November 27, 2022

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3D Mathematical Space Used To Map Human Color Perception

New research overturns 100-year 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 the distance between widely spaced colors do not add up correctly using previously accepted geometry. The research goes against long-standing assumptions and will improve a variety of practical applications of color theory. 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 can lead to more vibrant computer screens, televisions, textiles, printed materials, and more.

New research corrects a major error in 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 study has the potential to enhance scientific data visualizations, improve television sets, and recalibrate the textile and paint industries.

“The supposed shape of color space requires a paradigm shift,” said Roxana Bojak, a computer scientist with a background in mathematics who created science visualizations at Los Alamos National Laboratory. Bujack is the lead author of the paper on the mathematics of color perception by the Los Alamos team. Posted 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 proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – all giants in mathematics and physics – and to prove one wrong is largely a scientist’s dream.”

Human color perception modeling enables the automation of image processing, computer graphics, and visualization tasks.

The Los Alamos team corrects the math that scientists, including Nobel Prize-winning physicist Erwin Schrödinger, have used to describe how your eye distinguishes one color from another.

“Our original idea was to develop algorithms to automatically improve color maps for data visualization, to make it easier to understand and interpret,” Bojak said. So the research team was surprised when they found out that they were the first to discover that the long-term application of Riemann 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 establish industry standards. The first attempts used Euclidean spaces – the familiar geometry that is taught in many high schools. Later, more advanced models used Riemannian geometry. Models paint red, green, and blue in 3D space. These are the colors that are powerfully recorded by the cones that detect light on our retina, and not surprisingly – the colors that blend to create all the images on an RGB computer screen.

In the study, which combines psychology, biology, and mathematics, Bojak and her colleagues discovered that the use of Riemannian geometry exaggerates the perception of large differences in color. This is because humans understand that a large difference in color is less than the sum you would get if you added up small color differences that lie between two widely separated colors.

Riemannian geometry cannot explain this effect.

“We didn’t expect this, and we don’t yet know the exact geometry of this new color space,” Bujack said. “We might be able to think of it normally but with an additional hydration or weight function that pulls long distances, making it shorter. But we can’t prove that yet.”

Reference: “The Non-Riemannian Nature of Perceptual Color Space” By Roxana Bojak, Emily Tate, Jonah Miller, Electra Caffrey, and Teresh L. Turton, Apr 29, 2022 Available here Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2119753119

Funding: The Laboratory-Driven Research and Development Program of Los Alamos National Laboratory.

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