Abstract

Standard methods for color correction involve the use of a diagonal-matrix transformation. Zaidi proposes the use of a two-parameter affine model; we show that this offers no improvement in terms of accuracy over the diagonal model, especially if a sharpening transformation is also used.

© 2000 Optical Society of America

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References

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  1. Q. Zaidi, “Identification of illuminant and object colors: heuristic-based algorithms,” J. Opt. Soc. Am. A 15, 1767–1776 (1998).
    [CrossRef]
  2. 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]
  3. G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaption to give colour constancy,” J. Math. Biol. 15, 249–258 (1982).
    [CrossRef]
  4. G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
    [CrossRef]
  5. M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).
  6. E. L. Krinov, Spectral Reflectance Properties of Natural Formations, Technical Translation TT-439 (National Research Council of Canada, Ottawa, 1947).
  7. J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
    [CrossRef] [PubMed]
  8. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982), Eq. [5(3.3.9)].
  9. See Ref. 7, Eq. (26).

1998 (1)

1994 (2)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

1982 (1)

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaption to give colour constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef]

1979 (1)

1971 (1)

J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[CrossRef] [PubMed]

Boynton, R. M.

Brill, M. H.

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaption to give colour constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef]

Drew, M. S.

Finlayson, G. D.

Funt, B. V.

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Krinov, E. L.

E. L. Krinov, Spectral Reflectance Properties of Natural Formations, Technical Translation TT-439 (National Research Council of Canada, Ottawa, 1947).

MacLeod, D. I. A.

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982), Eq. [5(3.3.9)].

Vos, J. J.

J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[CrossRef] [PubMed]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Walraven, P. L.

J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[CrossRef] [PubMed]

West, G.

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaption to give colour constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982), Eq. [5(3.3.9)].

Zaidi, Q.

Color Res. Appl. (1)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

J. Math. Biol. (1)

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaption to give colour constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Vision Res. (1)

J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[CrossRef] [PubMed]

Other (3)

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982), Eq. [5(3.3.9)].

See Ref. 7, Eq. (26).

E. L. Krinov, Spectral Reflectance Properties of Natural Formations, Technical Translation TT-439 (National Research Council of Canada, Ottawa, 1947).

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Figures (3)

Fig. 1
Fig. 1

Coordinates of the six illuminants plotted in (l, m) space. 140 other illuminants are plotted as small dots.

Fig. 2
Fig. 2

Coordinates of the six illuminants plotted in (l, s) space. 140 other illuminants are plotted as small dots.

Fig. 3
Fig. 3

Coordinates of the six illuminants plotted in (m, s) space. 140 other illuminants are plotted as small dots.

Tables (3)

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Table 1 Illuminant 5 Spectral Information

Tables Icon

Table 2 Illuminant 6 Spectral Information

Tables Icon

Table 3 Mean ΔE Errors for the Three Transformation Methods under Various Illuminations Changes a

Equations (28)

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

WeDWe.
TWcDTWe.
T=U-1,
UDU-1=Wc[We]+
pi=E(λ)S(λ)Ri(λ)dλ,
pi=E(λ)S(λ)Ri(λ),
p=[LMS].
pi=E(λ)Ri(λ),
l=LL+M+S,
m=ML+M+S.
sa=SL+M,
la=LL+M.
sa=saσ,
la=la+τ.
τ=LtargetLtarget+Mtarget-LsourceLsource+Msource,
σ=StargetLtarget+Mtarget/SsourceLsource+Msource.
SL+M=σSL+M,
LL+M=LL+M+τ.
L+M+S=L+M+S=1;
S=σSσS+L+M,
L=1L+M+τ(1-S),
M=1-L-S.
LMS=a000b000c LMS.
a=LL=ll,
b=MM=mm,
c=SS=1-l-m1-l-m.
LsMsSs=T×LMS.
LsMsSs=a000b000c LsMsSs.

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