, 694–696 (1971).
[CrossRef]

Donley, N. J.

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

Donnelly, S. K.

Evans, R. M.

Fuld, K.

Geisler, W. S.

W. S. Geisler, D. G. Albrecht, R. J. Salvi, S. S. Saunders, “Discrimination performance of single neurons: rate and temporal-pattern information,” J. Neurophysiol. 66, 334–361 (1991).
[PubMed]

Guth, S. L.

S. L. Guth, N. J. Donley, R. T. Marrocco, “On luminance additivity and related topics,” Vision Res. 9, 537–575 (1969).
[CrossRef] [PubMed]

Harvey, L. O.

L. O. Harvey, “Efficient estimation of sensory thresholds,” Behav. Res. Methods Instrum. Comput. 18, 623–632 (1986).

Harwerth, R. S.

H. G. Sperling, R. S. Harwerth, “Red–green cone inter-actions in the increment-threshold spectral sensitivity of primates,” Science 172, 180–184 (1971).
[CrossRef] [PubMed]

Heeger, D. J.

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

D. J. Heeger, “Half-squaring in responses of cat striate cells,” Visual Neurosci. 9, 427–443 (1992).
[PubMed]

Heggelund, P.

P. Heggelund, “Simultaneous luminance contrast with chromatic colors,” Vision Res. 33, 1709–1722 (1993).
[CrossRef] [PubMed]

Hering, E.

E. Hering, “Zur Lehre vom Lichtsinne. II. Über simultanen Lichtcontrast,” Sitzungsber. Kaiserl. Akad. Wiss. Wien Math.-Naturwiss. Kl. Abt. 3 68, 186–201 (1874).

E. Hering, “Zur Lehre vom Lichtsinne. IV. Über die sogenannte Intensität der Lichtempfindung und über die Empfindung des Schwarzen,” Sitzungsberg. Kaiserl. Akad. Wiss. Wien Math.-Naturwiss. Kl. Abt. 3 69, 85–104 (1874).

E. Hering, Outlines of a Theory of the Light Sense, L. M. Hurvich, D. Jameson, trans. (Harvard U. Press, Cambridge, Mass., 1964).

Hubel, D.

D. Hubel, M. Livingstone, “Color puzzles,” Cold Spring Harbor Symp. Quant. Biol.LV, 643–649 (1990).

Hurvich, L. M.

Ikeda, M.

Y. Nakano, M. Ikeda, P. K. Kaiser, “Contributions of the opponent mechanisms to brightness and nonlinear models,” Vision Res. 28, 799–810 (1988).
[CrossRef] [PubMed]

M. Ikeda, Y. Nakano, “The Stiles summation index applied to heterochromatic brightness matching,” Perception 15, 765–776 (1986).
[PubMed]

Ingling, C. R.

C. R. Ingling, E. Martinez-Uriegas, “The spatiotemporal properties of the r–g X-cell channel,” Vision Res. 25, 33–38 (1985).
[CrossRef]

Jameson, D.

Kaiser, P. K.

Kambe, N.

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[CrossRef]

Kastner, S.

O. D. Creutzfeldt, J. M. Crook, S. Kastner, C-Y Li, X. Pei, “The neurophysiological correlates of colour and brightness contrast in lateral geniculate neurons,” Exp. Brain Res. 87, 3–21 (1991).

Kliegl, R.

Krantz, D. H.

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. II. Yellow/blue equilibria and nonlinear models,” Vision Res. 15, 723–731 (1975).
[CrossRef] [PubMed]

Krauskopf, J.

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

Kulp, T. D.

Larimer, J.

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. II. Yellow/blue equilibria and nonlinear models,” Vision Res. 15, 723–731 (1975).
[CrossRef] [PubMed]

Lee, B. B.

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

Lennie, P.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” CRC Critical Rev. Neurobiol. 3, 333–340 (1988).
[PubMed]

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

Li, C-Y

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Livingstone, M.

D. Hubel, M. Livingstone, “Color puzzles,” Cold Spring Harbor Symp. Quant. Biol.LV, 643–649 (1990).

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

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V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

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Movshon, J. A.

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Pokorny, J.

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

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V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

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[CrossRef] [PubMed]

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H. G. Sperling, A. A. Wright, S. L. Mills, “Color vision following intense green light exposure: data and model,” Vision Res. 31, 1797–1812 (1991).
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[CrossRef] [PubMed]

Uchikawa, H.

Uchikawa, K.

Valberg, A.

