Abstract

We explain a method for calculating the optimal sampling interval of color spectra. The 1269 measured Munsell matt reflectance spectra set is used as the test set. The effect of light sources on the required sampling interval with different types of spectra is studied. It is shown that a 20nm interval is enough for the smooth Munsell set alone, but 10nm is not enough for the same set matched with a fluorescent light source. However, 5nm is shown to be enough in most situations.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Morovic, "Metamer sets," Ph.D. dissertation (University of East Anglia, 2002).
  2. K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).
  3. C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
    [Crossref]
  4. P. Moon and D. Spencer, "Polynomial representation of reflectance curves," J. Opt. Soc. Am. 35, 597-600 (1945).
    [Crossref]
  5. W. Brewer and F. Holly, "Syntheses of spectral-distribution curves," J. Opt. Soc. Am. 38, 858-874 (1948).
    [Crossref] [PubMed]
  6. R. Schettini, "Deriving spectral reflectance functions of computer-simulated object colours," Comput. Graph. Forum 13, 211-217 (1994).
    [Crossref]
  7. J. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
    [Crossref]
  8. E. Early and M. Nadal, "Uncertainty analysis for reflectance colorimetry," Color Res. Appl. 29, 205-216 (2004).
    [Crossref]
  9. J. Gardner, "Uncertainty estimation in colour measurement," Color Res. Appl. 25, 349-355 (2000).
    [Crossref]
  10. A. Kaarna and J. Parkkinen, "Transform based lossy compression of multispectral images," Pattern Anal. Appl. 4, 39-50 (2001).
    [Crossref]
  11. G. Buchsbaum and A. Gottschalk, "Chromacity coordinates of frequency-limited functions," J. Opt. Soc. Am. A 1, 885-887 (1984).
    [Crossref] [PubMed]
  12. G. Wyszecki and W. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982).
  13. J. Romero, L. Jiménez del Barco, and E. Hita, "Mathematical reconstruction of color-matching functions," J. Opt. Soc. Am. A 9, 25-29 (1992).
    [Crossref]
  14. W. Stiles, G. Wyszecki, and N. Ohta, "Counting metameric object-color stimuli using frequency-limited spectral reflectance functions," J. Opt. Soc. Am. 67, 779-784 (1977).
    [Crossref]
  15. L. 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]
  16. J. Van Hateren, "Spatial, temporal and spectral preprocessing for colour vision," Proc. R. Soc. London, Ser. B 251, 61-68 (1993).
    [Crossref]
  17. V. Bonnardel and L. Maloney, "Daylight, biochrome surfaces and human chromatic response in the Fourier domain," J. Opt. Soc. Am. A 17, 677-686 (2000).
    [Crossref]
  18. J. Romero, E. Valero, J. Hernándes-Andrés, and J. Nieves, "Color-signal filtering in the Fourier-frequency domain," J. Opt. Soc. Am. A 20, 1714-1724 (2003).
    [Crossref]
  19. E. Ifeachor and B. Jervis, Digital Signal Processing: A Practical Approach (Prentice Hall, 2002).
  20. R. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).
  21. A. Kaarna, "Multispectral image compression using the wavelet transform," Ph.D. dissertation (Lappeenranta University of Technology, 2000).
  22. H. Fairman, "The calculation of weight factors for tristimulus integration," Color Res. Appl. 10, 199-203 (1985).
    [Crossref]
  23. J. Hernándes-Andrés, J. Romero, and R. L. Lee, Jr., "Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain," J. Opt. Soc. Am. A 18, 412-420 (2001).
    [Crossref]
  24. University of Joensuu Color Group, "Spectral Database," http://spectral.joensuu.fi.

2004 (3)

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
[Crossref]

E. Early and M. Nadal, "Uncertainty analysis for reflectance colorimetry," Color Res. Appl. 29, 205-216 (2004).
[Crossref]

2003 (1)

2001 (2)

2000 (2)

1994 (1)

R. Schettini, "Deriving spectral reflectance functions of computer-simulated object colours," Comput. Graph. Forum 13, 211-217 (1994).
[Crossref]

1993 (1)

J. Van Hateren, "Spatial, temporal and spectral preprocessing for colour vision," Proc. R. Soc. London, Ser. B 251, 61-68 (1993).
[Crossref]

1992 (1)

1989 (1)

1986 (1)

1985 (1)

H. Fairman, "The calculation of weight factors for tristimulus integration," Color Res. Appl. 10, 199-203 (1985).
[Crossref]

1984 (1)

1977 (1)

1948 (1)

1945 (1)

Ajito, T.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Berns, R.

R. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

Bonnardel, V.

Brewer, W.

Buchsbaum, G.

Early, E.

E. Early and M. Nadal, "Uncertainty analysis for reflectance colorimetry," Color Res. Appl. 29, 205-216 (2004).
[Crossref]

Fairman, H.

H. Fairman, "The calculation of weight factors for tristimulus integration," Color Res. Appl. 10, 199-203 (1985).
[Crossref]

Gardner, J.

J. Gardner, "Uncertainty estimation in colour measurement," Color Res. Appl. 25, 349-355 (2000).
[Crossref]

Gottschalk, A.

Hallikainen, J.

Haneishi, H.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Hernándes-Andrés, J.

Hita, E.

Holly, F.

Ifeachor, E.

E. Ifeachor and B. Jervis, Digital Signal Processing: A Practical Approach (Prentice Hall, 2002).

Jaaskelainen, T.

Jervis, B.

E. Ifeachor and B. Jervis, Digital Signal Processing: A Practical Approach (Prentice Hall, 2002).

Jiménez del Barco, L.

Kaarna, A.

