Abstract

This paper proposes that every color sensation be represented by a vector, in three-space, whose length indicates the color’s luminance and whose direction indicates its chromaticness. The color sensation produced by a mixture of component colors is represented by the vector resultant of the vectors representing the sensations of the component colors—as if the component vectors were forces. The construction of this color space, using the 2° color mixture data of Stiles and Burch and the 2° CIE luminosity data, is reported. The primaries are axes oblique to each other, the angles between the axes being specified by the present investigation. When color-matching data for the spectral color sensations are plotted in this frame, it is found that the lengths of the resultant vectors closely approximate the CIE luminosities, except in the extreme violet. Introduction of an arbitrary orthogonal frame into the configuration shows that the values on one axis are followed by (1)12, tentatively suggesting that one color construct may be an inhibitor while the remaining two are excitors.

© 1962 Optical Society of America

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References

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  1. W. D. Wright, The Measurement of Colour (Hilger and Watts, London, 1958), Chaps. 3–4.
  2. W. S. Stiles and J. M. Burch, Acta Optica 2, 168 (1955).
    [Crossref]
  3. See reference 2.
  4. H. G. Sperling, Natl. Phys. Lab. Symposia No. 8, Vol.  1, 249 (1957).
  5. Y. LeGrand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), Chap. 6; see also reference 4.
  6. L. L. Thurstone, Multiple-Factor Analysis (University of Chicago Press, Chicago, 1947).
  7. See reference 2.
  8. See reference 4.

1957 (1)

H. G. Sperling, Natl. Phys. Lab. Symposia No. 8, Vol.  1, 249 (1957).

1955 (1)

W. S. Stiles and J. M. Burch, Acta Optica 2, 168 (1955).
[Crossref]

Burch, J. M.

W. S. Stiles and J. M. Burch, Acta Optica 2, 168 (1955).
[Crossref]

LeGrand, Y.

Y. LeGrand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), Chap. 6; see also reference 4.

Sperling, H. G.

H. G. Sperling, Natl. Phys. Lab. Symposia No. 8, Vol.  1, 249 (1957).

Stiles, W. S.

W. S. Stiles and J. M. Burch, Acta Optica 2, 168 (1955).
[Crossref]

Thurstone, L. L.

L. L. Thurstone, Multiple-Factor Analysis (University of Chicago Press, Chicago, 1947).

Wright, W. D.

W. D. Wright, The Measurement of Colour (Hilger and Watts, London, 1958), Chaps. 3–4.

Acta Optica (1)

W. S. Stiles and J. M. Burch, Acta Optica 2, 168 (1955).
[Crossref]

Natl. Phys. Lab. Symposia No. 8 (1)

H. G. Sperling, Natl. Phys. Lab. Symposia No. 8, Vol.  1, 249 (1957).

Other (6)

Y. LeGrand, Light, Colour, and Vision (John Wiley & Sons, Inc., New York, 1957), Chap. 6; see also reference 4.

L. L. Thurstone, Multiple-Factor Analysis (University of Chicago Press, Chicago, 1947).

See reference 2.

See reference 4.

See reference 2.

W. D. Wright, The Measurement of Colour (Hilger and Watts, London, 1958), Chaps. 3–4.

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Figures (2)

Fig. 1
Fig. 1

Predidtion of the CIE luminosity function by the present model. Two predictions by Stiles and Burch using Abney’s law are also shown. ×, Proposed CIE; ● Abney’s law—Stiles and Burch primary luminositiers; ▲ Abney’s law CIE primary luminosities; ○ Present model—CIE primary luminosities.

Fig. 2
Fig. 2

Plot of the two components in the F matrix of Table I. The value of the third component is shown in parenthesis after each vector.

Tables (1)

Tables Icon

Table I An F matrix showing the projections of the spectral color standards on an arbitrary orthogonal reference frame, the principal axes of the matrix S. Luminosities of the standards are predicted by the square root of the sum of squares of each row.

Equations (19)

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i = l i ,
b = l b ,
g = l g ,
r = l r ,
i = a i b b + a i g g + a i r r .
( i ) 2 = i 2 = ( a i b b + a i g g + a i r r ) 2 = a i b 2 b 2 + a i g 2 g 2 + a i r 2 r 2 + 2 a i b a i g s b g + 2 a i b a i r s b r + 2 a i g a i r s g r .
2 a i b a i g s b g + 2 a i b a i r s b r + 2 a i g a i r s g r = l i 2 a i b 2 l b 2 a i g 2 l g 2 a i r 2 l r 2 .
B W = M ,
W = B 1 M .
W = ( B B ) 1 B M .
B G R B l b 2 s b g s b r G s b g l g 2 s g r R s b r s g r l r 2 .
s i b = a i b l b 2 + a i g s b g + a i r s b r ,
s i g = a i b s b g + a i g l g 2 + a i r s g r ,
s i r = a i b s b r + a i g s g r + a i r l r 2 ,
U i = A i S ,
U = A S ,
S = G G .
F = A G
R = F F = A S A