Development of Context-Sensitive Formulas to Obtain Constant Luminance Perception

In this article, we present a method to develop context-sensitive luminance correction formulas to produce constant luminance perception for a foreground object. Our formulas make the foreground object slightly transparent to mix with the blurred version of the background. This mix can be used to quickly produce any desired illusion of luminance in foreground objects based on the luminance of the background. The transparency formula has only one variable; the relative size of the foreground object. We identified the general structure of the transparency formula as a function of the relative size of the foreground object. We develop a method to intuitively control the coefficients of the transparency formula. We have implemented an interactive Web-based program in Shadertoy to identify coefficients. Using this program, we determined the coefficients of the transparency formula. We also identified a simpler affine formula, which requires only two coefficients. We made our program publicly available so that anyone can access and improve it. In this article, we also explain how to intuitively change the polynomial part of the formula. Using our explanation, users change the polynomial part of the formula to obtain their own perceptively constant luminance. This can be used as a crowd-sourcing experiment to further improve the formula.