Deriving and dissecting an equally bright reference boundary.

The Helmholtz-Kohlrausch effect signifies the discrepancy between brightness as a perceptual attribute and luminance as a physical metric across different chromaticities. Based on the concepts of brilliance and zero grayness proposed by Ralph Evans, equally bright colors were collected in Experiment 1 by asking observers to adjust the luminance for a given chromaticity to the glowing threshold. The Helmholtz-Kohlrausch effect is thus automatically incorporated. Similar to the diffuse white as a singular point along the luminance dimension, this reference boundary demarcates surface colors from illuminant colors and correlates with the MacAdam optimal colors, which provides not only an ecologically relevant basis but also a computational handle for interpolating to other chromaticities. By navigating across the MacAdam optimal color surface, the contributions of saturation and hue to the Helmholtz-Kohlrausch effect were further quantified via saturation scaling in Experiment 2. The implications of our findings for brightness modeling, color dimensions, and potential applications are discussed.