Abstract

The goal is to construct a simple model relating the conceptually defined Munsell color space to a physical representation of the relationship among the reflectance spectra obtained from the color chips comprising the Munsell color atlas. In the model both the Munsell conceptual system and the transformed reflectance spectra are shown to be well represented in Euclidean space, and the two spaces are related by a simple linear transformation. A practical implication is that the method allows one to compare the location of an empirical reflectance spectrum with the aiming point in the conceptual structure.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007 (1)

2006 (4)

M. Elias, C. Chartier, G. Prévot, H. Garay, and C. Vignaud, “The colour of ochres explained by their composition,” Mater. Sci. Eng., B 127, 70-80 (2006).
[CrossRef]

A. K. Romney and J. T. Fulton, “Transforming reflectance spectra into Munsell color space by using prime colors,” Proc. Natl. Acad. Sci. U.S.A. 103, 15698-15703 (2006).
[CrossRef] [PubMed]

H. Laamanen, T. Jaaskelainen, and J. Parkkinen, “Conversion between the reflectance spectra and the Munsell notation,” Color Res. Appl. 31, 57-66 (2006).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskelään, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

2005 (3)

F. Iova, A. Trutia, and V. Vasile, “Spectral analysis of the color of some pigments,” Rom. Rep. Phys. 57, 905-911 (2005).

A. Alsam and J. Y. Hardeberg, “Convex reduction of calibration charts,” Proc. SPIE 5667, 38-46 (2005).
[CrossRef]

A. K. Romney and R. G. D'Andrade, “Modeling lateral geniculate nucleus cell response spectra and Munsell reflectance spectra with cone sensitivity curves,” Proc. Natl. Acad. Sci. U.S.A. 102, 16512-16517 (2005).
[CrossRef] [PubMed]

2004 (1)

W. Li-Qin, D. Gao-Chao, W. Xiao-Qi, X. Zhou-Kuan, and L. Guo-Zheng, “Analysis and protection of one thousand hand Buddha in Dazu stone sculptures,” Chin. J. Chem. 22, 172-176 (2004).

2003 (3)

R. G. D'Andrade and A. K. Romney, “A quantitative model for transforming reflectance spectra into the Munsell color space using cone sensitivity functions and opponent process weights,” Proc. Natl. Acad. Sci. U.S.A. 100, 6281-6286 (2003).
[CrossRef] [PubMed]

A. K. Romney and T. Indow, “Munsell reflectance spectra represented in three-dimensional Euclidean space,” Color Res. Appl. 28, 182-196 (2003).
[CrossRef]

S. A. Burns, J. B. Cohen, and E. N. Kuznetsov, “The Munsell color system in fundamental color space,” Color Res. Appl. 28, 182-196 (2003).
[CrossRef]

2002 (1)

A. K. Romney and T. Indow, “A model for the simultaneous analysis of reflectance spectra and basis factors of Munsell color samples under D65 illumination in three-dimensional Euclidean space,” Proc. Natl. Acad. Sci. U.S.A. 99, 11543-11546 (2002).
[CrossRef] [PubMed]

2000 (1)

1999 (2)

T. Indow, “Predictions based on Munsell notation. I. Perceptual color differences,” Color Res. Appl. 24, 10-18 (1999).
[CrossRef]

R. Lenz and P. Meer, “Non-Euclidean structure of the spectral color space,” Proc. SPIE 3826, 101-112 (1999).
[CrossRef]

1996 (1)

1994 (1)

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

1992 (2)

1990 (1)

1986 (1)

1981 (1)

H. R. Davidson, “Formulations for the OSO Uniform Color Scales committee samples,” Color Res. Appl. 6, 38-52 (1981).
[CrossRef]

1980 (1)

T. Indow, “Global color metrics and color appearance systems,” Color Res. Appl. 5, 5-12 (1980).
[CrossRef]

1977 (1)

S. P. Gudder, “Convexity and mixtures,” SIAM Rev. 19, 221-240 (1977).
[CrossRef]

1975 (1)

D. H. Krantz, “Color measurement and color theory. 1. Representation theorem for Grassmann structures,” J. Math. Psychol. 12, 283-303 (1975).
[CrossRef]

1973 (1)

D. H. Krantz, “Fundamental measurement of force and Newton's first and second laws of motion,” Philos. Sci. 40, 481-495 (1973).
[CrossRef]

1964 (1)

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

1955 (1)

1943 (1)

1856 (1)

J. C. Maxwell, “Theory of the perception of colors,” Trans. R. Scottish Soc. Arts. 4, 394-400 (1856); reprinted as Sources of Color Science, D.L.MacAdam, ed. (MIT, 1970).

