Abstract

We analyze the sources of error in specifying color in CRT displays. Theseinclude errors inherent in the use of the color matching functions of theCIE 1931 standard observer when only colorimetric, not radiometric, calibrationsare available. We provide transformation coefficients that prove to correctthe deficiencies of this observer very well. We consider four different candidatesets of cone sensitivities. Some of these differ substantially; variationamong candidate cone sensitivities exceeds the variation among phosphors.Finally, the effects of the recognized forms of observer variation on thevisual responses (cone excitations or cone contrasts) generated by CRT stimuliare investigated and quantitatively specified. Cone pigment polymorphism givesrise to variation of a few per cent in relative excitation by the differentphosphors—a variation larger than the errors ensuing from the adoptionof the CIE standard observer, though smaller than the differences betweensome candidate cone sensitivities. Macular pigmentation has a larger influence,affecting mainly responses to the blue phosphor. The estimated combined effectof all sources of observer variation is comparable in magnitude with the largestdifferences between competing cone sensitivity estimates but is not enoughto disrupt very seriously the relation between the L and M cone weights andthe isoluminance settings of individual observers. It is also comparable withtypical instrumental colorimetric errors, but we discuss these only briefly.

© 2003 Optical Society of America

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References

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  1. A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
    [CrossRef]
  2. D. B. Judd, “Report of U.S. Secretariat Committee on Colorimetry and Artificial Daylight,” in Proceedings of the Twelfth Session of the CIE, Stockholm, Tech. Committee No. 7 (Bureau Central de la CIE, Paris, 1951).
  3. J. J. Vos, “Colorimetric and photometric properties of a 2-deg fundamental observer,” Color Res. Appl. 3, 125–128 (1978).
    [CrossRef]
  4. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  5. W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report,” Opt. Acta 6, 1–26 (1959).
    [CrossRef]
  6. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and500 nm,” Vision Res. 15, 161–171 (1975).
    [CrossRef] [PubMed]
  7. A. Stockman, L. T. Sharpe, “Spectral sensitivities of the middle- and long-wavelength sensitivecones derived from measurements in observers of known genotype,” Vision Res. 40, 1711–1737 (2000).
    [CrossRef]
  8. D. H. Brainard, B. A. Wandell, “Asymmetric color matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
    [CrossRef] [PubMed]
  9. R. Luther, “Aus dem Gebiet der Farbreizmetrik,” Z. Tech. Phys. 8, 540–558 (1927).
  10. D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. A 69, 1183–1186 (1979).
    [CrossRef]
  11. R. M. Boynton, “Frederic Ives Medal paper. History and current status of a physiologicallybased system of photometry and colorimetry,” J. Opt. Soc. Am. A 13, 1609–1621 (1996).
    [CrossRef]
  12. A. J. Shepherd, “Calibrating screens for continuous colour displays,” Spatial Vis. 11, 57–74 (1997).
    [CrossRef]
  13. A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
    [CrossRef] [PubMed]
  14. D. I. A. MacLeod, “Colour discrimination, colour constancy, and natural scene statistics,” in Proceedings of the Thomas Young Symposium of the International Colour Vision Society, J. D. Mollon, J. Pokorny, K. Knoblauch, eds. (Oxford U. Press, London, to be published).
  15. M. A. Webster, D. I. A. MacLeod, “Factors underlying individual differences in the color matches of normalobservers,” J. Opt. Soc. Am. A 5, 1722–1735 (1988).
    [CrossRef] [PubMed]
  16. L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).
  17. V. C. Smith, J. Pokorny, “Chromatic-discrimination axes, CRT phosphor spectra, and individualvariation in color vision,” J. Opt. Soc. Am. A 12, 27–35 (1995).
    [CrossRef]
  18. M. A. Webster, E. Miyahara, G. Malkoc, V. E. Raker, “Variations in normal color vision. I. Cone-opponent axes,” J. Opt. Soc. Am. A 17, 1535–1544 (2000).
    [CrossRef]
  19. A. Eisner, D. I. A. MacLeod, “Flicker photometric study of chromatic adaptation: Selective suppressionof cone inputs by colored backgrounds,” J. Opt. Soc. Am. 71, 705–718 (1981).
    [CrossRef] [PubMed]
  20. P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminancedependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
    [CrossRef]
  21. M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
    [CrossRef] [PubMed]
  22. K. L. Gunther, K. R. Dobkins, “Individual differences in chromatic (red/green) contrast sensitivityare constrained by the relative number of L- versus M-cones in the eye,” Vision Res. 42, 1367–1378 (2002).
    [CrossRef] [PubMed]

