New research overturns 100-year-old understanding of color perception

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 add up correctly using previously accepted geometry. The research contradicts long-held assumptions and will enhance 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 translate to computer screens, televisions, textiles, printed materials, and more. more dynamic.

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 science data visualizations, improve televisions, and recalibrate the textile and paint industries.

“The assumed shape of color space requires a paradigm shift,” said Roxana Bujack, a computer scientist with a background in math who creates science visualizations at Los Alamos National Laboratory. Bujack is the lead author of the Mathematics of Color Perception paper by a team at Los Alamos. It was published in the 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 science. 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 is correcting math that has been 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. The research team was therefore surprised when they discovered 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. Models plot red, green, and blue in 3D space. These are the colors registered most strongly by the light-detecting cones on our retinas and, unsurprisingly, the colors that mix together 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 to be less than the sum you would get if you added up small color differences that lie between two widely separated shades.

Riemannian geometry cannot account for this effect.

“We didn’t expect this and we don’t yet know the exact geometry of this new color space,” Bujack said. “We could maybe think of it normally, but with an added damping or weight function that pulls long distances, making them shorter. 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, April 29, 2022, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2119753119

Funding: Laboratory-led research and development program at Los Alamos National Laboratory.

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