Abstract

By use of the haploscopic color-matching method, the colors induced by chromatic surrounds into an achromatic central field of a constant lower luminance (10 mL) have been measured. For inducing colors of constant chromaticity, an increasing luminance yielded induced colors of lower lightness but of constant chromaticity. For 21 dominant and complementary wavelengths of the inducing stimuli, the induced colors have been measured as functions of the purity of the surround. The results can be described within an opponent color metric by means of simple simultaneous power equations in the partial and resultant opponent purities, with wavelength-dependent exponents and constants, and one linear equation for the luminance ratio. For a unit change of purity of the inducing color, the exponents of the power functions represent a measure of the strength of induction. The values of the exponents and the constants have been tabulated and plotted against wavelength. By interpolation in these curves, it is possible to predict the equivalent color-matching coordinates of an induced color, for any combination of dominant wavelength and purity of the inducing color stimulus. A quantitative formulation of color induction that also incorporates the dependence on (a) the photopic light adaptation level, (b) the angular size of the annular inducing stimulus, and (c) the time of fixation of the test field, is suggested.

© 1974 Optical Society of America

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References

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  1. A. Valberg, thesis (University of Oslo, 1967); T. Holtsmark and A. Valberg, Nature 224, 366 (1969); and Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven, Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), pp. 58–68.
    [CrossRef] [PubMed]
  2. A. Valberg, Appl. Opt. 10, 8 (1971).
    [CrossRef] [PubMed]
  3. A. Valberg, Vision Res. 11, 157 (1971).
    [CrossRef] [PubMed]
  4. Wratten filters from Eastman Kodak Company, Rochester, N. Y. and Cinemoid from Strand Electric Engineering Company, Ltd., London.
  5. Balzers Hochvakuumtechnik, Liechtenstein.
  6. D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 42, 1 (1949); R. M. Boynton, J. Opt. Soc. Am. 50, 929 (1960). B. Hassenstein, Kybernetik 4, 209 (1968).
    [CrossRef] [PubMed]
  7. D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
    [CrossRef]
  8. E. Q. Adams, J. Opt. Soc. Am. 32, 168 (1942).
    [CrossRef]
  9. L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 45, 602 (1955).
    [CrossRef] [PubMed]
  10. K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.
  11. pm= 0.014 corresponds closely to a MacAdam ellipse of one JND from white in the (x,y) diagram; D. L. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).
    [CrossRef]
  12. H. Terstiege, Die Farbe 16, 1 (1967).
  13. F. Heinrich, dissertation (Univ. München, 1967).
  14. I. Abramov, in Handbook of Sensory Physiology VII/2; Physiology of Photoreceptor Organs (Springer, Berlin1972), pp. 567–607.
    [CrossRef]
  15. In a preliminary study of this subject reported in Proceedings International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 237–245, the luminance LRS was occasionally below 8 mL. Subsequently, I repeated the experiments with improved experimental conditions and nearly constant luminance LRS above 8 mL. All results presented in this paper refer to the later investigations.
  16. The change of saturation with adaptation luminance LRS is represented by pm= pm° (LRS/LRS°)−0.19, where LRS° is the luminance for which we obtain the purity pm°.
  17. H. Pretori and M. Sachs, Pflügers Arch. ges. Physiol. 60, 71 (1895).
    [CrossRef]
  18. J. A. S. Kinney, Vision Res. 2, 503 (1962); H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
    [CrossRef] [PubMed]
  19. L. M. Hurvich and D. Jameson, in Visual Problems of Colour (Her Majesty’s Stationary Office, London, 1958), pp. 693–723; and Handbook of Sensory Physiology, VII/4, Visual Psychophysics (Springer, Berlin, 1972), pp. 568–581.
  20. H. Helson, J. Exp. Psychol. 23, 439 (1938); D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 24, 293 (1940).
    [CrossRef]
  21. In the cases I have studied, the time course of induction in the CIE x,y diagram followed the same loci as those obtained by changing the area of the inducing stimulus.
  22. T. N. Wiesel and D. H. Hubel, J. Neurophysiology 29, 1115 (1966).

1971 (2)

1967 (1)

H. Terstiege, Die Farbe 16, 1 (1967).

1966 (1)

T. N. Wiesel and D. H. Hubel, J. Neurophysiology 29, 1115 (1966).

1962 (1)

J. A. S. Kinney, Vision Res. 2, 503 (1962); H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
[CrossRef] [PubMed]

1961 (1)

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

1955 (2)

1949 (1)

D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 42, 1 (1949); R. M. Boynton, J. Opt. Soc. Am. 50, 929 (1960). B. Hassenstein, Kybernetik 4, 209 (1968).
[CrossRef] [PubMed]

1942 (2)

1938 (1)

H. Helson, J. Exp. Psychol. 23, 439 (1938); D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 24, 293 (1940).
[CrossRef]

1895 (1)

H. Pretori and M. Sachs, Pflügers Arch. ges. Physiol. 60, 71 (1895).
[CrossRef]

Abramov, I.