A. Kaarna and J. Parkkinen, "Transform based lossy compression of multispectral images," Pattern Anal. Appl. 4, 39-50 (2001).
[Crossref]

A. Kaarna, "Multispectral image compression using the wavelet transform," Ph.D. dissertation (Lappeenranta University of Technology, 2000).

Komiya, Y.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Lee, R. L.

Li, C.

C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
[Crossref]

Luo, M.

C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
[Crossref]

Maloney, L.

Moon, P.

Morovic, P.

P. Morovic, "Metamer sets," Ph.D. dissertation (University of East Anglia, 2002).

Nadal, M.

E. Early and M. Nadal, "Uncertainty analysis for reflectance colorimetry," Color Res. Appl. 29, 205-216 (2004).
[Crossref]

Nieves, J.

Ohsawa, K.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Ohta, N.

Ohyama, N.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Parkkinen, J.

A. Kaarna and J. Parkkinen, "Transform based lossy compression of multispectral images," Pattern Anal. Appl. 4, 39-50 (2001).
[Crossref]

J. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
[Crossref]

Rigg, B.

C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
[Crossref]

Romero, J.

Schettini, R.

R. Schettini, "Deriving spectral reflectance functions of computer-simulated object colours," Comput. Graph. Forum 13, 211-217 (1994).
[Crossref]

Spencer, D.

Stiles, W.

Valero, E.

Van Hateren, J.

J. Van Hateren, "Spatial, temporal and spectral preprocessing for colour vision," Proc. R. Soc. London, Ser. B 251, 61-68 (1993).
[Crossref]

Wyszecki, G.

Yamaguchi, M.

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

Color Res. Appl. (4)

C. Li, M. Luo, and B. Rigg, "A new method for computing optimum weights for calculating CIE tristimulus values," Color Res. Appl. 29, 91-103 (2004).
[Crossref]

E. Early and M. Nadal, "Uncertainty analysis for reflectance colorimetry," Color Res. Appl. 29, 205-216 (2004).
[Crossref]

J. Gardner, "Uncertainty estimation in colour measurement," Color Res. Appl. 25, 349-355 (2000).
[Crossref]

H. Fairman, "The calculation of weight factors for tristimulus integration," Color Res. Appl. 10, 199-203 (1985).
[Crossref]

Comput. Graph. Forum (1)

R. Schettini, "Deriving spectral reflectance functions of computer-simulated object colours," Comput. Graph. Forum 13, 211-217 (1994).
[Crossref]

J. Imaging Sci. Technol. (1)

K. Ohsawa, T. Ajito, Y. Komiya, H. Haneishi, M. Yamaguchi, and N. Ohyama, "Six band HDTV camera system for spectrum-based color reproduction," J. Imaging Sci. Technol. 48, 85-92 (2004).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (7)

Pattern Anal. Appl. (1)

A. Kaarna and J. Parkkinen, "Transform based lossy compression of multispectral images," Pattern Anal. Appl. 4, 39-50 (2001).
[Crossref]

Proc. R. Soc. London, Ser. B (1)

J. Van Hateren, "Spatial, temporal and spectral preprocessing for colour vision," Proc. R. Soc. London, Ser. B 251, 61-68 (1993).
[Crossref]

Other (6)

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

E. Ifeachor and B. Jervis, Digital Signal Processing: A Practical Approach (Prentice Hall, 2002).

R. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

A. Kaarna, "Multispectral image compression using the wavelet transform," Ph.D. dissertation (Lappeenranta University of Technology, 2000).

P. Morovic, "Metamer sets," Ph.D. dissertation (University of East Anglia, 2002).

University of Joensuu Color Group, "Spectral Database," http://spectral.joensuu.fi.

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 (3)

Fig. 1
Fig. 1

Spectra of some measured light sources.

Fig. 2
Fig. 2

Cumulative sum of the relative spectral energy.

Fig. 3
Fig. 3

Frequency-limited spectrum.

Tables (6)

Tables Icon

Table 1 Lowest Possible Frequency Limit and the Corresponding Sampling Interval for Relative Spectral Energy 99.0% and 99.9%

Tables Icon

Table 2 Achieved Relative Energy with Different Sampling Intervals for the Munsell Set without a Light Source

Tables Icon

Table 3 Achieved Relative Energy with Different Sampling Intervals for the Munsell Set with a Light Source a

Tables Icon

Table 4 Maximum Δ E of Different Sampling Intervals

Tables Icon

Table 5 Errors of Different Intervals

Tables Icon

Table 6 Optimal Sampling Interval for the Munsell Set with Some Light Sources

Equations (10)

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

F ( ω ) = f ( x ) exp ( i ϖ x ) , x Z .
E ( ω ) = F ( ω ) 2 .
n = 2 ( λ n λ 1 ) + 1 = λ n λ 1 Δ λ = 1 2 f l ,
s f ( λ ) = n = s ( m 2 f l ) sinc [ 2 f l ( λ n 2 f l ) ] .
Δ E = [ Δ L * 2 + Δ a * 2 + Δ b * 2 ] 1 2 ,
ε SNR = 10 log 10 [ 1 n i = 1 n s 1 ( λ i ) 2 ε MSE ] ,
ε MSE = 1 n i = 1 n Δ s ( λ i ) 2 .
ε PSNR = 10 log 10 ( S ̂ 2 ε MSE ) .
ε RMSE = [ 1 n i = 1 n Δ s ( λ i ) 2 ] 1 2 ,
ε GFC = [ i = 1 n s 1 ( λ i ) s 2 ( λ i ) ] [ i = 1 n s 1 ( λ i ) 2 ] 1 2 [ i = 1 n s 2 ( λ i ) 2 ] 1 2 ,

Metrics