3D Mathematical Space for Mapping Human Color Perception

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

This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation finds that line segments representing distances between widely separated colors do not stack correctly using previously accepted geometry. The research contradicts longstanding assumptions and will improve various practical applications of color theory.Image credit: Los Alamos National Laboratory

A paradigm shift from the 3D mathematical descriptions developed by Schrödinger and others to describe how we see color could lead to more vivid computer monitors, televisions, textiles, printed materials, and more.

New research corrects a major error in a 3D mathematical space developed by Nobel Prize-winning physicist Erwin Schrödinger and others that describes how your eyes distinguish one color from another. This incorrect model has been used by scientists and industry for over 100 years. The research has the potential to advance scientific data visualization, improve television, and recalibrate the textile and coatings industry.

“The hypothetical shape of color space requires a paradigm shift,” said Roxana Bujack, a computer scientist with a mathematics background who creates scientific visualizations at Los Alamos National Laboratory. Bujack is the lead author of the Los Alamos team’s paper on the mathematics of color perception.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. The model proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – both giants of mathematics and physics – proves One of them being wrong is almost a scientist’s dream.”

Modeling human color perception enables automation of image processing, computer graphics, and visualization tasks.

A Los Alamos team has corrected the math scientists (including Nobel laureate physicist Erwin Schrödinger) use to describe how your eyes distinguish one color from another.

“Our original idea was to develop algorithms to automatically improve colormaps for data visualizations, making them easier to understand and interpret,” Bujack said. So the research team was surprised when they discovered that they were the first to find that a long-standing application of Riemannian geometry (allowing the generalization of straight lines to curved surfaces) did not work.

An accurate mathematical model of the perceived color space is required to create an industry standard. First attempt at Euclidean space – a familiar geometry taught in many high schools. Later, more advanced models used Riemannian geometry. The model draws red, green, and blue in 3D space. These are the most intense colors recorded by the light-detecting cones on our retinas, and – unsurprisingly – these colors mixed together create all the images on your RGB computer screen.

In the study, which combines psychology, biology and mathematics, Bujack and her colleagues found that using Riemannian geometry overestimates the perception of large color differences. This is because humans perceive large differences in color to be smaller than the sum of small color differences between two shades located far apart.

Riemannian geometry cannot explain this effect.

“We didn’t expect this, and we didn’t know the exact geometry of this new color space,” Bujack said. “We might be able to think about it normally, but add damping or weighing to stretch the distances and make them shorter. But we can’t prove it yet.”

Reference: “The Non-Riemannian Properties of Perceptual Color Spaces,” 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 Directed Research and Development Program at Los Alamos National Laboratory.

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