Abstract

We describe illumination spectra in forests and show that they can be accurately recovered from recorded digital video images. Natural illuminant spectra of 238 samples measured in temperate forests were characterized by principal-component analysis. The spectra can be accurately approximated by the mean and the first two principal components. Compared with illumination under open skies, the loci of forest illuminants are displaced toward the green region in the chromaticity plots, and unlike open sky illumination they cannot be characterized by correlated color temperature. We show that it is possible to recover illuminant spectra accurately from digital video images by a linear least-squares-fit estimation technique. The use of digital video data in spectral analysis provides a promising new approach to the studies of the spatial and temporal variation of illumination in natural scenes and the understanding of color vision in natural environments.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]
  2. J. Cohen, “Dependency of the spectral reflectance curves of munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
    [CrossRef]
  3. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [CrossRef] [PubMed]
  4. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [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. G. Wyszecki, W. S. Stiles, Color Sciences: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  7. J. A. Endler, “The color of light in forests and its implications,” Ecol. Monogr. 63, 1–27 (1993).
    [CrossRef]
  8. J. L. Simonds, “Application of characteristic vector analysis to photographic and optical response data,” J. Opt. Soc. Am. 53, 968–974 (1963).
    [CrossRef]
  9. M. Vorobyev, “Costs and benefits of increasing the dimensionality of colour vision system,” in Biophysics of Photoreception: Molecular and Phototransductive Events, C. Tardei-Ferretti, ed. (World Scientific, Singapore, 1997), pp. 280–289.
  10. M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
    [CrossRef]
  11. V. I. Smirnov, A Course of Higher Mathematics (Pergamon, New York, 1964), Vol. III, Parts 1 and 2.
  12. J. A. Endler, “On the measurement and classification of colour in studies of animal colour patterns,” Biol. J. Linnean Soc. 41, 315–352 (1990).
    [CrossRef]
  13. J. N. Lythgoe, The Ecology of Vision (Clarendon, Oxford, UK, 1979).
  14. D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
    [CrossRef] [PubMed]
  15. D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef] [PubMed]

1997 (1)

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

1994 (1)

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

1993 (1)

J. A. Endler, “The color of light in forests and its implications,” Ecol. Monogr. 63, 1–27 (1993).
[CrossRef]

1992 (1)

1990 (1)

J. A. Endler, “On the measurement and classification of colour in studies of animal colour patterns,” Biol. J. Linnean Soc. 41, 315–352 (1990).
[CrossRef]

1989 (2)

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
[CrossRef]

1986 (1)

1964 (2)

1963 (1)

Brainard, D. H.

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
[CrossRef]

Cowan, W. B.

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Endler, J. A.

J. A. Endler, “The color of light in forests and its implications,” Ecol. Monogr. 63, 1–27 (1993).
[CrossRef]

J. A. Endler, “On the measurement and classification of colour in studies of animal colour patterns,” Biol. J. Linnean Soc. 41, 315–352 (1990).
[CrossRef]

Gershon, R.

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

Giurfa, M.

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

Gumbert, A.

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

Hallikainen, J.

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).

Jaaskelainen, T.

Judd, D. B.

Kunze, J.

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

Lythgoe, J. N.

J. N. Lythgoe, The Ecology of Vision (Clarendon, Oxford, UK, 1979).

MacAdam, D. L.

Maloney, L. T.

Marimont, D. H.

Menzel, R.

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

Parkkinen, J. P. S.

Simonds, J. L.

Smirnov, V. I.

V. I. Smirnov, A Course of Higher Mathematics (Pergamon, New York, 1964), Vol. III, Parts 1 and 2.

Stiles, W. S.

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

Vorobyev, M.

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

M. Vorobyev, “Costs and benefits of increasing the dimensionality of colour vision system,” in Biophysics of Photoreception: Molecular and Phototransductive Events, C. Tardei-Ferretti, ed. (World Scientific, Singapore, 1997), pp. 280–289.

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).

Wandell, B. A.

D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
[CrossRef] [PubMed]

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Wyszecki, G.

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

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

Biol. J. Linnean Soc. (1)

J. A. Endler, “On the measurement and classification of colour in studies of animal colour patterns,” Biol. J. Linnean Soc. 41, 315–352 (1990).
[CrossRef]

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).

Ecol. Monogr. (1)

J. A. Endler, “The color of light in forests and its implications,” Ecol. Monogr. 63, 1–27 (1993).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Isr. J. Plant Sci. (1)

M. Vorobyev, A. Gumbert, J. Kunze, M. Giurfa, R. Menzel, “Flowers through the insect eyes,” Isr. J. Plant Sci. 45, 93–102 (1997).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Psychon. Sci. (1)

J. Cohen, “Dependency of the spectral reflectance curves of munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
[CrossRef]

Other (4)

V. I. Smirnov, A Course of Higher Mathematics (Pergamon, New York, 1964), Vol. III, Parts 1 and 2.

J. N. Lythgoe, The Ecology of Vision (Clarendon, Oxford, UK, 1979).

M. Vorobyev, “Costs and benefits of increasing the dimensionality of colour vision system,” in Biophysics of Photoreception: Molecular and Phototransductive Events, C. Tardei-Ferretti, ed. (World Scientific, Singapore, 1997), pp. 280–289.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Normalized spectral sensitivity functions of RGB channels of our Sony DCR-VX1000 DV camera (dashed curves), together with the reflectance spectrum of the white cardboard (solid curve) used as a standard in this study. (b) Angular reflectance function of the white cardboard. The light source was set at 90° elevation, and reflectance was measured between 90° and 10° elevation. This plot gives reflectance at a wavelength of 550 nm, but the curve is similar for all other wavelengths.

