Chroma,chromatic luminance,and luminous reflectance. Part II: Related models of chroma,colorfulness, and brightness

Part I of this article found, inter alia, that chroma resembles log inverted luminance. This article develops three math models of Munsell chroma and associated colorfulness from (1) inverted luminous reflectance Y, (2) inverted chromatic luminance, and (3) inverted chromatic luminance combined (over the mid‐spectrum 480–580 nm) with the unimodal curve for spectral absorptance of M cones. The first two models are simple but of limited accuracy and demonstrate that inverted luminance (of any form) cannot fully account for varying relative chroma around the hue cycle, particularly the minor minimum and maximum about 490 and 520 nm (which also feature in B:L functions). The third model is rather complex but very accurate, apparently the only accurate model of Munsell chroma or other experimentally based scales of relative chromaticness in the literature. It adjusts to any level of luminance or purity, as demonstrated for several levels. Three models of brightness (B:L ratio) for 2⁰ field aperture colors are given, based on either Munsell chroma or log inverted chromatic luminance. The former provides two accurate and simple models of the CIE B:L function: (1) log chroma = B:L ratio ±0.1, and (2) (chroma/k)^x = B:L ratio ±0.1. The latter also predicts B:L for nonspectral colors and those of lower purities, e.g., object colors. The results finally solve the relationship between brightness and chroma and demonstrate that B:L ratio (a contrast in constant luminance) arises directly from chroma (also a form of contrast in constant luminance), or the reverse. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 55–67, 2009.