Abstract

Theoretical analyses of spectral reflectances of natural surfaces suggest that their perceived colors can be well reproduced by approximations comprising combinations of three or four spectral basis functions. The aim of the present work was to assess psychophysically the number of basis functions necessary to reproduce entire natural outdoor scenes. Hyperspectral images of 20 such scenes were each subjected to a principal component analysis and then reproduced with a variable number of basis functions. The quality of the color approximation under daylight illumination was quantified theoretically in CIELAB space and psychophysically by spatial and temporal two-alternative forced-choice measurements in which the original and the approximated images were compared on a calibrated color monitor. Although five basis functions produced on average unit error in CIELAB space, original images were visually indistinguishable from their approximations only if there were at least eight basis functions. The combination of the spectral diversity of the natural world and the observed levels of color discrimination suggest that estimates of the minimum number of basis functions necessary to reproduce natural scenes may need to be revised upward.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Nassau, The Physics and Chemistry of Color. The Fifteen Causes of Color (Wiley, New York, 1983).
  2. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonomic 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. 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]
  7. J. Romero, A. García-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
    [CrossRef]
  8. 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]
  9. D. H. Marimont, B. A. Wandell, “Linear-models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef] [PubMed]
  10. M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
    [CrossRef]
  11. L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999), pp. 387–416.
  12. C. C. Chiao, T. W. Cronin, D. Osorio, “Color signals in natural scenes: characteristics of reflectance spectra and effects of natural illuminants,” J. Opt. Soc. Am. A 17, 218–224 (2000).
    [CrossRef]
  13. J. L. Dannemiller, “Spectral reflectance of natural objects: how many basis functions are necessary?” J. Opt. Soc. Am. A 9, 507–515 (1992).
    [CrossRef]
  14. 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]
  15. E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).
  16. E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).
  17. E. K. Oxtoby, D. H. Foster, “Perceptual limits on low-dimensional models of Munsell reflectance spectra” (to be published).
  18. T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
    [CrossRef]
  19. M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
    [CrossRef]
  20. 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]
  21. G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
    [CrossRef]
  22. M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
    [CrossRef] [PubMed]
  23. M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 328–338 (1992).
    [CrossRef]
  24. S. M. C. Nascimento, F. P. Ferreira, D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
    [CrossRef]
  25. Principal components of spectral data can be calculated about the mean spectrum or about the zero spectrum. For a discussion of the two methods, see Ref. [26].
  26. M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
    [CrossRef]
  27. C. Loader, Local Regression and Likelihood (Springer, New York, 1999).
  28. D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
    [CrossRef]
  29. G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vision Res. 42, 559–563 (2002).
    [CrossRef] [PubMed]
  30. S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).
  31. S. M. C. Nascimento, D. H. Foster, “Chromatic quality of natural scenes represented by low-dimensional approximations to reflectance functions,” Perception S29, 72 (2000).

2003 (2)

E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).

M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
[CrossRef]

2002 (3)

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vision Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

S. M. C. Nascimento, F. P. Ferreira, D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

2001 (2)

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]

S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).

2000 (3)

1997 (1)

1994 (2)

M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
[CrossRef]

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

1992 (3)

1991 (1)

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

1990 (1)

1989 (1)

1986 (4)

1980 (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

1964 (2)

Amano, K.

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).

Baraas, R. C.

E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).

Bischof, W. F.

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

Bloch, O.

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vision Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

Brill, M. H.

M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
[CrossRef]

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

Buchsbaum, G.

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vision Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

Chiao, C. C.

Cohen, J.

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

Cronin, T. W.

D’Zmura, M.

Dannemiller, J. L.

Ferreira, F. P.

Foster, D. H.

E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).

S. M. C. Nascimento, F. P. Ferreira, D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).

S. M. C. Nascimento, D. H. Foster, “Chromatic quality of natural scenes represented by low-dimensional approximations to reflectance functions,” Perception S29, 72 (2000).

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

E. K. Oxtoby, D. H. Foster, “Perceptual limits on low-dimensional models of Munsell reflectance spectra” (to be published).

García-Beltrán, A.

Gershon, R.

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

Hallikainen, J.

Hernández-Andrés, J.

Iverson, G.

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.

Lee, R. L.

Lennie, P.

Loader, C.

C. Loader, Local Regression and Likelihood (Springer, New York, 1999).

MacAdam, D. L.

Maloney, L. T.

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]

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, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999), pp. 387–416.

Marimont, D. H.

Nascimento, S. M.

S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).

Nascimento, S. M. C.

S. M. C. Nascimento, F. P. Ferreira, D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

S. M. C. Nascimento, D. H. Foster, “Chromatic quality of natural scenes represented by low-dimensional approximations to reflectance functions,” Perception S29, 72 (2000).

Nassau, K.

