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

Abstract

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 2 0 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 ¼ B:L ratio 60.1, and (2) (chroma/k) x ¼ B:L ratio 60.1. 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.

Color constancy from invariant wavelength ratios. III: Chromatic adaptation theory, model and tests

“…The present theory of constant chroma derives from Ref. 24 where chroma is modeled from the proportion of chromatic luminance in total luminance (i.e., colorimetric purity, p c ). If p c is altered, it alters the chroma.…”

“…6). However, research24 has shown that chroma depends on, and can be accurately modeled from, chromatic luminance and its proportional measure colorimetric purity,18 whereas that is not true of excitation purity. Further, colorimetric purity (unlike excitation purity) is independent of the color space used.…”

Chroma, chromatic luminance, and luminous reflectance. Part I: Basic research and illustration of relations

“…21 Part II gives a detailed model of chroma (and colorfulness in general) and an outline model of brightness-to-luminance ratio, which (unlike luminance) is shown to be proportional and closely similar to chroma.…”

Vision Models for Wide Color Gamut Imaging in Cinema

“…The interaction between achromatic and chromatic signals that produces brightness perception has been shown to happen at V1 [65], not before; there are some models for this, e.g. [66], [67], with a review in [68].…”

“…6) Modify V to compensate for the Helmholtz-Kohlrausch effect, correcting V so that perceived brightness does not change for those colors whose saturation has been modified. This is done using a simplified version of the model by Pridmore [67] that As an enhancement to the method we can add a logistic function τ after step (4) that linearly combines S 2 with the original S, giving more importance to S in the case of lowsaturated values so as to preserve skin tones and other memory colors: S 2 = (1 − τ (S))S 2 + τ (S)S. The shape of function τ (S) is shown in Fig. 4 and the formula is:…”