Abstract

The (U*, V*, W*) system has been checked against the Munsell renotation system on the assumption that the latter provides an equispaced visual scale. As the result of the examination, it has been found that the formula for lightness index is in excellent agreement with the Munsell value function, in spite of its numerically simplified form and that the value effect appearing on the CIE 1960 UCS diagram is over corrected by making the chromaticness indexes depend upon the first power of W*. Twenty five times the 56-power of W* has been found to be more suitable for the weighting factors to be applied to the chromaticness indices. The value effect has been reduced to about 45% by the use of the modified chromaticness indices. On the basis of the modified system, a formula is proposed for computation of color differences for pairs of similar colors. In addition, a formula is proposed for specifying whiteness for practical purposes, based on the modified system.

© 1969 Optical Society of America

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References

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  1. CIE, Compt. Rendu, Quinzième Session (Vienne, 1963), Recommendation from Committee E-1.3.1., 113, Publication CIE No. 11A (Bureau Central de la Commissoin, 57 rue Cuvier, Paris 5e, 1964).
  2. G. Wyszecki, J. Opt. Soc. Am. 53, 1318 (1963).
    [CrossRef]
  3. CIE, Compt. Rendu, Quatorzième Session (Brussels, 1959), Official Recommendations, p. 36, Publication CIE No. 4, (Bureau Central de la Commission, 57 rue Cuvier, Paris 5e, 1960).
  4. D. L. MacAdam, J. Opt. Soc. Am. 27, 294 (1937).
    [CrossRef]
  5. G. Wyszecki, J. Opt. Soc. Am. 55, 1166 (1965).
    [CrossRef]
  6. S. M. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
    [CrossRef]
  7. D. L. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).
    [CrossRef]
  8. W. R. J. Brown and D. L. MacAdam, J. Opt. Soc. Am. 39, 808 (1949).
    [CrossRef] [PubMed]
  9. J. H. Ladd and J. E. Pinney, Proc. IRE 43, 1137 (1955).
  10. L. G. Glasser, A. H. McKinney, C. D. Reilly, and P. D. Schnelle, J. Opt. Soc. Am. 48, 736 (1958).
    [CrossRef]
  11. B. R. Bellamy and S. M. Newhall, J. Opt. Soc. Am. 32, 465 (1942).
    [CrossRef]
  12. M. Fuwa and Y. Sugiyama, Acta Chromatica 1, 199 (1965).
  13. R. Hioki and M. Sato, J. Opt. Soc. Am. 57, 840 (1967).
    [CrossRef]
  14. S. M. Newhall, J. Opt. Soc. Am. 30, 617 (1940).
    [CrossRef]
  15. E. Q. Adams, J. Opt. Soc. Am. 32, 168 (1942).
    [CrossRef]
  16. D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550 (1944).
    [CrossRef]
  17. D. Nickerson, Textile Research 6, 505 (1936).
    [CrossRef]
  18. I. H. Godlove, J. Opt. Soc. Am. 41, 760 (1951).
    [CrossRef]
  19. D. B. Judd, Colorimetry, Natt. Bur. Std. (U. S.) Circ. 478 (U. S. Gov’t. Printing Office, Washington, D. C., 1950), Ch. 3, p. 31.
  20. D. B. Judd, Color in Business, Science, and Industry (John Wiley & Sons, Inc., New York, 1952), 1st ed., Part II, p. 259.

1967 (1)

1965 (2)

M. Fuwa and Y. Sugiyama, Acta Chromatica 1, 199 (1965).

G. Wyszecki, J. Opt. Soc. Am. 55, 1166 (1965).
[CrossRef]

1963 (1)

1958 (1)

1955 (1)

J. H. Ladd and J. E. Pinney, Proc. IRE 43, 1137 (1955).

1951 (1)

1949 (1)

1944 (1)

1943 (1)

1942 (3)

1940 (1)

1937 (1)

1936 (1)

D. Nickerson, Textile Research 6, 505 (1936).
[CrossRef]

Adams, E. Q.

Bellamy, B. R.

Brown, W. R. J.

Fuwa, M.

M. Fuwa and Y. Sugiyama, Acta Chromatica 1, 199 (1965).

Glasser, L. G.

Godlove, I. H.

Hioki, R.

Judd, D. B.

S. M. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
[CrossRef]

D. B. Judd, Colorimetry, Natt. Bur. Std. (U. S.) Circ. 478 (U. S. Gov’t. Printing Office, Washington, D. C., 1950), Ch. 3, p. 31.

D. B. Judd, Color in Business, Science, and Industry (John Wiley & Sons, Inc., New York, 1952), 1st ed., Part II, p. 259.

Ladd, J. H.

J. H. Ladd and J. E. Pinney, Proc. IRE 43, 1137 (1955).

MacAdam, D. L.

McKinney, A. H.

Newhall, S. M.

Nickerson, D.

Pinney, J. E.

J. H. Ladd and J. E. Pinney, Proc. IRE 43, 1137 (1955).

Reilly, C. D.

Sato, M.

Schnelle, P. D.

Stultz, K. F.