2002 (1)

K. L. Gunther, K. R. Dobkins, “Individual differences in chromatic (red/green) contrast sensitivityare constrained by the relative number of L- versus M-cones in the eye,” Vision Res. 42, 1367–1378 (2002).
[CrossRef] [PubMed]

2000 (2)

A. Stockman, L. T. Sharpe, “Spectral sensitivities of the middle- and long-wavelength sensitivecones derived from measurements in observers of known genotype,” Vision Res. 40, 1711–1737 (2000).
[CrossRef]

M. A. Webster, E. Miyahara, G. Malkoc, V. E. Raker, “Variations in normal color vision. I. Cone-opponent axes,” J. Opt. Soc. Am. A 17, 1535–1544 (2000).
[CrossRef]

1998 (1)

M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
[CrossRef] [PubMed]

1997 (1)

A. J. Shepherd, “Calibrating screens for continuous colour displays,” Spatial Vis. 11, 57–74 (1997).
[CrossRef]

1996 (1)

1995 (1)

1993 (2)

A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

1992 (1)

1988 (2)

P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminancedependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
[CrossRef]

M. A. Webster, D. I. A. MacLeod, “Factors underlying individual differences in the color matches of normalobservers,” J. Opt. Soc. Am. A 5, 1722–1735 (1988).
[CrossRef] [PubMed]

1981 (1)

1979 (1)

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

1978 (1)

J. J. Vos, “Colorimetric and photometric properties of a 2-deg fundamental observer,” Color Res. Appl. 3, 125–128 (1978).
[CrossRef]

1975 (1)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

1959 (1)

W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report,” Opt. Acta 6, 1–26 (1959).
[CrossRef]

1927 (1)

R. Luther, “Aus dem Gebiet der Farbreizmetrik,” Z. Tech. Phys. 8, 540–558 (1927).

Bieber, M. L.

M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
[CrossRef] [PubMed]

Boynton, R. M.

R. M. Boynton, “Frederic Ives Medal paper. History and current status of a physiologicallybased system of photometry and colorimetry,” J. Opt. Soc. Am. A 13, 1609–1621 (1996).
[CrossRef]

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

Brainard, D. H.

Burch, J. M.

W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report,” Opt. Acta 6, 1–26 (1959).
[CrossRef]

Chaparro, A.

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Dobkins, K. R.

K. L. Gunther, K. R. Dobkins, “Individual differences in chromatic (red/green) contrast sensitivityare constrained by the relative number of L- versus M-cones in the eye,” Vision Res. 42, 1367–1378 (2002).
[CrossRef] [PubMed]

Eisner, A.

Eskew, R. T.

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Gunther, K. L.

K. L. Gunther, K. R. Dobkins, “Individual differences in chromatic (red/green) contrast sensitivityare constrained by the relative number of L- versus M-cones in the eye,” Vision Res. 42, 1367–1378 (2002).
[CrossRef] [PubMed]

Huang, E. P.

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Jägle, H.

L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).

Johnson, N. E.

Judd, D. B.

D. B. Judd, “Report of U.S. Secretariat Committee on Colorimetry and Artificial Daylight,” in Proceedings of the Twelfth Session of the CIE, Stockholm, Tech. Committee No. 7 (Bureau Central de la CIE, Paris, 1951).

Kaiser, P. K.

P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminancedependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
[CrossRef]

Kraft, J. M.

M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
[CrossRef] [PubMed]

Kronauer, R. E.

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Luther, R.

R. Luther, “Aus dem Gebiet der Farbreizmetrik,” Z. Tech. Phys. 8, 540–558 (1927).

MacLeod, D. I. A.

