Development of Context-Sensitive Formulas to Obtain Constant Luminance Perception for a Foreground Object in Front of Backgrounds of Varying Luminance

TL;DR

The paper addresses the problem of achieving constant luminance perception for a foreground object across backgrounds of varying luminance by introducing a context-sensitive translucency model. It proposes a forward framework where the foreground's effective opacity is $y = s^{f(s)}$, with $s\in[0,1]$ as the relative size and $f(s)$ a Bézier polynomial, culminating in a quadratic (and an affine) form that reliably yields constant perception when blended with a blurred background. A Web-based ShaderToy implementation is used to identify coefficients (e.g., $B_{2,0}=0.20$, $B_{2,1}=0.25$, $B_{2,2}=1.00$) and to provide an intuitive Bézier-based control of the polynomial part; the code is publicly available for crowd-sourced refinement and exploration. The approach reframes luminance perception as a forward, non-physically-based model that can be inverted rationally, enabling practical applications in vision science, graphic design, and color perception studies, with potential extensions to color and seamless integration in photographic workflows.

Abstract

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 Bézier 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.

Figures (20)

• Figure 1: This is a perspective recreation of Adelson's famous chessboard puzzle using moving shadow adelson200024. We have created a new version to demonstrate that it is easy to move the light source. This is not a rendered image. It is created by one of the authors using Procreate and Photoshop.
• Figure 2: Note that the squares A and B are almost the same with B being slightly darker. It is even possible to make B much darker in both cases and B squares will still look brighter.
• Figure 3: Intrinsic image analysis barrow1978recovering: Our conjecture is that animal visual systems are evolved to differentiate diffuse reflection terms to differentiate different objects.
• Figure 4: Comparison of our method with constant color. Note that the constant-luminescence rectangle appears to have variable luminosity in front of lightness-scale backgrounds. On the other hand, the rectangle with variable-luminescence rectangle band creates an illusion of constant-luminescence in front of lightness-scale backgrounds.
• Figure 5: A foreground rectangle in front of a photograph. We made the center line of the rectangle completely opaque to avoid an appearance of translucency as if we were looking at a shower door. Only the boundaries are translucent with the Equation given in \ref{['Eq_barycentric_final_linear']}. This creates an effect similar to subsurface scattering where the center is thicker and the boundaries are thinner.