I. Abramov, in Handbook of Sensory Physiology VII/2; Physiology of Photoreceptor Organs (Springer, Berlin1972), pp. 567–607.
[CrossRef]

Adams, E. Q.

Früh, M.

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

Heinrich, F.

F. Heinrich, dissertation (Univ. München, 1967).

Helson, H.

H. Helson, J. Exp. Psychol. 23, 439 (1938); D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 24, 293 (1940).
[CrossRef]

Hofmann, K.-D.

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

Hubel, D. H.

T. N. Wiesel and D. H. Hubel, J. Neurophysiology 29, 1115 (1966).

Hurvich, L. M.

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
[CrossRef]

L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 45, 602 (1955).
[CrossRef] [PubMed]

L. M. Hurvich and D. Jameson, in Visual Problems of Colour (Her Majesty’s Stationary Office, London, 1958), pp. 693–723; and Handbook of Sensory Physiology, VII/4, Visual Psychophysics (Springer, Berlin, 1972), pp. 568–581.

Jameson, D.

L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 45, 602 (1955).
[CrossRef] [PubMed]

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
[CrossRef]

L. M. Hurvich and D. Jameson, in Visual Problems of Colour (Her Majesty’s Stationary Office, London, 1958), pp. 693–723; and Handbook of Sensory Physiology, VII/4, Visual Psychophysics (Springer, Berlin, 1972), pp. 568–581.

Judd, D. B.

D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 42, 1 (1949); R. M. Boynton, J. Opt. Soc. Am. 50, 929 (1960). B. Hassenstein, Kybernetik 4, 209 (1968).
[CrossRef] [PubMed]

Kinney, J. A. S.

J. A. S. Kinney, Vision Res. 2, 503 (1962); H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
[CrossRef] [PubMed]

MacAdam, D. L.

Miescher, K.

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

Pretori, H.

H. Pretori and M. Sachs, Pflügers Arch. ges. Physiol. 60, 71 (1895).
[CrossRef]

Sachs, M.

H. Pretori and M. Sachs, Pflügers Arch. ges. Physiol. 60, 71 (1895).
[CrossRef]

Terstiege, H.

H. Terstiege, Die Farbe 16, 1 (1967).

Valberg, A.

A. Valberg, Vision Res. 11, 157 (1971).
[CrossRef] [PubMed]

A. Valberg, Appl. Opt. 10, 8 (1971).
[CrossRef] [PubMed]

A. Valberg, thesis (University of Oslo, 1967); T. Holtsmark and A. Valberg, Nature 224, 366 (1969); and Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven, Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), pp. 58–68.
[CrossRef] [PubMed]

Weisenhorn, P.

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

Wiesel, T. N.

T. N. Wiesel and D. H. Hubel, J. Neurophysiology 29, 1115 (1966).

Appl. Opt. (1)

Die Farbe (2)

H. Terstiege, Die Farbe 16, 1 (1967).

K. Miescher, K.-D. Hofmann, P. Weisenhorn, and M. Früh, Die Farbe 10, 115 (1961); K. Richter, Proceedings of the International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 403–417.

J. Exp. Psychol. (1)

H. Helson, J. Exp. Psychol. 23, 439 (1938); D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 24, 293 (1940).
[CrossRef]

J. Neurophysiology (1)

T. N. Wiesel and D. H. Hubel, J. Neurophysiology 29, 1115 (1966).

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stds. (U. S.) (1)

D. B. Judd, J. Res. Natl. Bur. Stds. (U. S.) 42, 1 (1949); R. M. Boynton, J. Opt. Soc. Am. 50, 929 (1960). B. Hassenstein, Kybernetik 4, 209 (1968).
[CrossRef] [PubMed]

Pflügers Arch. ges. Physiol. (1)

H. Pretori and M. Sachs, Pflügers Arch. ges. Physiol. 60, 71 (1895).
[CrossRef]

Vision Res. (2)

J. A. S. Kinney, Vision Res. 2, 503 (1962); H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
[CrossRef] [PubMed]

A. Valberg, Vision Res. 11, 157 (1971).
[CrossRef] [PubMed]

Other (9)

Wratten filters from Eastman Kodak Company, Rochester, N. Y. and Cinemoid from Strand Electric Engineering Company, Ltd., London.

Balzers Hochvakuumtechnik, Liechtenstein.

A. Valberg, thesis (University of Oslo, 1967); T. Holtsmark and A. Valberg, Nature 224, 366 (1969); and Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven, Proceedings of the 1971 AIC Symposium on Color Metrics (AIC/Holland, c/o Institute for Perception TNO, 1972), pp. 58–68.
[CrossRef] [PubMed]

F. Heinrich, dissertation (Univ. München, 1967).

I. Abramov, in Handbook of Sensory Physiology VII/2; Physiology of Photoreceptor Organs (Springer, Berlin1972), pp. 567–607.
[CrossRef]

In a preliminary study of this subject reported in Proceedings International Color Meeting “Color 69”, Stockholm 1969 (Musterschmidt, Göttingen, 1969), pp. 237–245, the luminance LRS was occasionally below 8 mL. Subsequently, I repeated the experiments with improved experimental conditions and nearly constant luminance LRS above 8 mL. All results presented in this paper refer to the later investigations.