A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

M. A. Webster, D. I. A. MacLeod, “Factors underlying individual differences in the color matches of normalobservers,” J. Opt. Soc. Am. A 5, 1722–1735 (1988).
[CrossRef] [PubMed]

A. Eisner, D. I. A. MacLeod, “Flicker photometric study of chromatic adaptation: Selective suppressionof cone inputs by colored backgrounds,” J. Opt. Soc. Am. 71, 705–718 (1981).
[CrossRef] [PubMed]

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

D. I. A. MacLeod, “Colour discrimination, colour constancy, and natural scene statistics,” in Proceedings of the Thomas Young Symposium of the International Colour Vision Society, J. D. Mollon, J. Pokorny, K. Knoblauch, eds. (Oxford U. Press, London, to be published).

Malkoc, G.

Miyahara, E.

Nathans, J.

L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).

Pokorny, J.

V. C. Smith, J. Pokorny, “Chromatic-discrimination axes, CRT phosphor spectra, and individualvariation in color vision,” J. Opt. Soc. Am. A 12, 27–35 (1995).
[CrossRef]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Raker, V. E.

Sharpe, L. T.

A. Stockman, L. T. Sharpe, “Spectral sensitivities of the middle- and long-wavelength sensitivecones derived from measurements in observers of known genotype,” Vision Res. 40, 1711–1737 (2000).
[CrossRef]

L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).

Shepherd, A. J.

A. J. Shepherd, “Calibrating screens for continuous colour displays,” Spatial Vis. 11, 57–74 (1997).
[CrossRef]

Smith, V. C.

V. C. Smith, J. Pokorny, “Chromatic-discrimination axes, CRT phosphor spectra, and individualvariation in color vision,” J. Opt. Soc. Am. A 12, 27–35 (1995).
[CrossRef]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

Stiles, W. S.

W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report,” Opt. Acta 6, 1–26 (1959).
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Stockman, A.

A. Stockman, L. T. Sharpe, “Spectral sensitivities of the middle- and long-wavelength sensitivecones derived from measurements in observers of known genotype,” Vision Res. 40, 1711–1737 (2000).
[CrossRef]

A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).

Stromeyer, C. F.

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Vos, J. J.

J. J. Vos, “Colorimetric and photometric properties of a 2-deg fundamental observer,” Color Res. Appl. 3, 125–128 (1978).
[CrossRef]

Wandell, B. A.

Webster, M. A.

Werner, J. S.

M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
[CrossRef] [PubMed]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Color Res. Appl. (1)

J. J. Vos, “Colorimetric and photometric properties of a 2-deg fundamental observer,” Color Res. Appl. 3, 125–128 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Nature (1)

A. Chaparro, C. F. Stromeyer, E. P. Huang, R. E. Kronauer, R. T. Eskew, “Colour is what the eye sees best,” Nature 361, 348–350 (1993).
[CrossRef] [PubMed]

Opt. Acta (1)

W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report,” Opt. Acta 6, 1–26 (1959).
[CrossRef]

Spatial Vis. (1)

A. J. Shepherd, “Calibrating screens for continuous colour displays,” Spatial Vis. 11, 57–74 (1997).
[CrossRef]

Vision Res. (5)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

A. Stockman, L. T. Sharpe, “Spectral sensitivities of the middle- and long-wavelength sensitivecones derived from measurements in observers of known genotype,” Vision Res. 40, 1711–1737 (2000).
[CrossRef]

P. K. Kaiser, “Sensation luminance: a new name to distinguish CIE luminance from luminancedependent on an individual’s spectral sensitivity,” Vision Res. 28, 455–456 (1988).
[CrossRef]

M. L. Bieber, J. M. Kraft, J. S. Werner, “Effects of known variations in photopigments on L/M cone ratios estimatedfrom luminous efficiency functions,” Vision Res. 38, 1961–1966 (1998).
[CrossRef] [PubMed]

K. L. Gunther, K. R. Dobkins, “Individual differences in chromatic (red/green) contrast sensitivityare constrained by the relative number of L- versus M-cones in the eye,” Vision Res. 42, 1367–1378 (2002).
[CrossRef] [PubMed]

Z. Tech. Phys. (1)

R. Luther, “Aus dem Gebiet der Farbreizmetrik,” Z. Tech. Phys. 8, 540–558 (1927).

Other (4)

L. T. Sharpe, A. Stockman, H. Jägle, J. Nathans, “Opsin genes, cone photopigments, color vision, and color blindness,” in Color Vision: from Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999).