V. C. Smith, B. B. Lee, J. Pokorny, P. R. Martin, A. Valberg, “Responses of macaque ganglion cells to the relative phase of heterochromatically modulated lights,” J. Physiol. (London) 458, 191–221 (1992).

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

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[CrossRef]

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E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

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K. Shinomori, Y. Nakano, K. Uchikawa, “The measurement of blackness on chromatic central field induced by achromatic surround field,” Kagaku (Tokyo) 21, 303–310 (1992).

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

H. G. Sperling, A. A. Wright, S. L. Mills, “Color vision following intense green light exposure: data and model,” Vision Res. 31, 1797–1812 (1991).
[CrossRef]

D. V. Norren, J. J. Vos, “Spectral transmission of the human ocular media,” Vision Res. 14, 1237–1244 (1974).
[CrossRef] [PubMed]

Y. Nakano, M. Ikeda, P. K. Kaiser, “Contributions of the opponent mechanisms to brightness and nonlinear models,” Vision Res. 28, 799–810 (1988).
[CrossRef] [PubMed]

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]

G. Westheimer, “The Maxwellian view,” Vision Res. 6, 669–682 (1966).
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Other (9)

In earlier versions of our modeling we introduced self-firing (Eigengrau) constants (Ref. 34) into our equations [mathematically equivalent to the constant value in Eq. (A4)] because, as Hering (Refs. 6-8) and Mach (Ref. 9) observed, some BI may result even in the absence of an annulus and a center. However, we found that when we applied various models to our data, the values of these constants were quite small, and thus this type of noise was not needed to explain our data.

E. Zrenner, I. Abramov, M. Akita, A. Cowey, M. Livingstone, A. Valberg, “Color perception. Retina to cortex,” in Visual Perception. The Neurophysiological Foundations, L. Spillmann, J. S. Werner, eds. (Academic, San Diego, Calif., 1990), pp. 163–204.

The CIE 1976 (u′, v′) uniform color space was originally defined to represent surface color with CIE 1976 psychometric lightness L*, which can be calculated only for the light coming from the surface of an object. It is nevertheless commonplace to transform CIE (x, y) coordinates of a light source to (u′, v′) coordinates with the use of the equations u′=4x/(-2x+12y+3) and v′=9y/(-2x+12y+3). For these calculations we used Vos’s (Ref. 30) color-matching functions.

J. J. Vos, Tabulated Characteristics of a Proposed 2° Fundamental Observer (Institute for Perception, Soesterberg, The Netherlands, 1978).

R. W. Rodieck, “Which cells code for color?” in From Pigments to Perception. Advances in Understanding Visual Processes, A. Valberg, B. B. Lee, eds. (Plenum, New York, 1991), pp. 83–93.

D. Hubel, M. Livingstone, “Color puzzles,” Cold Spring Harbor Symp. Quant. Biol.LV, 643–649 (1990).

E. Hering, Outlines of a Theory of the Light Sense, L. M. Hurvich, D. Jameson, trans. (Harvard U. Press, Cambridge, Mass., 1964).

E. Mach, The Analysis of Sensations and the Relation of the Physical to the Psychical, translated by C. M. Williams and revised by S. Waterlow (Dover, New York, 1959).

In their model L-, M-, and S-cone sensitivities are normalized to unity at each λmax. Thus 4L+2M in their equation is close to L+M in this paper’s equation given the use of Smith and Pokorny’s normalization. (Ref. 33).

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Figures (12)

Fig. 1
Fig. 1

Log reciprocal number of quanta per second in a monochromatic annulus required to induce blackness into a central broadband stimulus of 0.5 log td (filled circles) plotted as a function of wavelength. Error bars show ±1 standard deviation. Open squares show the log reciprocal number of quanta per second required to minimize flicker with the use of the surround portion of the stimulus as a function of wavelength. Dashed curves were fitted to the HFP data assuming a linear summation of M- and L-cone sensitivity and variable density of ocular media and macular pigment for each observer. Action spectra for blackness induction have been normalized to zero at 570 nm; HFP data and curves fitted to HFP have been vertically shifted for the best fit of HFP to blackness induction.

Fig. 2
Fig. 2

Log reciprocal number of quanta per second in a monochromatic center required to induce blackness when presented in a fixed-illuminance broadband annulus (triangles, 2.5 log td; circles, 3.5 log td) plotted as a function of wavelength. Error bars show ±1 standard deviation. Open squares show the log reciprocal number of quanta per second required to minimize flicker with the use of the central portion of the stimulus as a function of wavelength. Solid curves fitted to the blackness induction data are based on Eq. (2). Dashed curves were fitted to the HFP functions as described in Fig. 1. Action spectra for blackness induction with the 3.5-log td annulus have been normalized to zero at 570 nm. HFP data and the HFP theoretical function have been normalized with respect to the curves for blackness action spectra at 570 nm. Blackness data and the corresponding fitted function for a 2.5-log td broadband annulus were shifted upward by 1 log unit for presentation.

