Abstract

Three-dimensional discrimination ellipsoids are presented for a number of representative points in color space. These ellipsoids have been obtained not with the conventional split field but with flickering grating patterns. Thus our study extends the well-known results of Brown and MacAdam [ J. Opt. Soc. Am. 39, 808– 813 ( 1949)] to cases in which the image is structured in space and time. As expected, we find that the discrimination ellipsoids depend on the spatiotemporal structure of the stimulus. This has potential consequences for color-difference formulas as used in industry and commerce: no single formula will do when it is important to treat patterns with different structure. We present analytical descriptions, based on the Vos–Walraven [ Vision Res. 12, 1327– 1365 ( 1972)] line element augmented with spatiotemporal frequency-dependent coefficients that fit our results reasonably well. For coarse gratings (~1 cycle per degree) or slowly modulated fields (~1 Hz) our results prove to be compatable with the results of Brown and MacAdam obtained with a bipartite 2° field.

© 1983 Optical Society of America

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References

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  1. W. R. J. Brown and D. L. MacAdam, "Visual sensitivity to combined chromaticity and luminance contrast," J. Opt. Soc. Am. 39, 808–813 (1949).
    [CrossRef] [PubMed]
  2. J. G. Robson, "Spatial and temporal contrast-sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 422–429 (1961).
  3. F. L. van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, "Spatiotemporal modulation transfer in the human eye," J. Opt. Soc. Am. 57,1082–1088 (1967).
    [CrossRef] [PubMed]
  4. G. J. C. van der Horst and M. A. Bouman, "Spatiotemporal chromaticity discrimination," J. Opt. Soc. Am. 59, 1482–1488 (1969).
    [CrossRef] [PubMed]
  5. C. R. Cavonius and O. Estévez, "Sensitivity of human color mechanisms to grating and flicker," J. Opt. Soc. Am. 65, 966–968 (1975).
    [CrossRef] [PubMed]
  6. J. J. Wisowaty and R. M. Boynton, "Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation," Vision Res. 20, 805–909 (1980).
    [CrossRef]
  7. D. H. Kelly and D. van Norren, "Two-band model of heterochromatic flicker," J. Opt. Soc. Am. 67, 1081–1091 (1977).
    [CrossRef] [PubMed]
  8. C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Sensitivity to spatiotemporal combined luminance and chromaticity contrast," J. Opt. Soc. Am. 71, 453–459 (1981).
    [CrossRef] [PubMed]
  9. J. J. Vos and P. L. Walraven, "An analytical description of the line element in the zone-fluctuation model of colour vision," Vision Res. 12, 1327–1365 (1972).
    [CrossRef] [PubMed]
  10. P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).
    [CrossRef] [PubMed]
  11. D. B. Judd, "Colorimetry and artificial daylight," Proc. 12th Session CIE Stockholm, 1, Tech. Comm. 7, Bureau Central de la CIE, Paris, p. 11 (1951).
  12. C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Influence of the target size on the detection threshold for luminance and chromaticity contrast," J. Opt. Soc. Am. 70, 1116–1121 (1980).
    [CrossRef] [PubMed]
  13. W. R. J. Brown, "The influence of luminance level on visual sensitivity to color differences," J. Opt. Soc. Am. 41, 684–688 (1951).
    [CrossRef] [PubMed]
  14. P. R. Bevington, Data Reduction and Error Analysis for Physical Sciences (McGraw-Hill, New York, 1969).
  15. H. von Helmholtz, "Versuch das psychophysische Gesetz auf die Farbenunterschiede trichromatischer Augen anzuwenden," Z. Psychol. Physiol. Sinnesorg. 3, 1–20 (1892).
  16. E. H. Schrödinger, "Grundlinien einer Theorie der Farbenmetrik im Tagessehen," Ann. Phys. 63, 397-456; 481–520 (1920).
    [CrossRef]
  17. W. S. Stiles, "A modified Helmholtz line element in brightnesscolour space," Proc. Phys. Soc. Lond. 58,41–65 (1946).
    [CrossRef]
  18. S. L. Guth and A. L. Howard, "Heterochromatic additivity, foveal spectral sensitivity and a new color model," J. Opt. Soc. Am. 63, 450–462 (1973).
    [CrossRef] [PubMed]
  19. C. R. Ingling, Jr., and B. H.-P. Tsou, "Orthogonal combination of the three visual channels," Vision Res. 17, 1075–1082 (1977).
    [CrossRef] [PubMed]
  20. B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
    [CrossRef]

1981

1980

C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Influence of the target size on the detection threshold for luminance and chromaticity contrast," J. Opt. Soc. Am. 70, 1116–1121 (1980).
[CrossRef] [PubMed]

J. J. Wisowaty and R. M. Boynton, "Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation," Vision Res. 20, 805–909 (1980).
[CrossRef]

