R. Shamey, R. G. KuehniPioneers of Color Sciencehttps://doi.org/10.1007/978-3-319-30811-1_89

89. Cohen, Jozef B. 1921–1995

Renzo Shamey¹ and Rolf G. Kuehni¹

(1)

Color Science and Imaging Laboratory, North Carolina State University, Wilson College of Textiles, Raleigh, NC, USA

Renzo Shamey (Corresponding author)

Email: rshamey@ncsu.edu

Rolf G. Kuehni

Email: rolf_kuehni@ncsu.edu

89.1 Principle Component Analysis of Reflectance Functions

References

../images/336076_1_En_89_Chapter/336076_1_En_89_Figa_HTML.png — Donated by J. B. Cohen

Cohen was born in Brookline, M.A on July 21, 1921. He attended grade and high schools in Brookline and obtained an undergraduate degree in psychology from the University of Chicago. He moved on to Cornell University where he got involved in the psychophysics of color. In 1945, he graduated with a Ph.D. in psychology. After spending a year in S. S. Stevens’ laboratory at Harvard University and three years as a faculty member at Cornell, he moved in 1948 to the University of Illinois where he became a full professor in 1969 and a professor emeritus in 1991. Between 1946 and 1949, he worked mainly in the field of color, as can be judged by his publications. After an intermission, this subject was again his major interest in the mid-late 1960s. In 1974, he was the author of the article “Psychology” in the fifteenth edition of the Encyclopedia Brittanica. In the 1980s, Cohen began cooperation with his colleague W. E. Kappauf on what he named fundamental color metamers, the major color-related concept of his career. Cohen died on August 18, 1995 [1].

89.1 Principle Component Analysis of Reflectance Functions

A key and novel effort of Cohen was his principal component analysis of the reflectance functions of 150 Munsell color chips in 1964 where he found that the first three components accounted for over 99% of variability in the reflectance functions. This effort resulted over the next decades in a widespread principal component analysis of broader ranges of reflectance functions both of natural and artificial nature [2].

The nature of color stimulus space became of particular interest to him in the mid-1970s. In the early 1980s, together with his colleague W. E. Kappauf, he described a mathematical method to decompose a reflectance or a spectral power function into two components, a concept introduced by G. Wyszecki in 1953: the fundamental function and a metameric black function. These points are located in a related orthonormal space Cohen named the fundamental color space (Fig. 89.1). This concept was not accepted well by some key color scientists of the time. It gained wider traction from Cohen’s 1988 article in Color Research and Application “Color and color mixture: scalar and vector fundamentals” [3].

../images/336076_1_En_89_Chapter/336076_1_En_89_Fig1_HTML.png — Fig. 89.1
Rendering of Cohen’s fundamental color space, with the locations of the spectral color vectors and the equal energy vector shown [1]

A key component of the calculation of the fundamental metamer is what Cohen named “matrix R”, R = A (A′A)⁻¹ A′, where A is a matrix representing three color-matching functions on an orthonormal basis. If N is any given spectral power distribution function, he found that its fundamental metamer N* is calculated N* = RN. Cohen showed that a CIE tristimulus value-based color space is far from orthonormal, but there is as yet evidence neither for nor against the idea that the human color vision system has an orthonormal basis.

The broadest representation of Cohen’s work is found in his posthumously published book Visual color and color mixture of 2001 [1]. Since then, it has been shown that there are other mathematical methods possible to calculate fundamental metamers. While he only hinted at a possible connection between the fundamental space and perceptual color space, it is clear that solid evidence for such a conclusion is lacking, as the relationship between stimulus and perception remains to a substantial degree unknown and is, in any case, very complex as demonstrated by color appearance models. In the last two decades of the twentieth century, his findings provided much new insight into the nature of color stimuli.