Abstract

We extend previous work that addressed the problem of color changes on reflective surfaces resulting from changes in the daylight spectrum. In that work, we constrained the illuminants to a family represented by the Wien approximation to Planck’s formula in order to derive a function of the three camera outputs that is invariant to daylight changes. In this work, we show that the constraint on the form of the illuminants can be relaxed and that a much more general form is permissible. We use principal components analysis on the logarithm of the illumination to represent the CIE standard in the more general form and show that the result closely represents the standard. We recalculate the exponent used in the invariant for our camera from the extended theory and obtain a result that duplicates the one found by empirical means used in our previous work.

© 2001 Optical Society of America

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References

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  1. J. A. Marchant, C. M. Onyango, “Shadow-invariant classification for scenes illuminated by daylight,” J. Opt. Soc. Am. A 17, 1952–1961 (2000).
    [CrossRef]
  2. G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.
  3. G. Finlayson, S. Hordley, M. H. Brill, “Illuminant invariance at a single pixel,” in Proceedings of the IS&T/SID Eighth Color Imaging Conference (Society for Information Display, Santa Ana, Calif., 2000), pp. 85–90.
  4. G. D. Finlayson, S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–265 (2001).
    [CrossRef]
  5. G. D. Finlayson, M. S. Drew, B. F. Funt, “Color constancy: generalized diagonal transforms suffice,” J. Opt. Soc. Am. A 11, 3011–3019 (1994).
    [CrossRef]
  6. G. D. Finlayson, M. S. Drew, B. F. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
    [CrossRef]
  7. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  8. Commission Internationale de L’Eclairage (CIE) “Colorimetry.” 2nd ed. (CIE, Paris, 1986).
  9. D. B. Judd, D. L. MacAdam, G. W. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]

2001 (1)

2000 (1)

1994 (2)

1964 (1)

Brill, M. H.

G. Finlayson, S. Hordley, M. H. Brill, “Illuminant invariance at a single pixel,” in Proceedings of the IS&T/SID Eighth Color Imaging Conference (Society for Information Display, Santa Ana, Calif., 2000), pp. 85–90.

Drew, M. S.

Finlayson, G.

G. Finlayson, S. Hordley, M. H. Brill, “Illuminant invariance at a single pixel,” in Proceedings of the IS&T/SID Eighth Color Imaging Conference (Society for Information Display, Santa Ana, Calif., 2000), pp. 85–90.

G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.

Finlayson, G. D.

Funt, B. F.

Hordley, S.

G. Finlayson, S. Hordley, M. H. Brill, “Illuminant invariance at a single pixel,” in Proceedings of the IS&T/SID Eighth Color Imaging Conference (Society for Information Display, Santa Ana, Calif., 2000), pp. 85–90.

G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.

Hordley, S. D.

Judd, D. B.

MacAdam, D. L.

Marchant, J.

G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.

Marchant, J. A.

Onyango, C.

G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.

Onyango, C. M.

Stiles, W. S.

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

Wyszecki, G.

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

Wyszecki, G. W.

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Other (4)

G. Finlayson, S. Hordley, J. Marchant, C. Onyango, “Colour invariance at a pixel,” in Proceedings of The 11th British Machine Vision Conference (British Machine Vision Association, Worcester, UK, 2000) pp. 13–22.

G. Finlayson, S. Hordley, M. H. Brill, “Illuminant invariance at a single pixel,” in Proceedings of the IS&T/SID Eighth Color Imaging Conference (Society for Information Display, Santa Ana, Calif., 2000), pp. 85–90.

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

Commission Internationale de L’Eclairage (CIE) “Colorimetry.” 2nd ed. (CIE, Paris, 1986).

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Figures (3)

Fig. 1
Fig. 1

CIE daylight standard at different CCTs along with the Wien approximation to Planck’s formula.

Fig. 2
Fig. 2

(a) CIE daylight at 4000, 7000, and 20,000 K. (b) Reconstructions using mean and one eigenvector of log(illuminant). (c) b1 calculated from CIE daylight.

Fig. 3
Fig. 3

First eigenvector of log (illuminant).

Equations (15)

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CI=GISI(λ)ρ(λ)E(λ)dλ,
CI=gIρ(λcI)E(λcI),
E(λ, T)=c1λ-5 exp(-c2/Tλ)
F=r/gA.
A=1/λcR-1/λcB1/λcG-1/λcB.
E(λ, T)=h(λ)exp[u(λ)f(T)],
r=ar exp(cR-cB),g=ag exp(cG-cB),
ar=gRρ(λcR)h(λcR)gBρ(λcB)h(λcB),ag=gGρ(λcG)h(λcG)gBρ(λcB)h(λcB),
cR=u(λcR)f(T),cG=u(λcG)f(T), cB=u(λcB)f(T).
F=rgA=aragA exp[(cR-cB)-A(cG-cB)].
A=cR-cBcG-cB=u(λcR)-u(λcB)u(λcG)-u(λcB),
L(λ, T)=a(λ)+u(λ)f(T),
S=1Ns i=1NsdLidLiT,
L=Lm+p1b1+p2b2+p3b3+. .
L=Lm+p1b1

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