1977

C. R. Ingling, Jr., and B. H.-P. Tsou, "Orthogonal combination of the three visual channels," Vision Res. 17, 1075–1082 (1977).
[CrossRef] [PubMed]

D. H. Kelly and D. van Norren, "Two-band model of heterochromatic flicker," J. Opt. Soc. Am. 67, 1081–1091 (1977).
[CrossRef] [PubMed]

1976

B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
[CrossRef]

1975

1974

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).
[CrossRef] [PubMed]

1973

1972

J. J. Vos and P. L. Walraven, "An analytical description of the line element in the zone-fluctuation model of colour vision," Vision Res. 12, 1327–1365 (1972).
[CrossRef] [PubMed]

1969

1967

1961

J. G. Robson, "Spatial and temporal contrast-sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 422–429 (1961).

1951

1949

1946

W. S. Stiles, "A modified Helmholtz line element in brightnesscolour space," Proc. Phys. Soc. Lond. 58,41–65 (1946).
[CrossRef]

1920

E. H. Schrödinger, "Grundlinien einer Theorie der Farbenmetrik im Tagessehen," Ann. Phys. 63, 397-456; 481–520 (1920).
[CrossRef]

1892

H. von Helmholtz, "Versuch das psychophysische Gesetz auf die Farbenunterschiede trichromatischer Augen anzuwenden," Z. Psychol. Physiol. Sinnesorg. 3, 1–20 (1892).

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for Physical Sciences (McGraw-Hill, New York, 1969).

Bouman, M. A.

Boynton, R. M.

J. J. Wisowaty and R. M. Boynton, "Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation," Vision Res. 20, 805–909 (1980).
[CrossRef]

Brown, W. R. J.

Cavonius, C. R.

Estévez, O.

Guth, S. L.

Heuts, M. J. G.

Howard, A. L.

Ingling, Jr., C. R.

C. R. Ingling, Jr., and B. H.-P. Tsou, "Orthogonal combination of the three visual channels," Vision Res. 17, 1075–1082 (1977).
[CrossRef] [PubMed]

Judd, D. B.

D. B. Judd, "Colorimetry and artificial daylight," Proc. 12th Session CIE Stockholm, 1, Tech. Comm. 7, Bureau Central de la CIE, Paris, p. 11 (1951).

Kelly, D. H.

Koenderink, J. J.

Lorbeer, B.

B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
[CrossRef]

MacAdam, D. L.

Nas, H.

Noorlander, C.

Rentschler, I.

B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
[CrossRef]

Robson, J. G.

J. G. Robson, "Spatial and temporal contrast-sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 422–429 (1961).

Röhler, R.

B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
[CrossRef]

Schrödinger, E. H.

E. H. Schrödinger, "Grundlinien einer Theorie der Farbenmetrik im Tagessehen," Ann. Phys. 63, 397-456; 481–520 (1920).
[CrossRef]

Stiles, W. S.

W. S. Stiles, "A modified Helmholtz line element in brightnesscolour space," Proc. Phys. Soc. Lond. 58,41–65 (1946).
[CrossRef]

Tsou, B. H.-P.

C. R. Ingling, Jr., and B. H.-P. Tsou, "Orthogonal combination of the three visual channels," Vision Res. 17, 1075–1082 (1977).
[CrossRef] [PubMed]

van Nes, F. L.

van Norren, D.

van der Horst, G. J. C.

von Helmholtz, H.

H. von Helmholtz, "Versuch das psychophysische Gesetz auf die Farbenunterschiede trichromatischer Augen anzuwenden," Z. Psychol. Physiol. Sinnesorg. 3, 1–20 (1892).

Vos, J. J.

J. J. Vos and P. L. Walraven, "An analytical description of the line element in the zone-fluctuation model of colour vision," Vision Res. 12, 1327–1365 (1972).
[CrossRef] [PubMed]

Walraven, P. L.

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).
[CrossRef] [PubMed]

J. J. Vos and P. L. Walraven, "An analytical description of the line element in the zone-fluctuation model of colour vision," Vision Res. 12, 1327–1365 (1972).
[CrossRef] [PubMed]

Wisowaty, J. J.

J. J. Wisowaty and R. M. Boynton, "Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation," Vision Res. 20, 805–909 (1980).
[CrossRef]

Ann. Phys.

