Credit: Pixabay/CC0 Public Domain

Scientists and industry have used the 3D mathematical space for more than 100 years to describe how your eye distinguishes one color from another. The research could help the textile and paint industries.

The assumed shape of color space requires a paradigm shift according to a computer scientist. Bujack is one of the authors of a paper on the mathematics of color perception.

The current mathematical model of how the eye sees color differences is wrong. It's pretty much the dream of a scientist to prove that one of them is wrong.

Human color perception modeling can be used to automate image processing.

Bujack's original idea was to develop a way to make color maps easier to understand and interpret. The team was surprised when they found out that the longstanding application of Riemannian geometry, which allows generalizing straight lines to curved surfaces, did not work.

This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation has found that the line segments representing the distance between widely separated colors don't add up correctly using the previously accepted geometry. The research contradicts long-held assumptions and will improve a variety of practical applications of color theory. Credit: Los Alamos National Laboratory

A model of perceived color space is required to create industry standards. Many high schools teach the familiar geometry of Euclidean spaces. There are red, green and blue models. The colors that blend to create all the images on your computer screen are registered most strongly by light- detecting cones on our retinas.

Bujack and her colleagues found that using Riemannian geometry overstated the perception of large color differences. People think a big difference in color is less than the sum you would get if you added up small differences in color.

This effect can't be accounted for by the geometry.

Bujack said they don't know the exact geometry of the new color space. We might be able to think of it normally but with an added function that makes them shorter. We don't know yet if it's true.

More information: Roxana Bujack et al, The non-Riemannian nature of perceptual color space, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2119753119 Journal information: Proceedings of the National Academy of Sciences