This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation has revealed that line segments representing the distance between widely separated colors do not connect correctly using previously accepted geometry. The research challenges long-held assumptions and will advance various practical applications of color theory. Credit: Los Alamos National Laboratory
A paradigm moving away from the 3D mathematical representation developed by Schrödinger and others to describe how we see color is the more vivid computer screens, televisions, textiles, printed materials, etc. can result in
New research corrects a significant error in the 3D mathematical space developed by Nobel Prize-winning physicist Erwin Schrödinger and others to describe how your eyes distinguish one color from another. This false model has been used by scientists and industry for over 100 years. The research has the potential to enhance scientific data visualization, improve televisions, and recalibrate the textile and dye industries.
“The assumed shape of color space requires a paradigm shift,” said Roxana Bujak, a computer scientist with a background in mathematics who creates scientific visualizations at Los Alamos National Laboratory. Bujack is the lead author of a paper by the Los Alamos team on the mathematics of color perception. published in the magazine Proceedings of the National Academy of Sciences.
“Our research shows that the current mathematical model of how the eye perceives color differences is incorrect. This model was proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – giants of all mathematics and physics, and it is a scientist’s dream to prove one of them wrong.”
Modeling human color perception allows for the automation of image processing, computer graphics, and visualization tasks.
The Los Alamos team tweaks the math used by scientists, including Nobel Prize-winning physicist Erwin Schrödinger, to describe how your eyes distinguish one color from another.
“Our original idea was to automatically enhance color maps for data visualization, developing algorithms to make them easier to understand and interpret,” Bujack said. So the research team were surprised to discover that they were the first to discover that the long-term application of Riemannian geometry, which allows generalization of straight lines to curved surfaces, did not work.
Creating industry standards requires an accurate mathematical model of the perceived color space. Early attempts used Euclidean spaces—the familiar geometry taught in many high schools. Later, more advanced models used Riemannian geometry. Models draw red, green and blue colors in 3D space. These are the colors most strongly registered by the light-detecting cones in our retinas, and not surprisingly, RGB are the colors that mix to create all the images on your computer screen.
In research that combined psychology, biology, and mathematics, Bujack and his colleagues found that using Riemannian geometry overestimates the perception of large color differences. This is because people perceive a large difference in color as less than the amount you would get if you added the small color differences between two shades that are far apart.
Riemannian geometry cannot explain this effect.
“We didn’t expect that, and we don’t yet know the exact geometry of this new color space,” Bujack said. “We can think of it normally, but with the function of additional damping or weight, it pulls long distances and shortens them. But we can’t prove it yet.”
Reference: “The Non-Riemannian Nature of Perceptual Color Space” by Roxana Bujack, Emily Teti, Jonah Miller, Elektra Caffrey, and Terece L. Turton, 29 Apr 2022, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2119753119
Funding: Los Alamos National Laboratory Laboratory Directed Research and Development Program.