K. Nassau, The Physics and Chemistry of Color. The Fifteen Causes of Color (Wiley, New York, 1983).

Nieves, J. L.

Osorio, D.

Oxtoby, E. K.

E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

E. K. Oxtoby, D. H. Foster, “Perceptual limits on low-dimensional models of Munsell reflectance spectra” (to be published).

Parkkinen, J.

Parkkinen, J. P. S.

Romero, J.

Toyooka, S.

Trussell, H. J.

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

Vorobyev, M.

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).

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

Wandell, B. A.

West, G.

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

Wyszecki, G.

Color Res. Appl. (4)

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

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

S. M. Nascimento, D. H. Foster, K. Amano, “Repro- duction of colors of natural scenes by low-dimensional models,” Invest. Ophthalmol. Visual Sci. 42, S720 (2001).

J. Franklin Inst. (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (13)

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

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]

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

M. D’Zmura, G. Iverson, “Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 11, 2389–2400 (1994).
[CrossRef]

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]

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

M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
[CrossRef] [PubMed]

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]

C. C. Chiao, T. W. Cronin, D. Osorio, “Color signals in natural scenes: characteristics of reflectance spectra and effects of natural illuminants,” J. Opt. Soc. Am. A 17, 218–224 (2000).
[CrossRef]

J. L. Dannemiller, “Spectral reflectance of natural objects: how many basis functions are necessary?” J. Opt. Soc. Am. A 9, 507–515 (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]

S. M. C. Nascimento, F. P. Ferreira, D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

Perception (3)

S. M. C. Nascimento, D. H. Foster, “Chromatic quality of natural scenes represented by low-dimensional approximations to reflectance functions,” Perception S29, 72 (2000).

E. K. Oxtoby, D. H. Foster, K. Amano, S. M. C. Nascimento, “How many basis functions are needed to reproduce coloured patterns under illuminant changes?” Perception S31, 66 (2002).

E. K. Oxtoby, D. H. Foster, R. C. Baraas, “How many spectral basis functions do red-green dichromats need to discriminate surface colours under different lights?” Perception S32, 147 (2003).

Psychol. Bull. (1)

D. H. Foster, W. F. Bischof, “Thresholds from psychometric functions: superiority of bootstrap to incremental and probit variance estimators,” Psychol. Bull. 109, 152–159 (1991).
[CrossRef]

Psychonomic Sci. (1)

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

Vision Res. (1)

G. Buchsbaum, O. Bloch, “Color categories revealed by non-negative matrix factorization of Munsell color spectra,” Vision Res. 42, 559–563 (2002).
[CrossRef] [PubMed]

Other (5)

Principal components of spectral data can be calculated about the mean spectrum or about the zero spectrum. For a discussion of the two methods, see Ref. [26].

C. Loader, Local Regression and Likelihood (Springer, New York, 1999).

K. Nassau, The Physics and Chemistry of Color. The Fifteen Causes of Color (Wiley, New York, 1983).

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999), pp. 387–416.

E. K. Oxtoby, D. H. Foster, “Perceptual limits on low-dimensional models of Munsell reflectance spectra” (to be published).

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 (5)

Fig. 1
Fig. 1

Reproduction of an original scene under D 65 and approximations based on 1, 2, and 4 spectral basis functions.

Fig. 2
Fig. 2

Simultaneous and sequential procedures for stimulus presentation.

Fig. 3
Fig. 3

Average CIELAB color difference Δ E ¯ a b * between original and PCA-approximated images as a function of the number n of components in each approximation, calculated over ten rural scenes (squares) and over ten urban scenes (triangles). Overlapping points have been slightly displaced horizontally.

Fig. 4
Fig. 4

Discriminability of original and PCA-approximated images by one observer. Percent-correct discrimination based on 15 trials per level is plotted (circles) as a function of the number n of components in each approximation. The smooth curve is a locally weighted logistic regression. Chance level is 50%. For two criterion levels of performance of 75% and 55%, threshold numbers of components of n 75 % and n 55 % are indicated by crosses on the abscissa. Images were of a rural scene, the stimulus presentation was sequential, and the observer was JL.

Fig. 5
Fig. 5

Threshold numbers of components for discriminating original and PCA-approximated images. For two criterion levels of performance of 75% and 55% correct, thresholds n 75 % and n 55 % are shown for ten rural and ten urban scenes, three observers, and simultaneous and sequential stimulus presentations. Error bars represent ± 1 SE estimated from a bootstrap based on 1000 replications with resampling over scenes.

Tables (1)

Tables Icon

Table 1 Quality of Colorimetric Approximations as a Function of Number of Components

Equations (1)

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

Δ E ¯ a b * = 1 N i = 1 N [ ( L i * L ̂ i * ) 2 + ( a i * a ̂ i * ) 2 + ( b i * b ̂ i * ) 2 ] 1 2 .

Metrics