Abstract

Linear models have already been proved accurate enough to recover spectral functions. We have resorted to such linear models to recover spectral daylight with the response of no more than a few real sensors. We performed an exhaustive search to obtain the best set of Gaussian sensors with a combination of optimum spectral position and bandwidth. We also examined to what extent the accuracy of daylight estimation depends on the number of sensors and their spectral properties. A set of 2600 daylight spectra [J. Opt. Soc. Am. A 18, 1325 (2001)] were used to determine the basis functions in the linear model and also to evaluate the accuracy of the search. The estimated spectra are compared with the original ones for different spectral daylight and skylight sets of data within the visible spectrum. Spectral similarity, colorimetric differences, and integrated spectral irradiance errors were all taken into account. We compare our best results with those obtained by using a commercial CCD, revealing the CCD’s potential as a daylight-estimation device.

© 2004 Optical Society of America

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References

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  1. J. J. Michalsky, E. W. Kleckner, “Estimation of continuous solar spectral distributions from discrete filter measurements,” Sol. Energy 33, 57–64 (1984).
    [CrossRef]
  2. J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
    [CrossRef]
  3. S. K. Park, F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977).
    [CrossRef] [PubMed]
  4. D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
    [CrossRef]
  5. A. Garcı́a-Beltrán, J. L. Nieves, J. Hernández-Andrés, J. Romero, “Spectral reflectance recovering through linear model and narrow-band filters,” in Digest of 1995 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1995), p. 132.
  6. D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
    [CrossRef]
  7. D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.
  8. D. Connah, S. Westland, M. G. A. Thomson, “Parametric investigation of Multispectral imaging,” in 9th Congress of the International Color Association, R. Chung, A. Rodrigues, eds., Proc. SPIE4421, 943–946 (2001).
    [CrossRef]
  9. 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]
  10. L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999), pp. 393–398.
  11. D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef]
  12. L. T. Maloney, “Surface color perception and environmental constraints,” in Colour Vision: From Light to Object, R. Mausfeld, D. Heyer, eds. (Oxford U. Press, Oxford, UK, to be published).
  13. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated colour temperature,” J. Opt. Soc. Am. 54, 1031–1041 (1964).
    [CrossRef]
  14. G. T. Winch, M. C. Boshoff, C. J. Kok, A. G. du Toit, “Spectroradiometric and colorimetric characteristics of daylight in the southern hemisphere: Pretoria, South Africa,” J. Opt. Soc. Am. 56, 456–464 (1966).
    [CrossRef]
  15. V. D. P. Sastri, S. R. Das, “Typical spectral distributions and colour for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
    [CrossRef]
  16. A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).
  17. E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
    [CrossRef]
  18. J. Hernández-Andrés, J. Romero, J. L. Nieves, R. L. Lee, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
    [CrossRef]
  19. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 144–146.
  20. J. Hernández-Andrés, J. Romero, A. Garcı́a-Beltrán, J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971–977 (1998).
    [CrossRef]
  21. D. Slater, G. Healey, “Analyzing the spectral dimensionality of outdoor visible and near-infrared illumination functions,” J. Opt. Soc. Am. A 15, 2913–2920 (1998).
    [CrossRef]
  22. J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
    [CrossRef]
  23. J. Romero, A. Garcı́a-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
    [CrossRef]
  24. J. M. DiCarlo, B. A. Wandell, “Illuminant estimation: beyond the bases,” in Proceedings of Eighth Color Imaging Conference: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 91–96.
  25. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” ( Dissertation.com , Parkland, Fla., 2001). (Revised second edition of Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 157–174.
  26. J. Y. Hardeberg, “Filter selection for multispectral color image adquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.
  27. R. Piché, “Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra,” J. Opt. Soc. Am. A 19, 1946–1951 (2002).
    [CrossRef]
  28. R. Lenz, M. Österberg, J. Hiltunen, T. Jaaskelainen, J. Parkinnen, “Unsupervised filtering of color spectra,” J. Opt. Soc. Am. A 13, 1315–1324 (1996).
    [CrossRef]
  29. M. G. A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
    [CrossRef]
  30. F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.
  31. Note that the GFC is the multiple correlation coefficient R and the square root of the variance-accounted-for coefficient. Note that GFC ranges from 0 to 1, where 1 indicates a perfect reconstruction.
  32. See Ref. 19, pp. 306–310 and 828–829.
  33. ASTM Committee E-12, “Standard practice for computing the colors of objects by using the CIE system (E 308-95), in ASTM standards on color and appearance measurements” (American Society for Testing and Materials, Philadelphia, Pa., 1996), pp. 262–263.
  34. S. Quan, N. Ohta, “Evaluating hypothetical spectral sensitivities with quality factors,” J. Imaging Sci. Technol. 46, 8–14 (2002).
  35. S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).
  36. C.-C. Chiao, D. Osorio, M. Vorobyev, T. W. Cronin, “Characterization of natural illuminants in forests and the use of digital video data to reconstruct illuminant spectra,” J. Opt. Soc. Am. A 17, 1713–1721 (2000).
    [CrossRef]
  37. R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994).
    [CrossRef] [PubMed]