Fig. 2
Fig. 2

Chromaticities of 238 natural illuminants measured in forests. The chromaticity diagram is based on CIE (1931) color matching functions. (a) The overall chromaticity diagram. All illuminant spectra lie near the center of the diagram. The loci are constrained by a triangle with vertices at (0.250, 0.270), (0.325, 0.380), and (0.375, 0.360). (b) The central portion of the chromaticity diagram. The solid curve indicates the approximate loci of daylight spectra derived from Judd et al.1 (y=2.870x3.000x20.275). The dotted curve represents the quadratic regression line (y=4.226x5.411x20.458) that approximates loci of our forest illuminant spectra.

Fig. 3
Fig. 3

PCA of 238 forest illuminant spectra. (a) The first four characteristic vectors (principal components) derived from all illuminant spectra measured in forests. Vector 1 (V1, solid curve) explains 65.07% of the total variance, vector 2 (V2, dashed curve) explains 31.88% of the total variance, vector 3 (V3, dotted–dashed curve) explains 1.47% of the total variance, and vector 4 (V4, dotted curve) explains 1.03% of the total variance. (b) The mean spectrum of 238 forest illuminant spectra.

Fig. 4
Fig. 4

Approximation of forest illuminant spectra. Solid curves, illuminant spectrum measured by the S2000 spectroradiometer normalized to the spectral value at 560 nm. Dotted–dashed curves, reconstructed illuminant spectrum based on the linear combination of the first two principal components and the mean spectrum. Dashed curves, forest illuminant spectra approximated with the first two PCs of Judd et al.1 Dotted curves, illuminant spectrum reconstructed from the RGB values in the DV images of the white cardboard square. The spectrum is selected to represent a typical forest spectrum from one of four classes: (a) sunlight, (b) skylight, (c) green light shining through leaves, (d) a mixture of skylight and green light.

Fig. 5
Fig. 5

Comparison of the first two principal components of our 238 forest illuminant spectra (in energy units) and 622 daylight spectra of Judd et al.1 (in energy units).

Fig. 6
Fig. 6

Two vectors of the transformation matrix B¯. Vector B1 (solid curve) corresponds to the G/R value, and vector B2 (dashed curve) corresponds to the B/R value in Eq. (8) (see text for details).

Tables (3)

Tables Icon

Table 1 Errors of the Estimation of Forest Illuminant Spectra Based on the Different Linear Combinations of the Mean Spectrum and the First Four Principal Components of Forest Illuminants and of Judd et al . a Daylight Spectra

Tables Icon

Table 2 Distances between the Subspaces Spanned by Basis Functions of Forest Illuminant Spectra and Judd et al . a Daylight Spectra b

Tables Icon

Table 3 Errors of the Estimation of Forest Illuminant Spectra Based on the Direct Transformation of RGB Values Derived in This Study

Equations (31)

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

SN(λ)=S0(λ)+i=1NMiVi(λ),
Er=400700[S(λ)-SN(λ)]2dλ/L,
Er2=|z-B¯q|2=(z-B¯q)  (z-B¯q),
Er2=zc  zc-2B¯qc  zc+B¯qc  B¯qc.
Er2=Tr(zc×zc-qc×zcTB¯T-B¯qc×zc+B¯qc×qcB¯T),
d(Er2)/dB¯T=2[-qc×zcT+B¯qc×qc].
B¯=qc×zcTqc×qc-1.
zapprox=B¯qc+z0,
Sapprox(λ)=S0(λ)+M1V1(λ)+M2V2(λ),
X=400700Sapprox(λ)x(λ)dλ=400700[S0(λ)+M1V1(λ)+M2V2(λ)]x(λ)dλ,
X=X0+M1X1+M2X2,
Y=Y0+M1Y1+M2Y2,
Z=Z0+M1Z1+M2Z2.
x=X0/S0+M1X1/S0+M2X2/S01+M1S1/S0+M2S2/S0,
y=Y0/S0+M1Y1/S0+M2Y2/S01+M1S1/S0+M2S2/S0.
M1=X0Y2-X2Y0+(Y0S2-Y2S0)x+(X2S0-X0S2)yX2Y1-X1Y2+(Y2S1-Y1S2)x+(X1S2-X2S1)y,
M2=X1Y0-X0Y1+(Y1S0-Y0S1)x+(X0S1-X1S0)yX2Y1-X1Y2+(Y2S1-Y1S2)x+(X1S2-X2S1)y.
x=0.30742+0.00255M1+0.01255M21.00000+0.04531M1+0.03172M2,
y=0.32276+0.00380M1+0.00869M21.00000+0.04531M1+0.03172M2,
M1=-140.1297+165.4801x+272.4502y2.4813+26.5600x-47.4278y,
M2=-32.2696-1073.8x+1106.1y2.4813+26.5600x-47.4278y.
d2=a-aD2=(a-aD)  (a-aD)=a2-2aD  a+aD2.
d2=1-aD2.
a=k=1nakuk,
aD=i=1naDivi,
aD=k=1ni=1nak(uk  vi)vi.
aD2=k=1ni=1nj=1nak(uk  vi)(uj  vi)aj.
aD2=aWWTa=aMa,
aD2=k=1n(a˜k)2Lk,
(aD2)min=Lmin,
dmax=(1-Lmin).

Metrics