Abstract

From larger—smaller judgments of color differences, compared visually two at a time, the perceived sizes may be evaluated on an interval scale. Given numbers <i>B</i> so evaluated, and such that <i>B</i> is linearly connected to some power <i>p</i>, of the physical measure <i>D</i> (such as distance on any chromaticity diagram) of the differences, the additive constant <i>K<sub>br</sub></i> such that the numbers <i>B</i>+<i>K<sub>br</sub></i> are expressed on a ratio scale may be found from judgments of the ratio of sizes of pairs of differences. To evaluate <i>p</i>, it is sufficient to observe the three differences, 12, 23, and 13 between the pairs of three colors, 1, 2, 3, forming a geodesic series, and chosen so that <i>B</i><sub>12</sub> is not much different from <i>B</i><sub>23</sub>. The scale formed by the numbers (<i>B</i>+<i>K<sub>br</sub></i>)<sup>1/<i>p</i></sup> is additive if the <i>D</i> scale is additive. If the largest of the color differences judged exceeds the smallest by a factor not greater than 3, a close approximation to the (<i>B</i>+<i>K<sub>br</sub></i>)<sup>1/<i>p</i></sup>scale may be found without evaluating <i>K<sub>br</sub></i> discovery that scales based on the additivity condition: (<i>B</i><sub>12</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup>+(<i>B</i><sub>13</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup> = (<i>B</i><sub>13</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup>, though it implies that <i>K<sub>bd</sub></i> depends strongly on <i>p</i>, are essentially identical regardless of the choice of <i>p</i> between 1 and ⅓. It is sufficient therefore, to derive the additive scale by setting <i>p</i>= 1, and computing <i>K<sub>bd</sub></i> as <i>B</i><sub>13</sub>—<i>B</i><sub>12</sub>—<i>B</i><sub>23</sub>.

PDF Article

References

  • View by:
  • |
  • |

  1. G. Wyszecki, J. Opt. Soc. Am. 414, 725 (1954); D. B. Judd, J. Opt. Soc. Am. 45, 673 (1955).
  2. H. A. David, The Method of Paired Comparisons (Hafner Publishing Co., New York, 1963), Sec. 1.3 and Ch. 4, especially p. 55.
  3. J. E. Jackson and M. Fleckenstein, Biometrics 13, 51 (1957).
  4. W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, New York, 1958), p. 271.
  5. D. L. MacAdam, J. Opt. Soc. Am. 53, 754 (1963).
  6. G. L. Howett, Report of Eighth Meeting of OSA Committee on Uniform Color Scales, 20 November 1964, p. 4, unpublished.

David, H. A.

H. A. David, The Method of Paired Comparisons (Hafner Publishing Co., New York, 1963), Sec. 1.3 and Ch. 4, especially p. 55.

Fleckenstein, M.

J. E. Jackson and M. Fleckenstein, Biometrics 13, 51 (1957).

Howett, G. L.

G. L. Howett, Report of Eighth Meeting of OSA Committee on Uniform Color Scales, 20 November 1964, p. 4, unpublished.

Jackson, J. E.

J. E. Jackson and M. Fleckenstein, Biometrics 13, 51 (1957).

MacAdam, D. L.

D. L. MacAdam, J. Opt. Soc. Am. 53, 754 (1963).

Torgerson, W. S.

W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, New York, 1958), p. 271.

Wyszecki, G.

G. Wyszecki, J. Opt. Soc. Am. 414, 725 (1954); D. B. Judd, J. Opt. Soc. Am. 45, 673 (1955).

Other

G. Wyszecki, J. Opt. Soc. Am. 414, 725 (1954); D. B. Judd, J. Opt. Soc. Am. 45, 673 (1955).

H. A. David, The Method of Paired Comparisons (Hafner Publishing Co., New York, 1963), Sec. 1.3 and Ch. 4, especially p. 55.

J. E. Jackson and M. Fleckenstein, Biometrics 13, 51 (1957).

W. S. Torgerson, Theory and Methods of Scaling (John Wiley & Sons, New York, 1958), p. 271.

D. L. MacAdam, J. Opt. Soc. Am. 53, 754 (1963).

G. L. Howett, Report of Eighth Meeting of OSA Committee on Uniform Color Scales, 20 November 1964, p. 4, unpublished.

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.