2002

S. Quan, N. Ohta, “Evaluating hypothetical spectral sensitivities with quality factors,” J. Imaging Sci. Technol. 46, 8–14 (2002).

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

R. Piché, “Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra,” J. Opt. Soc. Am. A 19, 1946–1951 (2002).
[CrossRef]

2001

J. Hernández-Andrés, J. Romero, J. L. Nieves, R. L. Lee, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
[CrossRef]

M. G. A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

2000

1998

1997

1996

1994

R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–4638, 4959 (1994).
[CrossRef] [PubMed]

1992

1986

1985

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

1984

J. J. Michalsky, E. W. Kleckner, “Estimation of continuous solar spectral distributions from discrete filter measurements,” Sol. Energy 33, 57–64 (1984).
[CrossRef]

1978

1977

1968

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

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

1966

1964

Berns, R. S.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Boshoff, M. C.

Brainard, D. H.

Chiao, C.-C.

Connah, D.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Parametric investigation of Multispectral imaging,” in 9th Congress of the International Color Association, R. Chung, A. Rodrigues, eds., Proc. SPIE4421, 943–946 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Cronin, T. W.

Das, S. R.

DiCarlo, J. M.

J. M. DiCarlo, B. A. Wandell, “Illuminant estimation: beyond the bases,” in Proceedings of Eighth Color Imaging Conference: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 91–96.

Dixon, E. R.

du Toit, A. G.

Freeman, W. T.

Garci´a-Beltrán, A.

J. Hernández-Andrés, J. Romero, A. Garcı́a-Beltrán, J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971–977 (1998).
[CrossRef]

J. Romero, A. Garcı́a-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[CrossRef]

A. Garcı́a-Beltrán, J. L. Nieves, J. Hernández-Andrés, J. Romero, “Spectral reflectance recovering through linear model and narrow-band filters,” in Digest of 1995 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1995), p. 132.

Hardeberg, J. Y.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” ( Dissertation.com , Parkland, Fla., 2001). (Revised second edition of Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 157–174.

J. Y. Hardeberg, “Filter selection for multispectral color image adquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.

Healey, G.

Hernández-Andrés, J.

Hiltunen, J.

Huck, F. O.

Imai, F. H.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Jaaskelainen, T.

Jiang, X.

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Judd, D. B.

Kleckner, E. W.

J. J. Michalsky, E. W. Kleckner, “Estimation of continuous solar spectral distributions from discrete filter measurements,” Sol. Energy 33, 57–64 (1984).
[CrossRef]

Kok, C. J.

Lee, R. L.

Lenz, R.

MacAdam, D. L.

Maloney, L. T.

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]

L. T. Maloney, “Surface color perception and environmental constraints,” in Colour Vision: From Light to Object, R. Mausfeld, D. Heyer, eds. (Oxford U. Press, Oxford, UK, to be published).

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999), pp. 393–398.

Marimont, D. H.

Michalsky, J. J.

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

J. J. Michalsky, E. W. Kleckner, “Estimation of continuous solar spectral distributions from discrete filter measurements,” Sol. Energy 33, 57–64 (1984).
[CrossRef]

Nieves, J. L.

J. Hernández-Andrés, J. Romero, J. L. Nieves, R. L. Lee, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

J. Hernández-Andrés, J. Romero, A. Garcı́a-Beltrán, J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971–977 (1998).
[CrossRef]

A. Garcı́a-Beltrán, J. L. Nieves, J. Hernández-Andrés, J. Romero, “Spectral reflectance recovering through linear model and narrow-band filters,” in Digest of 1995 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1995), p. 132.

Ohta, N.

S. Quan, N. Ohta, “Evaluating hypothetical spectral sensitivities with quality factors,” J. Imaging Sci. Technol. 46, 8–14 (2002).

