Abstract

By the principal-value decomposition process, we have obtained two linear bases for representing the spectral power distributions of illuminants, applicable for algorithms of color synthesis and analysis in artificial vision: one from experimental measurements of daylight and another combining both natural and artificial illuminants. The first basis adequately represents daylight with dimension 3, in accordance with the previous results of Judd et al. [J. Opt. Soc. Am. 54, 1031 (1964)]; however, it does not adequately represent artificial illuminants, even with a higher dimension. In the case of the second basis, many good results are obtained in the reconstruction of the spectral power distribution both of daylight and of artificial illuminants, including some fluorescent lights, with dimension 7 or even less. In consequence, we show the possibility of obtaining linear bases of a low dimension, even when the set of illuminants that we try to represent presents a certain variability in shape.

© 1997 Optical Society of America

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References

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  1. L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
    [CrossRef] [PubMed]
  2. B. A. Wandell, “The synthesis and analysis of color images,” IEEE. Trans. Patt. Anal. Machine Intell. PAMI-9, 2–13 (1987).
    [CrossRef]
  3. 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]
  4. E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
    [CrossRef]
  5. V. D. P. Sastri, S. R. Das, “Typical spectral distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
    [CrossRef]
  6. V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
    [CrossRef]
  7. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  8. Colorimetry, 2nd ed., CIE Publ. 15.2 (Central Bureau of the CIE, Vienna, 1986), pp. 70–72.

1989

1987

B. A. Wandell, “The synthesis and analysis of color images,” IEEE. Trans. Patt. Anal. Machine Intell. PAMI-9, 2–13 (1987).
[CrossRef]

1986

1978

1971

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

1968

1964

Das, S. R.

Dixon, E. R.

Hallikainen, J.

Jaaskelainen, T.

Judd, D. B.

MacAdam, D. L.

Maloney, L. T.

Manamohanan, S. B.

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

Parkkinen, J. P. S.

Sastri, V. D. P.

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

V. D. P. Sastri, S. R. Das, “Typical spectral distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
[CrossRef]

Wandell, B. A.

B. A. Wandell, “The synthesis and analysis of color images,” IEEE. Trans. Patt. Anal. Machine Intell. PAMI-9, 2–13 (1987).
[CrossRef]

L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
[CrossRef] [PubMed]

Wyszecki, G.

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Figures (7)

Fig. 1
Fig. 1

Example of reconstruction with (a) a GFC of 0.995688, (b) a GFC of 0.999566, (c) a GFC of 0.999939. Solid curve: original curve; points: reconstruction.

Fig. 2
Fig. 2

Spectral power distribution of some experimental daylight measurements.

Fig. 3
Fig. 3

Spectral profile of the first three eigenvectors of the basis of experimental measurements. Solid curve: eigenvector 1; dotted curve: eigenvector 2; dashed curve: eigenvector 3.

Fig. 4
Fig. 4

Chromaticity coordinates of daylight measurements in Granada, and Planckian locus (solid curve) and CIE daylight locus (dashed curve).

Fig. 5
Fig. 5

Spectral profile of the first six eigenvectors of the global basis. (a) Eigenvectors 1 to 3. Solid curve: eigenvector 1; dotted curve: eigenvector 2; dashed curve: eigenvector 3. (b) Eigenvectors 4 to 6. Solid curve: eigenvector 4; dotted curve: eigenvector 5; dashed curve: eigenvector 6. (c) Eigenvectors 7 to 10. Solid curve: eigenvector 7; dotted curve: eigenvector 8; dashed curve: eigenvector 9; points: eigenvector 10.

Fig. 6
Fig. 6

Examples of reconstructions of some standard CIE illuminants using four vectors of the global basis. (a) Illuminant A. GFC= 0.999425. Solid curve: illuminant A; points: reconstruction. (b) Illuminant D65. GFC = 0.999657. Solid curve: illuminant D65; points; reconstruction. (c) Illuminant F2. GFC = 0.997532. Solid curve: illuminant F2; points; reconstruction. (d) Illuminant F11. GFC = 0.999904. Solid curve: illuminant F11; points: reconstruction.

Fig. 7
Fig. 7

Examples of reconstructions of some fluorescent illuminants using the global basis. (a) Illuminant F3 with seven eigenvectors. GFC = 0.999304. Solid curve: illuminant F3; points: reconstruction. (b) Illuminant F6 with seven eigenvectors. GFC=0.998886. Solid curve: illuminant F6; points: reconstruction. (c) Illuminant F8 with seven eigenvectors. GFC = 0.998660. Solid curve: illuminant F8; points: reconstruction. (d) Commercial fluorescent tube with seven eigenvectors. GFC = 0.991128. Solid curve: commercial fluorescent tube; points: reconstruction.

Tables (3)

Tables Icon

Table 1 Chromaticity Coordinates of the Three Examples of Reconstructions Shown in Fig. 1

Tables Icon

Table 2 Atmospheric Conditions of the Days on Which the Experimental Measurements Were Taken

Tables Icon

Table 3 GFC Obtained in Each of the Standard CIE Illuminants with the Global Basis and the Basis of Experimental Measurements with Use of Different Numbers of Vectors

Equations (6)

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

E(λi)=Ee(λi)j[Ee(λj)]21/2,
Rij=E(λi)E(λj),λi=395+i5nm,
λj=395+j5nm,
Ea(λ)=n=1pE(λ)|Vn(λ)Vn(λ),
GFC=j=161E(λj)Ea(λj)j=161[E(λj)]21/2j=161[Ea(λj)]21/2,
λj=395+j5nm,

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