Abstract

We develop a method for calculating invariant spectra of light reflected from surfaces under changing daylight illumination conditions. A necessary part of the method is representing the illuminant in a suitable form. We represent daylight by a function E(λ, T)=h(λ)exp[u(λ)f(T)], where λ is the wavelength, T is the color temperature, h(λ) and u(λ) are any functions of λ but not T, and f(T) is any function of T but not λ. We use an eigenvalue decomposition on the logarithm of the CIE daylight standard at various color temperatures to obtain the necessary functions and show that this gives an extremely good fit to CIE daylight over our experimental range. We obtain experimental data over the range 350–830 nm from a range of standard colored surfaces for 50 daylight conditions covering a wide range of illumination spectra. Despite a considerable variation in the spectra of the reflected light, we show only small variations when the transformation is used. We investigate the possible causes of the residual variation and conclude that using the above approximation to daylight is unlikely to be a major cause. Some variation is caused by local daylight conditions being different from the CIE standard and the rest by measurement and modeling errors.

© 2002 Optical Society of America

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References

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  1. E. Vrindts, J. de Baerdemaeker, “Optical discrimination of crop, weed and soil for on-line weed detection,” in Proceedings of the First European Conference on Precision Agriculture (Bios Scientific, Oxford, UK, 1997), Vol. 2, pp. 537–544.
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  4. S. K. Nayar, R. Bolle, “Computing reflectance ratios from an image,” Pattern Recogn. 26, 1529–1542 (1993).
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    [CrossRef]
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2001 (2)

2000 (2)

B. J. Erickson, C. J. Johannsen, J. J. Vorst, “Using remote sensing to quantify weather-induced crop damage,” Aspects Appl. Biol. 60, 131–138 (2000).

J. A. Marchant, C. M. Onyango, “Shadow-invariant classification for scenes illuminated by daylight,” J. Opt. Soc. Am. A 17, 1952–1961 (2000).
[CrossRef]

1999 (1)

G. Healey, D. Slater, “Models and methods for automated material identification,” IEEE Trans. Geosci. Remote Sens. 37, 2706–2717 (1999).
[CrossRef]

1995 (1)

B. V. Funt, G. D. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

1994 (1)

1993 (1)

S. K. Nayar, R. Bolle, “Computing reflectance ratios from an image,” Pattern Recogn. 26, 1529–1542 (1993).
[CrossRef]

1990 (1)

H.-C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for color computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

1989 (1)

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1964 (1)

Bolle, R.

S. K. Nayar, R. Bolle, “Computing reflectance ratios from an image,” Pattern Recogn. 26, 1529–1542 (1993).
[CrossRef]

Breneman, E. J.

H.-C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for color computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

de Baerdemaeker, J.

E. Vrindts, J. de Baerdemaeker, “Optical discrimination of crop, weed and soil for on-line weed detection,” in Proceedings of the First European Conference on Precision Agriculture (Bios Scientific, Oxford, UK, 1997), Vol. 2, pp. 537–544.

Erickson, B. J.

B. J. Erickson, C. J. Johannsen, J. J. Vorst, “Using remote sensing to quantify weather-induced crop damage,” Aspects Appl. Biol. 60, 131–138 (2000).

Finlayson, G. D.

G. D. Finlayson, S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–265 (2001).
[CrossRef]

B. V. Funt, G. D. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

Funt, B. V.

B. V. Funt, G. D. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

Gevers, T.

T. Gevers, H. M. G. Stokman, J. van de Weijer, “Color constancy from hyper-spectral data,” in Proceedings of the British Machine Vision Conference (British Machine Vision Association, Malvern, UK, 2000), Vol. 1, pp. 292–301.

Healey, G.

G. Healey, D. Slater, “Models and methods for automated material identification,” IEEE Trans. Geosci. Remote Sens. 37, 2706–2717 (1999).
[CrossRef]

G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
[CrossRef]

Hordley, S. D.

Johannsen, C. J.

B. J. Erickson, C. J. Johannsen, J. J. Vorst, “Using remote sensing to quantify weather-induced crop damage,” Aspects Appl. Biol. 60, 131–138 (2000).

Judd, D. B.

Lee, H.-C.

H.-C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for color computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

MacAdam, D. L.

Marchant, J. A.

Nayar, S. K.

S. K. Nayar, R. Bolle, “Computing reflectance ratios from an image,” Pattern Recogn. 26, 1529–1542 (1993).
[CrossRef]

Onyango, C. M.

Schulte, C. P.

H.-C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for color computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Shafer, S. A.

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Slater, D.

G. Healey, D. Slater, “Models and methods for automated material identification,” IEEE Trans. Geosci. Remote Sens. 37, 2706–2717 (1999).
[CrossRef]

G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
[CrossRef]

Stiles, W. S.

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

Stokman, H. M. G.

T. Gevers, H. M. G. Stokman, J. van de Weijer, “Color constancy from hyper-spectral data,” in Proceedings of the British Machine Vision Conference (British Machine Vision Association, Malvern, UK, 2000), Vol. 1, pp. 292–301.