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Osorio, D.

Österberg, M.

Park, S. K.

Parkinnen, J.

Piché, R.

Quan, S.

S. Quan, N. Ohta, “Evaluating hypothetical spectral sensitivities with quality factors,” J. Imaging Sci. Technol. 46, 8–14 (2002).

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

Romero, J.

Rosen, M. R.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Sastri, V. D. P.

Slater, D.

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 144–146.

Tarrant, A. W. S.

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

Thomson, M. G. A.

M. G. A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Parametric investigation of Multispectral imaging,” in 9th Congress of the International Color Association, R. Chung, A. Rodrigues, eds., Proc. SPIE4421, 943–946 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Vorobyev, M.

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]

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]

J. M. DiCarlo, B. A. Wandell, “Illuminant estimation: beyond the bases,” in Proceedings of Eighth Color Imaging Conference: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 91–96.

Westland, S.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

M. G. A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Parametric investigation of Multispectral imaging,” in 9th Congress of the International Color Association, R. Chung, A. Rodrigues, eds., Proc. SPIE4421, 943–946 (2001).
[CrossRef]

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

Winch, G. T.

Wyszecki, G.

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated colour temperature,” J. Opt. Soc. Am. 54, 1031–1041 (1964).
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 144–146.

Appl. Opt.

Color Res. Appl.

M. G. A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

Color Technol.

D. Connah, S. Westland, M. G. A. Thomson, “Recovering spectral information using digital camera systems,” Color Technol. 117, 309–312 (2001).
[CrossRef]

J. Imaging Sci. Technol.

S. Quan, N. Ohta, “Evaluating hypothetical spectral sensitivities with quality factors,” J. Imaging Sci. Technol. 46, 8–14 (2002).

S. Quan, N. Ohta, R. S. Berns, X. Jiang, “Unified measure of goodness and optimal design of spectral sensitivity functions,” J. Imaging Sci. Technol. 46, 485–497 (2002).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

C.-C. Chiao, D. Osorio, M. Vorobyev, T. W. Cronin, “Characterization of natural illuminants in forests and the use of digital video data to reconstruct illuminant spectra,” J. Opt. Soc. Am. A 17, 1713–1721 (2000).
[CrossRef]

J. Hernández-Andrés, J. Romero, R. L. Lee, “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412–420 (2001).
[CrossRef]

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

J. Hernández-Andrés, J. Romero, J. L. Nieves, R. L. Lee, “Color and spectral analysis of daylight in southern Europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

R. Piché, “Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra,” J. Opt. Soc. Am. A 19, 1946–1951 (2002).
[CrossRef]

D. Slater, G. Healey, “Analyzing the spectral dimensionality of outdoor visible and near-infrared illumination functions,” J. Opt. Soc. Am. A 15, 2913–2920 (1998).
[CrossRef]

J. Romero, A. Garcı́a-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[CrossRef]

D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
[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]

R. Lenz, M. Österberg, J. Hiltunen, T. Jaaskelainen, J. Parkinnen, “Unsupervised filtering of color spectra,” J. Opt. Soc. Am. A 13, 1315–1324 (1996).
[CrossRef]

Sol. Energy

J. J. Michalsky, E. W. Kleckner, “Estimation of continuous solar spectral distributions from discrete filter measurements,” Sol. Energy 33, 57–64 (1984).
[CrossRef]

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439–445 (1985).
[CrossRef]

Trans. Illum. Eng. Soc.

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

Other

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), pp. 144–146.

J. M. DiCarlo, B. A. Wandell, “Illuminant estimation: beyond the bases,” in Proceedings of Eighth Color Imaging Conference: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 91–96.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches” ( Dissertation.com , Parkland, Fla., 2001). (Revised second edition of Ph.D. dissertation, Ecole Nationale Supérieure des Télécommunications, Paris, 1999), pp. 157–174.

J. Y. Hardeberg, “Filter selection for multispectral color image adquisition,” in Proceedings of PICS 2003 (Society for Imaging Science and Technology, Springfield, Va., 2003), pp. 177–182.

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, New York, 1999), pp. 393–398.

L. T. Maloney, “Surface color perception and environmental constraints,” in Colour Vision: From Light to Object, R. Mausfeld, D. Heyer, eds. (Oxford U. Press, Oxford, UK, to be published).

