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Color Mixture and Fundamental Metamers: Theory, Algebra, Geometry, Application
Oleh:
Cohen, Jozef B
;
Kappauf, William E.
Jenis:
Article from Journal - ilmiah internasional
Dalam koleksi:
The American Journal of Psychology vol. 98 no. 2 (1985)
,
page 171.
Topik:
Algebra
;
Geometry
;
Application
Fulltext:
1422442.pdf
(7.74MB)
Isi artikel
This paper explores the consequences of Wyszecki's hypothesis concerning metameric stimuli, that any radiometric function (column matrix N) comprises two components - a fundamental metamer (column matrix N*) and a metameric black (column matrix B); N* = N - B. The fundamental metamer is unique and identical for all radiometric functions in a metameric suite. The metameric black has tristimulus values of 0, 0, 0 with all functions in color space and is different for each radiometric function in a metameric suite. Matrix R, derived by Cohen and Kappauf in 1982, is equal to A(A'A)-A', where A is any matrix of color mixture functions. Premultiplication of matrix N by matrix R "kicks out" the metameric black, leaving the fundamental metamer, and thus mathematically simulates the color-processing mechanism of the visual system; RN = N*. Given any matrix A, the fundamental metamers of the primaries generating matrix A may be derived from the color mixture functions in matrix A. The paper proves and demonstrates that tristimulus values (rows of matrix A) are dimensionless weights on the fundamental metamers of the primaries (columns of matrix E). A given color mixture function does not invariably weight the same fundamental metamer, but depends on the entire triplet of primaries. The paper develops an invariant fundamental metamer space, governed by the theorems of Euclidean geometry, where every fundamental metamer has two representations: (a) a unique, invariant vector - the vector fundamental metamer and (b) the locus of scalar products between the vector fundamental metamer (for the color stimulus) and all vector fundamental metamers representing monochromatic stimuli spanning the visible spectrum - which is the invariant scalar fundamental metamer as originally conceived by Wyszecki. Two systems of color specification (other than tristimulus values) are disclosed. Strategic observation locates three orthogonal fundamental metamers of monochromatic stimuli. Various theoretical properties of the fundamental metamer space are developed. Several applications are discussed.
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