Tominaga, S.

van de Weijer, J.

T. Gevers, H. M. G. Stokman, J. van de Weijer, “Color constancy from hyper-spectral data,” in Proceedings of the British Machine Vision Conference (British Machine Vision Association, Malvern, UK, 2000), Vol. 1, pp. 292–301.

Vorst, J. J.

B. J. Erickson, C. J. Johannsen, J. J. Vorst, “Using remote sensing to quantify weather-induced crop damage,” Aspects Appl. Biol. 60, 131–138 (2000).

Vrindts, E.

E. Vrindts, J. de Baerdemaeker, “Optical discrimination of crop, weed and soil for on-line weed detection,” in Proceedings of the First European Conference on Precision Agriculture (Bios Scientific, Oxford, UK, 1997), Vol. 2, pp. 537–544.

Wandell, B. A.

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.

Aspects Appl. Biol. (1)

B. J. Erickson, C. J. Johannsen, J. J. Vorst, “Using remote sensing to quantify weather-induced crop damage,” Aspects Appl. Biol. 60, 131–138 (2000).

Color Res. Appl. (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

G. Healey, D. Slater, “Models and methods for automated material identification,” IEEE Trans. Geosci. Remote Sens. 37, 2706–2717 (1999).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

B. V. Funt, G. D. Finlayson, “Color constant color indexing,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 522–529 (1995).
[CrossRef]

H.-C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for color computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Pattern Recogn. (1)

S. K. Nayar, R. Bolle, “Computing reflectance ratios from an image,” Pattern Recogn. 26, 1529–1542 (1993).
[CrossRef]

Other (4)

T. Gevers, H. M. G. Stokman, J. van de Weijer, “Color constancy from hyper-spectral data,” in Proceedings of the British Machine Vision Conference (British Machine Vision Association, Malvern, UK, 2000), Vol. 1, pp. 292–301.

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

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

E. Vrindts, J. de Baerdemaeker, “Optical discrimination of crop, weed and soil for on-line weed detection,” in Proceedings of the First European Conference on Precision Agriculture (Bios Scientific, Oxford, UK, 1997), Vol. 2, pp. 537–544.

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Figures (6)

Fig. 1
Fig. 1

(a) Mean and (b) first eigenvector of log(E) for CIE data.

Fig. 2
Fig. 2

(a) Derived values of b1 plotted against CCT along with fitted curve. (b) CIE daylight (heavy curves) and reconstructions (light curves) calculated with the mean and the first eigenvector of log(E).

Fig. 3
Fig. 3

Spectra of light reflected from a sample of seven surfaces from the experimental set. (a) Original spectra; (b) invariant spectra. Row 1 (top), barium sulfate block; row 2, blue representative; row 3, red representative; row 4, green representative; row 5, blue/green representative; row 6, yellow representative, row 7, red/blue representative.

Fig. 4
Fig. 4

Simulations of spectra from two surfaces. Top, blue surface; bottom, yellow surface. (a) Reflected light, (b) invariant spectra calculated with the eigenvector from CIE illumination, (c) invariant spectra calculated with the eigenvector from estimated Silsoe illumination.

Fig. 5
Fig. 5

First eigenvector of log(E) for Silsoe data.

Fig. 6
Fig. 6

Simulation of spectra from the yellow surface as the amount of specular reflection is changed. Dotted curve, no specular reflection; heavy solid curve, complete specular reflection; light curves, intermediate values.

Tables (2)

Tables Icon

Table 1 Standard Deviation of the Spectral Angle from the Mean for Each Surface

Tables Icon

Table 2 Performance Indicators When the Normalizing Wavelengths Are Changed

Equations (21)

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E(λ, T)=c1λ-5 exp(-c2/Tλ)
E(λ, T)=h(λ)exp[u(λ)f(T)],
CI=GISI(λ)ρ(λ)E(λ, T)dλ,
Cλ=gρ(λ)E(λ, T),
F=r/gA
A=u(λcR)-u(λcB)u(λcG)-u(λcB),
yλ=CλCλn=ρ(λ)E(λ, T)ρ(λn)E(λn, T),
F12=yλ1/yλ2A12,
A12=u(λ1)-u(λn)u(λ2)-u(λn).
F12=a1/a2A12,
a1=ρ(λ1)h(λ1)ρ(λn)h(λn);a2=ρ(λ2)h(λ2)ρ(λn)h(λn).
Fλ=yλ/yλ2Aλ,
L(λ, T)=a(λ)+u(λ)f(T),
L=Lm+p1b1+p2b2+p3b3+,
L=Lm+p1b1
b1=2.3-21.0 exp(-T/4000.0).
cos(λ)=Ca·Cb|CaCb|,
Fλ=1.0.
CI=GISI(λ)E(λ, T)dλ+GIsSI(λ)ρs(λ)E(λ, T)dλ
CI=GISI(λ)ρ(λ)+GIsGIρs(λ)E(λ, T)dλ,
CI=GISI(λ)[ρ(λ)+r]E(λ, T)dλ.

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