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

D. B. Judd, “Report of U.S. Secretariat Committee on Colorimetry and Artificial Daylight,” in Proceedings of the Twelfth Session of the CIE, Stockholm, Tech. Committee No. 7 (Bureau Central de la CIE, Paris, 1951).

D. I. A. MacLeod, “Colour discrimination, colour constancy, and natural scene statistics,” in Proceedings of the Thomas Young Symposium of the International Colour Vision Society, J. D. Mollon, J. Pokorny, K. Knoblauch, eds. (Oxford U. Press, London, to be published).

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Figures (4)

Fig. 1
Fig. 1

Spectral power distributions of the typical red, green, and blue phosphors.Before averaging, the individual spectra were scaled for equality in luminanceamong all phosphors. This leads to the differences in peak power of the threetypical phosphors.

Fig. 2
Fig. 2

Errors for L, M, and S cone excitation measures for the R, G, and Bphosphors resulting from the following sources: (a) rms errors among monitorsresulting from use of the 1931 CIE color matching functions, when the transformationderived for the average monitor [Eq. (3)]is applied to all individual monitors; (b) rms errors among monitors resultingfrom using R, G, B phosphor intensity measures with the transformation specifiedin Eq. (8); (c) rms errors among observers resultingfrom all sources of individual variation for the typical phosphors; (d) rmserrors among monitors resulting from differences between measurement devices(based on data provided by Shepherd12). Note that the scales of all subplots are equal.

Fig. 3
Fig. 3

Differences between candidate cone sensitivities. (a) SP, (b) SMJ10,(c) SS. For each of these three candidate cone sensitivity sets, the fractionaldeviations of the L, M, and S cone excitation measures for the R, G, and Bphosphors from the corresponding SMJ2 values are calculated. A value of +0.1corresponds to an increase of 10% in cone excitation relative to theSMJ2 value. The effects of different choices of units for cone excitationsare eliminated by scaling the estimated L, M, and S values to equality for the red, green,and blue phosphors, respectively.

Fig. 4
Fig. 4

Locus of spectral lights (curves) and equal-energy white point (symbolmarkers) of each of the four candidate cone sensitivities introduced in Section1. The l axis is the luminance-normalized L-cone excitation,and the s axis is the luminance-normalized S-cone excitation.

Tables (14)

Tables Icon

Table 1 Mean and StandardDeviation of the CIE 1931 Chromaticity Coordinates for the Sampled Monitors

Tables Icon

Table 2 Rms ErrorsResulting from Use of the 1931 CIE Color Matching Functionswith the Transformation Specified in Eq. (3) a

Tables Icon

Table 3 Maximum ErrorsResulting from Use of the 1931 CIE Color Matching Functions with the TransformationSpecified in Eq. (3) a

Tables Icon

Table 4 Rms Errorsin Chromaticity and Luminance Resulting from Use of the 1931 CIE Color MatchingFunctions with the Transformation Specified in Eq. (3) a

Tables Icon

Table 5 Rms ErrorsResulting from Observer Variation in Visual Pigment Absorption Spectra forOur Average Monitor Phosphors a

Tables Icon

Table 6 Changes inCone Excitations Resulting from Displacements of Visual Pigment AbsorptionSpectra a

Tables Icon

Table 7 Rms ErrorsResulting from Individual Variation in Macular Pigmentation a

Tables Icon

Table 8 Rms ErrorsResulting from Individual Variation in Lens Pigmentation a

Tables Icon

Table 9 Rms ErrorsResulting from Individual Variation in Visual Pigment Density a

Tables Icon

Table 10 Rms ErrorsResulting from Individual Variation in Visual Pigment Density a

Tables Icon

Table 11 Rms ErrorsResulting from All Sources of Individual Variation

Tables Icon

Table 12 Rms ErrorsResulting from all Sources of Individual Variation a

Tables Icon

Table 13 FractionalChanges in Sensation Luminance of the Red and Blue PhosphorRelative to That of the Green Phosphor Resulting from Different Sourcesof Individual Variation a