E. H. Schrödinger, "Grundlinien einer Theorie der Farbenmetrik im Tagessehen," Ann. Phys. 63, 397-456; 481–520 (1920).
[CrossRef]

J. Opt. Soc. Am.

J. G. Robson, "Spatial and temporal contrast-sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 422–429 (1961).

W. R. J. Brown, "The influence of luminance level on visual sensitivity to color differences," J. Opt. Soc. Am. 41, 684–688 (1951).
[CrossRef] [PubMed]

G. J. C. van der Horst and M. A. Bouman, "Spatiotemporal chromaticity discrimination," J. Opt. Soc. Am. 59, 1482–1488 (1969).
[CrossRef] [PubMed]

S. L. Guth and A. L. Howard, "Heterochromatic additivity, foveal spectral sensitivity and a new color model," J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef] [PubMed]

D. H. Kelly and D. van Norren, "Two-band model of heterochromatic flicker," J. Opt. Soc. Am. 67, 1081–1091 (1977).
[CrossRef] [PubMed]

C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Influence of the target size on the detection threshold for luminance and chromaticity contrast," J. Opt. Soc. Am. 70, 1116–1121 (1980).
[CrossRef] [PubMed]

C. Noorlander, M. J. G. Heuts, and J. J. Koenderink, "Sensitivity to spatiotemporal combined luminance and chromaticity contrast," J. Opt. Soc. Am. 71, 453–459 (1981).
[CrossRef] [PubMed]

F. L. van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, "Spatiotemporal modulation transfer in the human eye," J. Opt. Soc. Am. 57,1082–1088 (1967).
[CrossRef] [PubMed]

W. R. J. Brown and D. L. MacAdam, "Visual sensitivity to combined chromaticity and luminance contrast," J. Opt. Soc. Am. 39, 808–813 (1949).
[CrossRef] [PubMed]

C. R. Cavonius and O. Estévez, "Sensitivity of human color mechanisms to grating and flicker," J. Opt. Soc. Am. 65, 966–968 (1975).
[CrossRef] [PubMed]

Proc. Phys. Soc. Lond.

W. S. Stiles, "A modified Helmholtz line element in brightnesscolour space," Proc. Phys. Soc. Lond. 58,41–65 (1946).
[CrossRef]

Vision Res.

C. R. Ingling, Jr., and B. H.-P. Tsou, "Orthogonal combination of the three visual channels," Vision Res. 17, 1075–1082 (1977).
[CrossRef] [PubMed]

B. Lorbeer, I. Rentschler, and R. Röhler, "Pseudo-tritan effect and the Vos—Walraven line element at low luminance levels," Vision Res. 16, 221–223 (1976).
[CrossRef]

J. J. Vos and P. L. Walraven, "An analytical description of the line element in the zone-fluctuation model of colour vision," Vision Res. 12, 1327–1365 (1972).
[CrossRef] [PubMed]

P. L. Walraven, "A closer look at the tritanopic convergence point," Vision Res. 14, 1339–1343 (1974).
[CrossRef] [PubMed]

J. J. Wisowaty and R. M. Boynton, "Temporal modulation sensitivity of the blue mechanism: measurements made without chromatic adaptation," Vision Res. 20, 805–909 (1980).
[CrossRef]

Z. Psychol. Physiol. Sinnesorg.

H. von Helmholtz, "Versuch das psychophysische Gesetz auf die Farbenunterschiede trichromatischer Augen anzuwenden," Z. Psychol. Physiol. Sinnesorg. 3, 1–20 (1892).

Other

P. R. Bevington, Data Reduction and Error Analysis for Physical Sciences (McGraw-Hill, New York, 1969).

D. B. Judd, "Colorimetry and artificial daylight," Proc. 12th Session CIE Stockholm, 1, Tech. Comm. 7, Bureau Central de la CIE, Paris, p. 11 (1951).

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Figures (7)

Fig. 1
Fig. 1

The 16 modulation directions used for the experiments plotted in the (dR/R, dG/G, dB/B) space. The modulation was such that the mean stimulation of the R, G, and B cone systems remained constant.

Fig. 2
Fig. 2

The orientation angles of (a) the first and (b) the second semiaxis of an ellipsoid in the (dR/R, dG/G, dB/B) space: ϕ is the angle between the projection of a on the plane dB/B = 0 and the dR/R axis, θ is the angle between a and the plane dB/B = 0, α is the angle between b and the secant of the plane dB/B = 0 and the plane through the b and c axes. The third (c) semiaxis is perpendicular to a and b.

Fig. 3
Fig. 3

The temporal modulation transfer functions of subject RW. The abscissa is the temporal frequency Ft (in hertz), the ordinate is the modulation depth (in percent). Filled circles, luminance modulation; open circles, modulation of the red system; squares, modulation of the green system; triangles, modulation of the blue system.

Fig. 4
Fig. 4

The temporal modulation transfer functions of subject CN. The method of plotting is similar to Fig. 3.

Fig. 5
Fig. 5

The spatial modulation transfer functions of subject CN. The abscissa is the spatial frequency Fs (in cycles per degree), the ordinate is the modulation depth (in percent). The method of plotting is similar to Fig. 3.

