New research turns 100-year-old understanding of color perception on its head

3D Mathematical Space Used To Map Human Color Perception
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Mathematical 3D space to map human color perception

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 colors that are far apart do not add up correctly when using the previously accepted geometry. The research contradicts long-held assumptions and will improve a variety of practical applications of color theory. Photo credit: Los Alamos National Laboratory

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

New research corrects a significant error in 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 more than 100 years. The study has the potential to advance the visualization of scientific data, improve televisions and recalibrate the textile and dyes industries.

“The assumed shape 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 article 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 wrong. This model was proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – all giants in 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 is correcting mathematical calculations 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. Therefore, the research team was surprised to find 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 required 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 draw red, green, and blue in 3D space. These are the colors most strongly registered by light detection cones on our retinas and, unsurprisingly, the colors that mix to create all images on your RGB computer screen.

In the study, which combined psychology, biology, and mathematics, Bujack and her colleagues discovered that using Riemannian geometry overestimated the perception of large color differences. This is because people perceive a large color difference as less than the sum you would get if you added small color differences that fall between two hues 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 perhaps think of it as normal, but with an added cushioning or cradle function that pulls in long stretches and makes them shorter. But we can’t prove it yet.”

References: “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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