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

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

This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation found that line segments representing distances between widely separated colors do not add up correctly using previously accepted geometry. The research will challenge long-standing assumptions and advance various 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 vivid computer displays, TVs, textiles, printed materials and more.

New research corrects a significant flaw 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 incorrect model has been used by scientists and industry for over 100 years. The research has the potential to improve scientific data visualization, television, and reshape the textile and paint industries.

“The assumed shape of color space requires a paradigm shift,” said Roxana Bujac, a computer scientist with a background in mathematics who develops scientific visualizations at Los Alamos National Laboratory. Bujack is lead author of the paper on the mathematics of color perception by a team at Los Alamos. It was published 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 of mathematics and physics – and it is a scientist who proved one of them wrong. dream.”

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

A Los Alamos team revised 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 develop algorithms to automatically improve color maps for data visualization, making them easier to understand and interpret,” Bujac said. So the research team was surprised when they discovered that they were the first to discover that the long-standing application of Riemannian geometry, which allowed straight lines to be generalized to curved surfaces, did not work.

A precise mathematical model of the perceived color space is needed to create industry standards. The first attempt used Euclidean space – the familiar geometry taught in many high schools. Later, more advanced models used Riemannian geometry. Models plot red, green and blue in 3D space 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 combined psychology, biology and mathematics, Bujac and his colleagues discovered that using Riemannian geometry overestimates the perception of large color differences. This is because people perceive a large difference in color as less than what you would get if you added small differences in color that are between two widely different shades.

Riemannian geometry cannot account for this effect.

“We didn’t expect this, and we still don’t know the exact geometry of this new color space,” Bujac said. “We might be able to think of it in general as an additional damping or weighting function that drags long distances, making them shorter. But we haven’t been able to prove that yet.”

Reference: “The Non-Riemannian Nature of Perceptual Color Spaces” by Roxana Bujac, Emily Teti, Jonah Miller, Electra Caffrey, and Terese L. Turton, 29 April 2022. Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2119753119

Funding: Laboratory Directed Research and Development Program of Los Alamos National Laboratory.

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