The change of saturation with adaptation luminance LRS is represented by pm= pm° (LRS/LRS°)−0.19, where LRS° is the luminance for which we obtain the purity pm°.

L. M. Hurvich and D. Jameson, in Visual Problems of Colour (Her Majesty’s Stationary Office, London, 1958), pp. 693–723; and Handbook of Sensory Physiology, VII/4, Visual Psychophysics (Springer, Berlin, 1972), pp. 568–581.

In the cases I have studied, the time course of induction in the CIE x,y diagram followed the same loci as those obtained by changing the area of the inducing stimulus.

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Figures (8)

Fig. 1
Fig. 1

Experimental arrangement for haploscopic matches of induced colors. Lower right: test and reference fields separate. Upper right: fields as seen while matching.

Fig. 2
Fig. 2

Spread of induced colors for various luminances of seven inducing stimuli of constant chromaticity.

Fig. 3
Fig. 3

Double-logarithmic representation of concurrent values of the partial purities pm1 and pm2 for inducing and induced colors. Different symbols show results for four different dates of measurement.

Fig. 4
Fig. 4

Example of a double-logarithmic plot of concurrent values of the resultant purity pm for inducing and induced color. Only for one data point does the maximum deviation extend beyond the size of the symbol.

Fig. 5
Fig. 5

aλ plotted versus dominant and complementary wavelengths.

Fig. 6
Fig. 6

Induction coefficient bλ plotted versus dominant and complementary wavelengths. The dotted curve represents bλ as computed from aiλ, biλ, i = 1, 2.

Fig. 7
Fig. 7

Chromaticities of induced colors for 16 inducing wavelengths represented in the opponent-purity diagram pm1, pm2. The loci (heavy curves) are computed by inserting the constants of Table II into Eq. (13). The dashed part of each curve represents an extrapolation beyond the experimental data.

Fig. 8
Fig. 8

Same computed loci of induced colors as in Fig. 7 represented in the CIE x, y diagram. Black dots represent the maximum purity of the inducing color for each dominant or complementary wavelength. The notations refer to Table II. In the insert are shown the chromaticity triangles used to obtain the best color matches.

Tables (2)

Tables Icon

Table I Corresponding CIE tristimulus values for inducing stimulus and induced color; the inducing color being of constant dominant or complementary wavelength. The data are separated for different days of measurement.

Tables Icon

Table II Induction coefficients b, b, bλ and constants a, a, aλ derived from double logarithmic plots of the experimental data. The pm1 and pm2 values (relative to xw = 0.286, yw = 0.322 as origin) serve for the calculation of qλ in Eq. (12).

Equations (23)

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L C = L T · τ .
Y R = L RC / L RS ,             Y T = L TC / L TS .
M 1 = X - Y ,             M 2 = k ( Y - Z ) ,             Y .
C ( C ) = X ( X ) + Y ( Y ) + Z ( Z )
C ( C ) = X ( X ) + Y ( Y ) + Z ( Z ) .
X = 100 X / X w ,             Y = 100 Y / Y w ,             Z = 100 Z / Z w
p m 1 = M 1 / Y ,             p m 2 = M 2 / Y .
M = ( M 1 2 + M 2 2 ) 1 2 ,             p m = M / Y .
p m = p m λ p c ,
X = 0.8882 ( p m 1 + 1 ) Y , Y = Y , Z = 1.2174 ( 1 - p m 2 k ) Y .
p m ( t ) = 0.48 [ 1 - exp { - ( c t ) 2 } ] ,
p m ( x ) = 0.48 [ 1 - exp { - ( 3 4 R ) 2 } ] ,
p 1 c = [ a 1 λ p 1 s ] b 1 λ ,
p 2 c = [ a 2 λ p 2 s ] b 2 λ ,
p m c = [ a λ p m s ] b λ ,
log p m c = b λ [ log a λ + log p m s ] .
q λ = p 1 λ s p 2 λ s ,
p 2 c = r λ b 2 λ p 1 c b 2 λ / b 1 λ ,
r λ = 1 q λ a 2 λ a 1 λ .
Y R = k Y T + c ,
p m ( x , t ) = C · p max ( λ ) · p m ( x ) · p m ( t ) ,
p m ( L TC , L RS , x , t ) = p max ( λ ) · f ( L TC ) · g ( L RS ) · ( 1 - e - ( α x ) 2 ) ( 1 - e - ( β t ) 2 ) .
p m = k ( t 0 , A 0 , L 0 ) · p max ( λ ) · f ( L TC ) ,