Fig. 6
Fig. 6

A comparison of the constant luminance cross sections of ellipsoids of (a) Brown and (b) MacAdam and the constant luminance cross sections of the spatial ellipsoids of CN. (c) Fs = 1 cpd; (d) Fs = 4 cpd. The enlargement of the ellipses is shown in the upper right-hand corner of the plots.

Fig. 7
Fig. 7

Constant luminance cross sections of the temporal ellipsoids of (a)–(c) subject RW and (d)–(f) subject CN. The temporal frequencies are (a) and (d), 1 Hz; (b) and (e), 4 Hz; (c) and (f), 15 Hz.

Tables (7)

Tables Icon

Table 1 The 16 Modulation Directions in the (dR/R, dG/G, dB/B) Space Used for the Determination of the Discrimination Ellipsoids

Tables Icon

Table 2 Parameters of the Spatial Discrimination Ellipsoids of Subject CNa

Tables Icon

Table 3 Parameters of the Temporal Discrimination Ellipsoids of Subjects CN and RWa

Tables Icon

Table 4 Parameters of the Color-Matching Ellipsoids of Brown (WRJB) and MacAdam (DLM) Converted to the (dR/R, dG/G, dB/B) spacea

Tables Icon

Table 5 The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Spatial Contrast Detection Thresholds Besta

Tables Icon

Table 6 The Weighting Coefficients ηL, ηF, and ηS (in Inverse Trolands) for Which the Vos–Walraven Line Element for the De Vries–Rose Luminance Domain Approximates the Temporal Contrast Detection Thresholds Besta

Tables Icon

Table 7 The Metrical Coefficients gij in the (dx, dy, dl) Space Used by Brown and MacAdama

Equations (26)

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( R G B ) = ( 0.81860 0.60302 0.48957 0.18047 0.39525 0.42836 0.00093 0.00173 0.08207 ) ( R f G f B f ) .
χ 2 = i = 1 N ( r i - e i SE i ) 2 .
χ 2 = i = 1 N ( d r i SE i ) 2 .
χ 2 N - M ,
χ 2 = i = 1 N ( d r i f r i ) 2 .
η L ( dL ) 2 L + η F RG Y ( dR R - dG G ) 2 + η S YB L ( dY Y - dB B ) 2 = 1 ,
χ 2 = N - M = 16 - 3 = 13.
η = η ( F S , F t ) .
S L ( dL ) 2 + S F ( dR R - dG G ) 2 + S S ( dY Y - dB B ) 2 = 1.
S = S ( F s , F t , R , G , B ) .
CN : dL L = dR + dG + dB R + G + B 2 3 dR R + 1 3 dG G + 1 150 dB B , RW : dL L = dR + 0.5 dG + dB R + 0.5 G + B 4 5 dR R + 1 5 dG G + 1 125 dB B .
W L ( dL ) 2 + W F { dR R [ 1 + ( R / R o ) ] - dG G [ 1 + ( G / G o ) ] } 2 + W S { dY Y [ 1 + ( Y / Y o ) ] - dB B [ 1 + ( B / B o ) ] } 2 = 1.
R o = R o ( F s , F t ) etc .
1 1 + R / R o dR R = 1 1 + G / G o dG G
1 1 + Y / Y o dY Y = 1 1 + B / B o dB B ,
dR R = dG G ,             dY Y = dB B .
U L ( dL ) 2 + U f ( dR - 2 dG ) 2 + U S ( dY - 150 dB ) 2 = 1.
dR = 2 dG ,             dY = 150 dB
dR R = 2 G R dG G ,             dY Y = 150 B Y dB B .
g 11 d X 2 + 2 g 12 d X d Y + g 22 d Y 2 + 2 g 23 d Y d Z + g 33 d Z 2 + 2 g 13 d X d Z = 1.
[ g ] = ( g 11 g 12 g 13 g 12 g 22 g 23 g 13 g 23 g 33 ) .
( dR R dG G dB B ) = O ( dR dG dB ) ,             P = ( 100 R 0 0 0 100 G 0 0 0 100 B ) .
( dR dG dB ) = F ( dR f dG f dB f ) ,             F = ( 0.81860 0.60302 0.48957 0.18047 0.39525 0.42836 0.00093 0.00173 0.08207 ) .
( dR f dG f dB f ) = J ( d R f d G f d B f ) ,             J = ( 1.0004 0.0 0.0 0.0 1.0005 0.0 0.0 0.0 1.0757 ) .
( d X d Y d Z ) = Q ( d R f d G f d B f ) ,             Q = ( 1.8674 0.4458 2.1331 1.0000 1.0000 1.0000 0.0982 0.2258 10.5844 ) .
( d x d y d l ) = H ( d X d Y d Z ) ,             H = ( Y + Z s - X s - X s - Y s X + Z s - Y s 0 log ( e ) 5 Y 0 )             [ s = ( X + Y + Z ) 2 ] .