This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation has found that line segments representing the distance between widely separated colors do not add up correctly using 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 paradigm shift from the 3D mathematical description developed by Schrödinger and others to describe how we see color could lead to more vibrant computer screens, televisions, textiles, printed materials, and more.
New research corrects a major error in the 3D mathematical space developed by Nobel Prize-winning physicist Erwin Schrödinger and others to describe how your eye distinguishes one color from another. This incorrect model has been used by scientists and industry for over 100 years. The study has the potential to boost scientific data visualizations, improve televisions, and recalibrate the textile and paint industries.
“The assumed form of color space requires a paradigm shift,” said Roxana Bujack, a computer scientist with a math background who creates scientific visualizations at Los Alamos National Laboratory. Bujack is the lead author of the paper on the mathematics of color perception by a Los Alamos team. It was published in 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 suggested by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger, all giants of mathematics and physics, and proving one of them wrong is pretty much a scientist’s dream.”
Modeling human color perception enables the automation of image processing, computer graphics, and visualization tasks.
A Los Alamos team corrects the math used by scientists, including Nobel Prize-winning physicist Erwin Schrödinger, to describe how your eye distinguishes one color from another.
“Our original idea was to develop algorithms to automatically enhance color maps for data visualization, to make them easier to understand and interpret,” Bujack said. So the research team was surprised to discover that they were the first to discover that the long-standing application of Riemannian geometry, which allows straight lines to be generalized to curved surfaces, did not work.
An accurate mathematical model of the perceived color space is needed to create industry standards. Early attempts used Euclidean spaces, the familiar geometry taught in many high schools. Later, more advanced models used Riemannian geometry. The models represent red, green and blue in 3D space. These are the colors most strongly registered by the light-detecting cones in our retinas and, not surprisingly, the colors that mix to create all the images on your RGB computer screen.
In the study, which combines psychology, biology and mathematics, Bujack and his colleagues found that using Riemannian geometry overestimates the perception of large color differences. This is because humans perceive a large color difference as less than the sum you would get if you added small color differences that are between two widely separated shades.
Riemannian geometry cannot explain this effect.
“We didn’t expect this, and we still don’t know the exact geometry of this new color space,” Bujack said. “We could think of it as normal, but with an additional damping or weight function that pulls long distances, making them shorter. But we can’t prove that yet.”
Reference: “The non-Riemannian nature of perceptual color space” by Roxana Bujack, Emily Teti, Jonah Miller, Elektra Caffrey, and Terece L. Turton, April 29, 2022, Proceedings of the National Academy of Sciences. DOI: 10.1073 /pnas.211975311975
Funding: Laboratory Directed Research and Development Program at Los Alamos National Laboratory.