D. Connah, S. Westland, M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 619–622.

D. Connah, S. Westland, M. G. A. Thomson, “Parametric investigation of Multispectral imaging,” in 9th Congress of the International Color Association, R. Chung, A. Rodrigues, eds., Proc. SPIE4421, 943–946 (2001).
[CrossRef]

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Colour in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Note that the GFC is the multiple correlation coefficient R and the square root of the variance-accounted-for coefficient. Note that GFC ranges from 0 to 1, where 1 indicates a perfect reconstruction.

See Ref. 19, pp. 306–310 and 828–829.

ASTM Committee E-12, “Standard practice for computing the colors of objects by using the CIE system (E 308-95), in ASTM standards on color and appearance measurements” (American Society for Testing and Materials, Philadelphia, Pa., 1996), pp. 262–263.

A. Garcı́a-Beltrán, J. L. Nieves, J. Hernández-Andrés, J. Romero, “Spectral reflectance recovering through linear model and narrow-band filters,” in Digest of 1995 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1995), p. 132.

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Figures (6)

Fig. 1
Fig. 1

Spectral distribution of eigenvectors V1(λ), V2(λ), V3(λ), and V4(λ) for our 2600 daylight measurements (see Ref. 18). Plain solid curve, V1(λ); dashed curve, V2(λ); dotted curve, V3(λ); solid curve with triangles, V4(λ).

Fig. 2
Fig. 2

Optimized spectral sensitivities of Gaussian sensors to recover daylight: (a) three optimum Gaussian sensors, (b) four optimum Gaussian sensors, (c) five optimum Gaussian sensors, (d) spectral response function of the sensors of the JVC TK-1270E CCD color camera.

Fig. 3
Fig. 3

GFC results obtained with the three optimum Gaussian sensors in Fig. 2(a) versus our set of 2600 daylight spectra. Solid curves, original; dashed curves, recovery.

Fig. 4
Fig. 4

GFC results obtained with the four optimum Gaussian sensors in Fig. 2(b) versus our set of 2600 daylight spectra. Solid curves, original; dashed curves, recovery.

Fig. 5
Fig. 5

GFC results obtained with the five optimum Gaussian sensors in Fig. 2(c) versus our set of 2600 daylight spectra. Solid curves, original; dashed curves, recovery.

Fig. 6
Fig. 6

GFC results obtained with the sensors of a CCD color camera (JVC TK-1270E), shown in Fig. 2(d) versus our set of 2600 daylight spectra. Solid curves, original; dashed curves, recovery.

Tables (7)

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Table 1 Optimum Spectral Sensitivities of the Gaussian Sensors for Daylight Recovery

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Table 2 Mean, Standard Deviations, and 99th Percentile Results Obtained with the Optimum Sensors (Table 1) and Our Daylight Eigenvectors (Fig. 1) Tested against a Set of 2600 Daylight Spectraa

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Table 3 Means and Standard Deviations Obtained with the Optimum Sensors (Table 1) and Our Daylight Eigenvectors (Fig. 1) Tested against a Set of 2600 Daylight Spectra, Compared (in Italics) with the Results Obtained with a Theoretical Eigenvector Expansion [(Eq. 4)]a

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Table 4 Means and Standard Deviations Obtained with Our Optimum Sensors (Table 1) and Our Daylight Eigenvectors (Fig. 1) Tested against Nine Typical CIE Daylight Spectra of Different CCTsa

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Table 5 Means and Standard Deviations Obtained with Our Optimum Sensors (Table 1) and Our Daylight Eigenvectors (Fig. 1) versus 12 Daylight Spectra Measured in the US by Lee37a

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Table 6 Means and Standard Deviations Obtained with Our Optimum Sensors (Table 1) and Daylight Eigenvectors (Fig. 1) versus Our Set of 1567 Skylight Spectra with a Sampling Rate of 5 nma

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Table 7 Means and Standard Deviations Obtained with Our Optimum Sensors (Table 1) and Our Skylight Eigenvectors (see Ref. 22) versus Our Set of 1567 Skylight Spectra with a Sampling Rate of 5 nm

Equations (9)

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E(λ)=i=1piVi(λ),
Vj|Vk=0=i=1NVj(λi)Vk(λi),jk,
i=E(λ)|Vi(λ).
ER(λ)=i=1pE(λ)|Vi(λ)Vi(λ),
ρk=n=1NE(λn)Rk(λn).
ρ¯=Λˆ¯,
(Λˆ)ki=n=1NVi(λn)Rk(λn),
(¯)i=E(λ)|Vi(λ).
ER(λ)=i=1p(¯)iVi(λ).

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