Tables Icon

Table 14 Rms ErrorsResulting from Measurement-Device Variation a

Equations (30)

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

LMS = LMS   _ XYZ * XYZ .
L M S = 0.15282 0.54383 - 0.02795 - 0.15254 0.45524 0.03355 - 0.00045 0.00145 0.95449 * X Y Z .
L M S = 0.18772 0.60445 - 0.02517 - 0.14014 0.43056 0.03773 0.02017 - 0.04189 1.08472 * X Y Z .
L M S = 0.14460 0.62421 - 0.00429 - 0.14506 0.42265 0.05084 0.03105 - 0.06416 1.10923 * X Y Z .
L M S = 0.17156 0.52901 - 0.02199 - 0.15955 0.48553 0.04298 0.01916 - 0.03989 1.03993 * X Y Z .
X Y Z = 2.59795 - 3.62903 0.18651 0.84694 1.13166 - 0.01971 - 0.01560 0.11119 0.91767 * L M S .
l = 0.21289 x + 0.62962 y - 0.02517 0.03502 x + 1.0224 y + 0.01256 ,
s = - 1.06455 x - 1.12661 y + 1.08472 0.03502 x + 1.0224 y + 0.01256 .
L M S = 0.9417 0.6901 0.7359 0.1809 0.3703 0.5432 0.1138 0.1764 12.0757 * R G B .
LMS = LMS   _ XYZ * XYZ = LMS   _ X Y Z * X Y Z = LMS   _ X Y Z * ( X Y Z   _ XYZ * XYZ ) .
X J Y J Z J = 0.98409 0.00765 - 0.00140 0.00046 0.99902 0.00569 0.00003 0.00052 0.93581 * X Y Z .
X V Y V Z V = 0.98398 0.00799 - 0.00215 0.00029 0.99911 0.00560 - 0.00044 0.00141 0.93294 * X Y Z .
X 10 Y 10 Z 10 = 0.97008 0.09864 0.01738 - 0.00046 1.04684 0.04655 0.02256 - 0.04707 1.10164 * X Y Z .
0.067 2 - 0.0494 2 = 0.0453 .
r ¯ ( λ ) = i r i ( λ ) , g ¯ ( λ ) = i g i ( λ ) ,
b ¯ ( λ ) = i b i ( λ ) ( λ = 380 , . . , 780 ) .
LMS   _ XYZ
= L ( λ ) M ( λ ) S ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T * INV x ¯ ( λ ) y ¯ ( λ ) z ¯ ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T .
L X L Y L Z M X M Y M Z S X S Y S Z
l = ( L X - L Z ) * x + ( L Y - L Z ) * y + L Z ( L X + M X - L Z - M Z ) * x + ( L Y + M Y - L Z - M Z ) * y + L Z + M Z ,
s = ( S X - S Z ) * x + ( S Y - S Z ) * y + S Z ( L X + M X - L Z - M Z ) * x + ( L Y + M Y - L Z - M Z ) * y + L Z + M Z .
LMS   _ RGB = L ( λ ) M ( λ ) S ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T .
X Y Z   _ XYZ = x ¯ J ( λ ) y ¯ J ( λ ) z ¯ J ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T * INV x ¯ ( λ ) y ¯ ( λ ) z ¯ ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T .
LMS   _ XYZ i = L ( λ ) M ( λ ) S ( λ ) * r i ( λ ) g i ( λ ) b i ( λ ) T * INV x ¯ ( λ ) y ¯ ( λ ) z ¯ ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T
( i = 1 , . . ,   15 ) .
L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯ = LMS   _ XYZ * x ¯ ( λ ) y ¯ ( λ ) z ¯ ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T ;
L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯ i
= LMS   _ XYZ i * x ¯ ( λ ) y ¯ ( λ ) z ¯ ( λ ) * r ¯ ( λ ) g ¯ ( λ ) b ¯ ( λ ) T .
( i = 1 , . . ,   15   )
fractional rms L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯ = 1 / 15 i L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯ - L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯ i 2 / L r ¯ L g ¯ L b ¯ M r ¯ M g ¯ M b ¯ S r ¯ S g ¯ S b ¯

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