Sugiyama, Y.

M. Fuwa and Y. Sugiyama, Acta Chromatica 1, 199 (1965).

Wyszecki, G.

Acta Chromatica (1)

M. Fuwa and Y. Sugiyama, Acta Chromatica 1, 199 (1965).

J. Opt. Soc. Am. (13)

Proc. IRE (1)

J. H. Ladd and J. E. Pinney, Proc. IRE 43, 1137 (1955).

Textile Research (1)

D. Nickerson, Textile Research 6, 505 (1936).
[CrossRef]

Other (4)

D. B. Judd, Colorimetry, Natt. Bur. Std. (U. S.) Circ. 478 (U. S. Gov’t. Printing Office, Washington, D. C., 1950), Ch. 3, p. 31.

D. B. Judd, Color in Business, Science, and Industry (John Wiley & Sons, Inc., New York, 1952), 1st ed., Part II, p. 259.

CIE, Compt. Rendu, Quinzième Session (Vienne, 1963), Recommendation from Committee E-1.3.1., 113, Publication CIE No. 11A (Bureau Central de la Commissoin, 57 rue Cuvier, Paris 5e, 1964).

CIE, Compt. Rendu, Quatorzième Session (Brussels, 1959), Official Recommendations, p. 36, Publication CIE No. 4, (Bureau Central de la Commission, 57 rue Cuvier, Paris 5e, 1960).

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Figures (11)

Fig. 1
Fig. 1

Loci of constant hue and constant chroma on the (U*,V*) diagram, at value 1/, Y=1.210, W*=9.64. The loci of constant chroma are for every second chroma step from zero to the theoretical maximum.

Fig. 2
Fig. 2

Loci of constant hue and constant chroma on the (U*,V*) diagram, at value 3/, Y=6.555, W*=29.79. The loci of constant chroma are for every second chroma step from zero to the theoretical maximum.

Fig. 3
Fig. 3

Loci of constant hue and constant chroma on the (U*,V*) diagram, at value 5/, Y=19.77, W*=50.60. The loci of constant chroma are for every second chroma step from zero to the theoretical maximum.

Fig. 4
Fig. 4

Loci of constant hue and constant chroma on the (U*,V*) diagram, at value 7/, Y=43.06, W*=70.63. The loci of constant chroma are for every second chroma step from zero to the theoretical maximum.

Fig. 5
Fig. 5

Loci of constant hue and constant chroma on the (U*,V*) diagram, at value 9/, Y=78.66, W*=90.12. The loci of constant chroma are for every second chroma step from zero to the theoretical maximum.

Fig. 6
Fig. 6

Munsell renotations of hues 5P and 5GY in the (U*,V*,W*) system. The open and the closed circles indicate the smoothed and the extrapolated colors, respectively.

Fig. 7
Fig. 7

Distance between adjacent colors which are placed at the interval of 2.5 Munsell hue steps on the (U*,V*) diagram at value 5/.

Fig. 8
Fig. 8

Relationship between the ratio k and the lightness index W*. Open circles, measured; line, calculated.

Fig. 9
Fig. 9

Comparative plot of the value effects in the modified and the original system, as functions of hue. The open circles and the open triangles indicate the chromas referred to the modified and the original system respectively.

Fig. 10
Fig. 10

Comparison of the value effect, as a function of value, in the modified and the original system. The open circles and the open triangles indicate the averaged chromas referred to the modified and the original system respectively.

Fig. 11
Fig. 11

Munsell renotations of hues 5P and 5GY in the modified system. The open and the closed circles indicate the smoothed and the extrapolated colors, respectively.

Equations (13)

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W * = 25 Y 1 3 - 17 ,             1 Y 100 ;
U * = 13 W * ( u - u 0 ) ;
V * = 13 W * ( v - v 0 ) ,
u = 4 X / ( X + 15 Y + 3 Z ) ;
v = 6 Y / ( X + 15 Y + 3 Z ) ,
k = 1.92 ( W * ) - 1 6 .
W = 25 Y 1 3 - 17 ,             1 Y 100 ;
U = 25 W ˜ ( u - u 0 ) ;
V = 25 W ˜ ( v - v 0 ) ,
Δ E = f [ ( U 1 - U 2 ) 2 + ( V 1 - V 2 ) 2 + n 2 ( W 1 - W 2 ) 2 ] 1 2 ,
W = 1 - Δ E MgO to specimen Δ E MgO to black .
W = 1 - ( 1 / 100 ) { ( 13 ) 2 ( 100 ) 2 [ ( 400 + Y ) / 500 ] [ ( u - 0.2009 ) 2 + ( v - 0.3073 ) 2 ] + ( 2 5 ) 2 ( 100 - Y ) 2 } 1 2 ,
W = 1 - ( 1 / 100 ) n - 1 { ( 25 ) 2 ( 100 ) 5 / 3 [ ( 50 + Y ) / 150 ] [ ( u - 0.2009 ) 2 + ( v - 0.3073 ) 2 ] + n 2 ( 2 5 ) 2 ( 100 - Y ) 2 } 1 2 .