Development of Context-Sensitive Formulas to Obtain Constant Luminance
  Perception for a Foreground Object in Front of Backgrounds of Varying
  Luminance
Ergun Akleman Bekir Tevfik Akgun Adil Alpkocak
In this article, we present a framework for developing context-sensitive
luminance correction formulas that can produce constant luminance perception
for foreground objects. Our formulas make the foreground object slightly
translucent to mix with the blurred version of the background. This mix can
quickly produce any desired illusion of luminance in foreground objects based
on the luminance of the background. The translucency formula has only one
parameter; the relative size of the foreground object, which is a number
between zero and one. We have identified the general structure of the
translucency formulas as a power function of the relative size of the
foreground object. We have implemented a web-based interactive program in
Shadertoy. Using this program, we determined the coefficients of the polynomial
exponents of the power function. To intuitively control the coefficients of the
polynomial functions, we have used a B\'{e}zier form. Our final translucency
formula uses a quadratic polynomial and requires only three coefficients. We
also identified a simpler affine formula, which requires only two coefficients.
We made our program publicly available in Shadertoy 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 for further
improvement of the formula.