Abstract

The characteristics of the whole set of tristimulus values for “all” object surfaces can be studied by applying statistical methods. This leads to the determination (a) of the relative numbers of object colors that are metameric with respect to any fixed reference color, and (b) of the distribution of the tristimulus values in one trichromatic system of all object surfaces that are metameric in another trichromatic system. Subject to certain restrictions, Gaussian distributions are found to apply. The conclusions bear on important colorimetric problems such as color-rendering and degree of metamerism.

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  1. International Commission on Illumination: Proceedings 8th Session, Cambridge, 1931 (Cambridge University Press, London, England, 1932), p. 19.
  2. E. Schrödinger, Ann. Physik 62, 603 (1920).
  3. S. Rösch, Fortschr. Mineral., Krist., Petrog. 13, 143 (1929).
  4. D. L. MacAdam, J. Opt. Soc. Am. 25, 249 (1935).
  5. This multiple integral with simple limits is valid provided it is understood that F(x1,x2xM) is defined to be zero if any xi lies outside the interval 0≤xi≤1.
  6. See for example:H. Cramér, Mathematical Methods of Statistics. (Princeton University Press, Princeton, New Jersey, 1946).
  7. H. Cramér, Random variables and probability distributions. Cambridge Tracts in Mathematics and Mathematical Physics No. 36. (Cambridge University Press, London, 1937).
  8. See, for example: S. Goldman, Information Theory (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1953).
  9. G. Wyszecki, J. Opt. Soc. Am. 48, 451 (1958).
  10. G. Wyszecki, CIE Proc. Brussels 1959, Vol. A, 146 (1960).
  11. G. Wyszecki, J. Opt. Soc. Am. 49, 811 (1959).
  12. R. Courant and D. Hilbert, Methoden der Mathematischen Physik I (Verlag Julius Springer, Berlin, 1931), p. 19.

Courant, R.

R. Courant and D. Hilbert, Methoden der Mathematischen Physik I (Verlag Julius Springer, Berlin, 1931), p. 19.

Cramér, H.

See for example:H. Cramér, Mathematical Methods of Statistics. (Princeton University Press, Princeton, New Jersey, 1946).

H. Cramér, Random variables and probability distributions. Cambridge Tracts in Mathematics and Mathematical Physics No. 36. (Cambridge University Press, London, 1937).

Goldman, S.

See, for example: S. Goldman, Information Theory (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1953).

Hilbert, D.

R. Courant and D. Hilbert, Methoden der Mathematischen Physik I (Verlag Julius Springer, Berlin, 1931), p. 19.

MacAdam, D. L.

D. L. MacAdam, J. Opt. Soc. Am. 25, 249 (1935).

Rösch, S.

S. Rösch, Fortschr. Mineral., Krist., Petrog. 13, 143 (1929).

Schrödinger, E.

E. Schrödinger, Ann. Physik 62, 603 (1920).

Wyszecki, G.

G. Wyszecki, J. Opt. Soc. Am. 49, 811 (1959).

G. Wyszecki, J. Opt. Soc. Am. 48, 451 (1958).

G. Wyszecki, CIE Proc. Brussels 1959, Vol. A, 146 (1960).

Other

International Commission on Illumination: Proceedings 8th Session, Cambridge, 1931 (Cambridge University Press, London, England, 1932), p. 19.

E. Schrödinger, Ann. Physik 62, 603 (1920).

S. Rösch, Fortschr. Mineral., Krist., Petrog. 13, 143 (1929).

D. L. MacAdam, J. Opt. Soc. Am. 25, 249 (1935).

This multiple integral with simple limits is valid provided it is understood that F(x1,x2xM) is defined to be zero if any xi lies outside the interval 0≤xi≤1.

See for example:H. Cramér, Mathematical Methods of Statistics. (Princeton University Press, Princeton, New Jersey, 1946).

H. Cramér, Random variables and probability distributions. Cambridge Tracts in Mathematics and Mathematical Physics No. 36. (Cambridge University Press, London, 1937).

See, for example: S. Goldman, Information Theory (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1953).

G. Wyszecki, J. Opt. Soc. Am. 48, 451 (1958).

G. Wyszecki, CIE Proc. Brussels 1959, Vol. A, 146 (1960).

G. Wyszecki, J. Opt. Soc. Am. 49, 811 (1959).

R. Courant and D. Hilbert, Methoden der Mathematischen Physik I (Verlag Julius Springer, Berlin, 1931), p. 19.

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