Chin. J. Chem. (1)

W. Li-Qin, D. Gao-Chao, W. Xiao-Qi, X. Zhou-Kuan, and L. Guo-Zheng, “Analysis and protection of one thousand hand Buddha in Dazu stone sculptures,” Chin. J. Chem. 22, 172-176 (2004).

Color Res. Appl. (8)

S. A. Burns, J. B. Cohen, and E. N. Kuznetsov, “The Munsell color system in fundamental color space,” Color Res. Appl. 28, 182-196 (2003).
[CrossRef]

H. Laamanen, T. Jaaskelainen, and J. Parkkinen, “Conversion between the reflectance spectra and the Munsell notation,” Color Res. Appl. 31, 57-66 (2006).
[CrossRef]

O. Kohonen, J. Parkkinen, and T. Jääskelään, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

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

A. K. Romney and T. Indow, “Munsell reflectance spectra represented in three-dimensional Euclidean space,” Color Res. Appl. 28, 182-196 (2003).
[CrossRef]

T. Indow, “Global color metrics and color appearance systems,” Color Res. Appl. 5, 5-12 (1980).
[CrossRef]

T. Indow, “Predictions based on Munsell notation. I. Perceptual color differences,” Color Res. Appl. 24, 10-18 (1999).
[CrossRef]

H. R. Davidson, “Formulations for the OSO Uniform Color Scales committee samples,” Color Res. Appl. 6, 38-52 (1981).
[CrossRef]

J. Math. Psychol. (1)

D. H. Krantz, “Color measurement and color theory. 1. Representation theorem for Grassmann structures,” J. Math. Psychol. 12, 283-303 (1975).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Mater. Sci. Eng., B (1)

M. Elias, C. Chartier, G. Prévot, H. Garay, and C. Vignaud, “The colour of ochres explained by their composition,” Mater. Sci. Eng., B 127, 70-80 (2006).
[CrossRef]

Philos. Sci. (1)

D. H. Krantz, “Fundamental measurement of force and Newton's first and second laws of motion,” Philos. Sci. 40, 481-495 (1973).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (4)

R. G. D'Andrade and A. K. Romney, “A quantitative model for transforming reflectance spectra into the Munsell color space using cone sensitivity functions and opponent process weights,” Proc. Natl. Acad. Sci. U.S.A. 100, 6281-6286 (2003).
[CrossRef] [PubMed]

A. K. Romney and R. G. D'Andrade, “Modeling lateral geniculate nucleus cell response spectra and Munsell reflectance spectra with cone sensitivity curves,” Proc. Natl. Acad. Sci. U.S.A. 102, 16512-16517 (2005).
[CrossRef] [PubMed]

A. K. Romney and T. Indow, “A model for the simultaneous analysis of reflectance spectra and basis factors of Munsell color samples under D65 illumination in three-dimensional Euclidean space,” Proc. Natl. Acad. Sci. U.S.A. 99, 11543-11546 (2002).
[CrossRef] [PubMed]

A. K. Romney and J. T. Fulton, “Transforming reflectance spectra into Munsell color space by using prime colors,” Proc. Natl. Acad. Sci. U.S.A. 103, 15698-15703 (2006).
[CrossRef] [PubMed]

Proc. SPIE (2)

A. Alsam and J. Y. Hardeberg, “Convex reduction of calibration charts,” Proc. SPIE 5667, 38-46 (2005).
[CrossRef]

R. Lenz and P. Meer, “Non-Euclidean structure of the spectral color space,” Proc. SPIE 3826, 101-112 (1999).
[CrossRef]

Psychon. (1)

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

Rom. Rep. Phys. (1)

F. Iova, A. Trutia, and V. Vasile, “Spectral analysis of the color of some pigments,” Rom. Rep. Phys. 57, 905-911 (2005).

SIAM Rev. (1)

S. P. Gudder, “Convexity and mixtures,” SIAM Rev. 19, 221-240 (1977).
[CrossRef]

Trans. R. Scottish Soc. Arts. (1)

J. C. Maxwell, “Theory of the perception of colors,” Trans. R. Scottish Soc. Arts. 4, 394-400 (1856); reprinted as Sources of Color Science, D.L.MacAdam, ed. (MIT, 1970).

