A survey of transforms of the CIE 1931 chromaticity diagram with some new non-linear transforms and histological illustrations of their utility.

Surveys are presented of the published data on colour matching, and of the published transforms of the CIE 1931 chromaticity diagram. All transforms are given in the form of standardized equations and tables of coefficients. Both linear and non-linear transforms are considered, although the latter are given special attention. The concept of a uniform chromaticity space (UCS) is discussed, and the published transforms are assessed for uniformity using the colour matching data. 2 series of new, non-linear transforms are presented, both based on 2-dimensional polynomial equations, and both derived using iterative optimization techniques. The 1st series attempts to approximate Farnsworth's (1961) diagram. The 2nd uses Nutting's colour matching points directly. The coefficients of these transforms are tabulated. It was found that increasing the number of coefficients in the 2-dimensional polynomial, beyond 15 each for x and y, does little to increase the uniformity of the resulting transform. The usefulness of UCS's in assessing stain performance is illustrated by examples drawn from the areas of azure B/eosin staining of blood cells and Papanicolaou staining of epithelial cells from the uterine cervix.