Abstract

The 1257 reflectance spectra of the chips in the Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976) were measured with a rapid acousto-optic spectrophotometer. Measured spectra were sampled from 400 to 700 nm at 5-nm intervals. The correlation matrix of this sample set was formed, and the characteristic vectors of this matrix were computed. It is shown, contradictory to earlier recommendations [ Psychon. Sci. 1, 369 ( 1964)], that as many as eight characteristic spectra are needed to achieve good representation for all spectra.

© 1989 Optical Society of America

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References

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  1. Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976).
  2. M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
    [CrossRef]
  3. 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]
  4. H. Sobagaki, “New approach to the calorimetric standardization for object colors,” Bull. Electrotech. Lab. Jpn. 48, 875–792 (1984) (in Japanese).
  5. R. A. Young, “Principal-component analysis of macaque lateral geniculate nucleus chromatic data,” J. Opt. Soc. Am. A 3, 1735–1742 (1986).
    [CrossRef] [PubMed]
  6. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
  7. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small number of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [CrossRef] [PubMed]
  8. J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).
  9. T. Jaaskelainen, J. Parkkinen, E. Oja, “Color discrimination by optical recognition,” in Proceedings of the 18th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 766–768.
  10. J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
    [CrossRef]
  11. J. Parkkinen, T. Jaaskelainen, “Color representation using statistical pattern recognition,” Appl. Opt. 26, 4240–4245 (1987).
    [CrossRef] [PubMed]
  12. E. Oja, Subspace Method of Pattern Recognition (Research Studies, Letchworth, England, 1983).

1988

J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
[CrossRef]

1987

1986

1985

J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).

1984

H. Sobagaki, “New approach to the calorimetric standardization for object colors,” Bull. Electrotech. Lab. Jpn. 48, 875–792 (1984) (in Japanese).

1964

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

Cohen, J.

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

D’Zmura, M.

Hallikainen, J.

J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
[CrossRef]

Jaaskelainen, T.

J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
[CrossRef]

J. Parkkinen, T. Jaaskelainen, “Color representation using statistical pattern recognition,” Appl. Opt. 26, 4240–4245 (1987).
[CrossRef] [PubMed]

J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).

T. Jaaskelainen, J. Parkkinen, E. Oja, “Color discrimination by optical recognition,” in Proceedings of the 18th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 766–768.

Lennie, P.

Maloney, L. T.

Oja, E.

J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).

T. Jaaskelainen, J. Parkkinen, E. Oja, “Color discrimination by optical recognition,” in Proceedings of the 18th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 766–768.

E. Oja, Subspace Method of Pattern Recognition (Research Studies, Letchworth, England, 1983).

Parkkinen, J.

J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
[CrossRef]

J. Parkkinen, T. Jaaskelainen, “Color representation using statistical pattern recognition,” Appl. Opt. 26, 4240–4245 (1987).
[CrossRef] [PubMed]

T. Jaaskelainen, J. Parkkinen, E. Oja, “Color discrimination by optical recognition,” in Proceedings of the 18th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 766–768.

Parkkinen, J. P. S.

J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).

Sobagaki, H.

H. Sobagaki, “New approach to the calorimetric standardization for object colors,” Bull. Electrotech. Lab. Jpn. 48, 875–792 (1984) (in Japanese).

Wandell, B. A.

Young, R. A.

Acta Polytech. Scand.

J. P. S. Parkkinen, T. Jaaskelainen, E. Oja, “Pattern recognition approach to color measurement and discrimination,” Acta Polytech. Scand. 149, 171–174 (1985).

Appl. Opt.

Bull. Electrotech. Lab. Jpn.

H. Sobagaki, “New approach to the calorimetric standardization for object colors,” Bull. Electrotech. Lab. Jpn. 48, 875–792 (1984) (in Japanese).

J. Opt. Soc. Am. A

Psychon. Sci.

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

Rev. Sci. Instrum.

J. Hallikainen, J. Parkkinen, T. Jaaskelainen, “An acousto-optic color spectrometer,” Rev. Sci. Instrum. 59, 81–83 (1988).
[CrossRef]

Other

E. Oja, Subspace Method of Pattern Recognition (Research Studies, Letchworth, England, 1983).

Munsell Book of Color—Matte Finish Collection (Munsell Color, Baltimore, Md., 1976).

T. Jaaskelainen, J. Parkkinen, E. Oja, “Color discrimination by optical recognition,” in Proceedings of the 18th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 766–768.

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Figures (6)

Fig. 1
Fig. 1

The four first eigenvectors of the set of 1257 reflectance spectra measured from the Munsell book of colors.

Fig. 2
Fig. 2

A measured spectrum (5 B 7/8) and its reconstruction with four eigenvectors.

Fig. 3
Fig. 3

A measured spectrum (5 R 6/14) and its reconstruction with eight eigenvectors.

Fig. 4
Fig. 4

Error bands for four-dimensional (area between dotted curves) and eight-dimensional (area between solid curves) reconstructions. The upper and lower limits of the bands represent the maximum positive and the maximum negative differences in the absolute reflectance scale.

Fig. 5
Fig. 5

Error distribution in the band of eight-dimensional reconstructions at 500 nm. Here N0 is the number of samples, and error intervals are 0.005. The ith bar represents the error interval, which is i0.005 apart from the error 0.

Fig. 6
Fig. 6

The worst fit obtained using four eigenvectors (dotted curve). The dashed curve represents the worst-case eight-dimensional reconstruction, and the solid curve represents the original spectrum.

Tables (4)

Tables Icon

Table 1 Eight Characteristic Vectors and Corresponding Eigenvalues for Munsell Colorsa

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Table 2 xy Color Coordinates of Two Munsell Samples and Their Reconstructions with Two, Four, Six, and Eight Eigenvectorsa

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Table 3 Maximum and Average Errors of xy Color Coordinates

Tables Icon

Table 4 Cumulative Error Distributions for 4–10-Dimensional Reconstructions

Equations (4)

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s ( λ ) = [ s ( λ 1 ) , s ( λ 2 ) , , s ( λ n ) ] T ,
R = i = 1 p s i ( λ ) s i ( λ ) T ,
R Φ = σ Φ ,
s a ( λ ) = j = 1 n [ s a ( λ ) Φ j ( λ ) ] Φ j ( λ ) ,

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