Other (11)

R. J. D. Tilley, Colour and Optical Properties of Materials (Wiley, 2000).

K. Nassau, The Physics and Chemistry of Color, 2nd ed. (Wiley, 2001).

J. J. Koenderink and A. J. van Doorn, “The structure of colorimetry,” in Algebraic Frames for Perception-Action Cycle, G.Sommer and Y.Y.Zeevi, eds. (Springer, 2000), pp. 69-77.
[CrossRef]

A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Wiley, 1974).

S. Wolfram, The Mathematica Book, 4th ed. (Cambridge U. Press, 1999).

T. H. Wonnacott and R. J. Wonnacott, Regression: A Second Course in Statistics (Wiley, 1981).

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

F. W. Billmeyer and M. Saltzman, Principles of Color Technology, 2nd ed. (Wiley, 1981), pp. 141-142.

Munsell Color Company, Inc., Munsell Book of Color. Matte Finish Collection (Munsell, 1976).

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

E. L. Krinov, “Spectral reflectance properties of natural formations,” translated by G.Beldov (National Research Council of Canada, Technical Translation: TT-439, 1953).

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Figures (6)

Fig. 1
Fig. 1

Conceptual Munsell color system represented in Cartesian coordinates with arbitrary color coding meant to convey hue locations in an approximate fashion.

Fig. 2
Fig. 2

Sample illustrations of reflectance spectra of all varying values that occur at chroma level 6 of four equally spaced Munsell hues, where untransformed spectra are shown in the left column, spectra after cube root transformations are shown in the middle column, and reconstructed transformed reflectance spectra of the ideal conceptual Munsell chips are shown in the right column. The Munsell hues represented in the four rows are, starting at the top, 5 red, 10 yellow, 5 blue-green, and 10 purple-blue.

Fig. 3
Fig. 3

Three basis functions computed from the Munsell reflectance spectra after cube root transformation, shown with solid curves, compared to the basis function derived from the original reflectance spectra, shown with dotted curves.

Fig. 4
Fig. 4

Location of the Munsell color chips represented in Euclidean space as calculated using Eq. (5).

Fig. 5
Fig. 5

Plot showing the location of the Munsell color chips after a linear transformation from the Euclidean system to the Munsell coordinate system. Orientation is the same as in Fig. 1.

Fig. 6
Fig. 6

Plot showing a comparison of the locations of selected empirical Munsell chips with their conceptual locations (after being transformed to Munsell space). The chips are eight equally spaced hues beginning at 5 red, all of chroma 6 with all degrees of value or lightness. The empirical locations are plotted as circles, while the conceptual locations are plotted as squares; the size of the symbols indicates value, with the largest circles being darkest. The thickness of the squares is produced by the superposition of symbols representing various values.

Equations (14)

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S 1269 × 301 = A 3 1269 × 301 .
S N × M = U Δ V T , N M K , U N × K = ( u i k ) ,
V M × K = ( v j k ) , k = 1 , 2 , , K ,
S ̂ 1269 × 301 = U 1269 × 3 Δ 3 x 3 V T 3 × 301 .
PRE = 1 i = 1 1269 j = 1 301 ( s i j s ̂ i j ) 2 i = 1 1269 j = 1 301 s i j 2 = k = 1 3 d k 2 k = 1 301 d k 2 = 0.9992 .
P 1269 × 3 = { p 1 , p 2 , p 3 } = U 1269 × 3 Δ 3 × 3 .
p ̂ 1 m = 2.8204 + ( 1.3423 × m 1 ) + ( 0.1484 × m 2 ) + ( 0.2831 × m 3 ) ,
p ̂ 2 m = 0.0065 + ( 0.0256 × m 1 ) + ( 0.4789 × m 2 ) + ( 0.2688 × m 3 ) ,
p ̂ 3 m = 0.2028 + ( 0.0395 × m 1 ) + ( 0.1723 × m 2 ) + ( 0.2809 × m 3 ) .
S ̂ 1269 × 301 M = P ̂ 1269 × 3 M V 3 × 301 T .
m 1 = 1.9401 + ( 0.7304 × p ̂ 1 m ) + ( 0.0235 × p ̂ 2 m ) + ( 0.7031 × p ̂ 3 m ) ,
m 2 = 0.4825 + ( 0.0719 × p ̂ 1 m ) + ( 1.5681 × p ̂ 2 m ) + ( 1.4040 × p ̂ 3 m ) ,
m 3 = 0.6990 + ( 0.0583 × p ̂ 1 m ) + ( 0.9286 × p ̂ 2 m ) + ( 2.5996 × p ̂ 3 m ) .
α 1 x 1 + α 2 x 2 + + α n x n ,

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