Fig. 3
Fig. 3

Log illuminance contrast (annulus/center) for a broadband annulus of 3.5 log td and a series of monochromatic centers that were adjusted to appear black. Error bars show ±1 standard deviation. Solid curves fitted to the data are based on Eq. (2).

Fig. 4
Fig. 4

Illuminance of the center or the annulus required for the spatial induction of blackness relative to a fixed illuminance of the annulus or the center, respectively. The wavelength of both the center and the surround was 570 nm. The method of adjustment procedure is represented by open circles and filled circles for adjustment of the annulus and the center, respectively. Results for the 2AFC staircase procedure are shown as open triangles and closed triangles for variations of the annulus and the center, respectively. Error bars denote ±1 standard deviation. Solid curves fitted to the data are based on Eq. (6).

Fig. 5
Fig. 5

CIE (u, v) coordinates of stimuli used to test additivity (based on in situ spectroradiometric measurement). Different symbols denote combinations of 450 and 570 nm (filled squares), 493 and 630 nm (filled diamonds), 450 and 650 nm (open triangles), and 510 and 630 nm (open circles). For (450 + 650)- and (510+630)-nm combinations the illuminance ratios were calculated for each observer (see the text for details). The coordinates of stimuli for the (510+630)-nm combination of observer KS are arbitrarily shifted upward by 0.1. The coordinates of stimuli for the (450+650)-nm combinations of observers KF and KS are shifted horizontally by 0.15 and 0.25, respectively.

Fig. 6
Fig. 6

Relative percentage sums for bichromatic mixtures in a central stimulus adjusted to appear black when presented in a broadband annulus (3.5 log td). Triangles, circles, and squares show results of combinations with 430, 530, and 650 nm, respectively. Combinations with the 430- and 650-nm addends are arbitrarily shifted upward by 100% and 200%, respectively. Open symbols denote controls in which two monochromatic lights of the same wavelength were added together. Error bars denote ±2 standard errors of the mean. Curves are model predictions from Eq. (2); horizontal portions passing through wavelengths of the control conditions denote predictions of perfect additivity.

Fig. 7
Fig. 7

Additivity tests of spatially induced blackness with a bichromatic mixture of 450 and 570 nm and an achromatic annulus of 3.5 log td. In each plot the percentage of 570-nm light is plotted as a function of the intensity percentage of 450-nm light. In these coordinates, although it is not shown, additivity is described by a diagonal line between (0, 100) and (100, 0). Error bars show ±1 standard deviation. Contours: model predictions; dotted lines: model 1 [Eq. (7)]; dashed lines: model 2 [Eq. (8)]; dotted–dashed lines: model 3 [Eq. (9)]; and solid lines: model 4 [Eq. (2)].

Fig. 8
Fig. 8

Results of additivity tests as in Fig. 7, but with 650-nm percentage plotted as a function of 450-nm percentage.

Fig. 9
Fig. 9

Results of additivity tests as in Fig. 7, but with 630-nm percentage plotted as a function of 493-nm percentage.

Fig. 10
Fig. 10

Results of additivity tests as in Fig. 7, but with 630-nm percentage plotted as a function of 510-nm percentage.

Fig. 11
Fig. 11

Scheme of model 4. Model 4 consists of a receptor level, three intermediary stages of signal processing, and a higher level. Receptor level: L, M, and S cones. First stage: L+M cells and 2M-L, L-2M, and S-(L+M) cells in the retina and the lateral geniculate nucleus. Second stage: rectification at the cortex. Third stage: antagonistic interaction between S-cone on-center receptive field (denoted as Son) and rectified L, M opponent responses (denoted as Ψ). Higher level: logarithmic transformation and a mechanism determining blackness appearance (BA). (See the text for details.)

