DIMINISHING RETURNS IN COLOR PERCEPTION

It is accepted that a perceptually uniform color space cannot be modeled with Euclidean geometry. The next most complex geometry is Riemannian or a geometry with inherent curvature. Riemann, Schrodinger, and Helmholtz introduced and strengthened the theory that a Riemannian geometry can be used to model an ideal color space, to borrow language from Judd. While the addition of curvature in color space increases its ability to capture human color perception, such a geometry is insufficient if small distances along a shortest path do not add up to the length of the entire path. This phenomenon is referred to as diminishing returns and would necessitate a more complicated, non-Riemannian geometry to accurately quantify human color perception. This work includes (1) the invention and validation of new analysis techniques to investigate the existence of diminishing returns, (2) empirical evidence for diminishing returns in color space that varies throughout the current standard space (CIELAB), and (3) suggests that paths through perceptual color space may still coincide with paths through the induced Riemannian metric.
The new analysis methods are shown to be robust to increased difficulty of a two-alternative forced choice task (2AFC) and a limited understanding of how to quantify stimuli. Using a 2AFC task and the new methods, strong evidence for diminishing returns in the grayscale is demonstrated. These data were collected using a crowd-sourced platform that has very little experimental control over how the stimuli are presented, yet these results were validated using a highly-controlled in-person study. A follow-up study also suggests that diminishing returns exists throughout color space and to varying degrees. Lastly, shortest paths in perceived color space were investigated to determine whether diminishing returns, and hence a non-Riemannian perceptual color space, impact only the perceived size of the differences, or the shortest paths themselves in color space. The results of this study found that, although there was weak evidence the paths do not coincide, this effect was smaller than a response bias. Therefore, we did not find evidence that shortest paths in color space were impacted by the non-Riemannianness of human color perception.