Fig. 12
Fig. 12

Chromatic influence defined in terms of the illuminance of equal-energy white to the illuminance of the chromatic central test field at the blackness criterion calculated by model 4 [Eq. (2)] and the parameters in Table 3 plotted in CIE (u, v) coordinates. The numbers denote the value of the ratio for closed solid lines. Solid contours show lines of the same ratio in steps of unity. Dotted contours show lines of the same ratio in steps of 0.25. Open and filled circles in each plot denote the coordinates of equal-energy white and the theoretical minimum of chromatic influence, respectively. The inset at upper right shows active chromatic processes in various regions of color space. The solid line shows coordinates where the S-cone term in Eq. (2) is zero, and the dotted line shows coordinates where 2M-L and L - 2M terms are zero. Both lines appear as the change of orientation of contours in data figures. Wavelengths show the coordinates where local minima approximately appear in action spectra shown in Fig. 2.

Tables (4)

Tables Icon

Table 1 Log Illuminance Contrast (Annulus/Center Mean Across Wavelength ±1 Standard Deviation)

Tables Icon

Table 2 Parameter Values [Eq. (6), Fig. 4]

Tables Icon

Table 3 Parameter Values for Fits to Blackness Induction Data for a 3.5-Log-Td Annulus

Tables Icon

Table 4 Root-Mean-Square Error of Model Predictionsa

Equations (34)

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

[Iλ1(mix)/Iλ1(single)+Iλ2(mix)/Iλ2(single)]×100%=100%.
Fcenter(Lc, Mc, Sc)=ln((Lc+Mc)+Ψ+β|Sc-γ[(Lc+Mc)+Ψ]|),
Ψ=α12Mc-Lc+α2Lc-2Mc.
Fannulus(La, Ma)=ln(La+Ma).
BI=Fannulus(La, Ma)-ξFcenter(Lc, Mc, Sc)=ln(La+Ma){(Lc+Mc)+Ψ+β|Sc-γ[(Lc+Mc)+Ψ]|}ξ.
BA=1-exp[-(BI/p)-q].
Ic/(Ia)1/ξ=W.
Fcenter(Lc, Mc, Sc)=ln[(Lc+Mc)+α1pMc-Lc+α2Lc-pMc+βSc];
fFcenter(Lc, Mc, Sc)=ln[(Lc+Mc)+α12Mc-Lc+α2Lc-2Mc+β|Sc-γ(Lc+Mc)|];
Fcenter(Lc, Mc, Sc)=ln{(Lc+Mc)+|α1(Lc-2Mc)+β1[Sc-γ1(Lc+Mc)]|+|α2(Lc-2Mc)-β2[Sc-γ2(Lc+Mc)]|}.
ΔL[(L+M)+α|2M-L|+βS]=W,
ΔFcenter(L, M, S)=const=cΔL[(L+M)+α|2M-L|+βS],
Fcenter(L, M, S)=c1[(L+M)+α|2M-L|+βS]L.
Fcenter(L, M, S)=c[1/(1-α)]ln[(L+M)+α|2M-L|+βS]+const.
Fcenter(L, M, S)=ln[(L+M)+α|2M-L|+βS].
Fcenter(L, M, S)=ln[(L+M)+α1pM-L+α2L-pM+βS].
Fcenter(L, M, S)=ln[(L+M)+α12M-L+α2L-2M+β|S-γ(L+M)|].
Lo=L-kL(L+M),
Mo=M-kM(L+M),
So=S-kS(L+M),
Fcenter(L, M, S)=ln[(L+M)+β|S-γ(L+M)|],
R/Gchannel=α1Lo-2α1Mo+β1So=α1(L-2M)+β1[S-γ1(L+M)],
Y/Bchannel=α2Lo-2α2Mo-β2So=α2(L-2M)-β2[S-γ2(L+M)]
Fcenter(L, M, S)=ln{(L+M)+|α1(L-2M)+β1[S-γ1(L+M)]|+|α2(L-2M)-β2[S-γ2(L+M)]|},
Fcenter(L, M, S)=ln((L+M)+α12M-L+α2L-2M+β|[S-γ1(L+M)]-γ2(α12M-L+α2L-2M)|),
Fcenter(lc, mc, sc, Ic)=ln[IcΩ(lc, mc, sc)],
Ω(lc, mc, sc)=1+α12mc-lc+α2lc-2mc+β|sc-γ(1+α12mc-lc+α2lc-2mc)|.
lc=Lc/(Lc+Mc)=Lc/Ic,
mc=Mc/(Lc+Mc)=Mc/Ic,
sc=Sc/(Lc+Mc)=Sc/Ic.
BI=ln(Ia)-ξ ln(Ic)-ξ ln[Ω(lc, mc, sc)],
ln(Ic)-(1/ξ)ln(Ia)=const.
Ic/(Ia)1/ξ=W,
Ic=const./Ω(lc, mc, sc)

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