New research overturns 100 years of understanding color perception

This visualization captures the 3D mathematical space used to map human color perception. A new math view finds that line segments representing the distance between widely spaced colors don’t 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

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

New research corrects a major flaw 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 improve scientific data visualizations, improve television sets and recalibrate the textile and dye industry.

“The assumed shape of color space requires a paradigm shift,” said Roxana Bojak, a computer scientist with a background in mathematics who made scientific 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 van de 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 there is an error is largely a scientist’s dream.”

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

The Los Alamos team is correcting the math 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 enhance color maps for data visualization so that they are easier to understand and interpret,” says Bojak. So the research team was surprised to find 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, didn’t work.

An accurate mathematical model of the perceived color space is needed to establish industry standards. The first attempts made use of Euclidean spaces—the familiar geometry taught in many secondary schools. Later, more advanced models used the Riemann geometry. Models paint red, green and blue in 3D space. These are the colors that are captured powerfully by the cones that detect light on our retina, and unsurprisingly, the colors that blend together to create all the images on an RGB computer screen.

In the study, which combines psychology, biology and mathematics, Bojak and her colleagues found that using Riemann geometry exaggerates the perception of large color differences. This is because people understand that a large color difference is less than the sum you would get when you add up small color differences that are between two widely separated colors.

Riemannian geometry cannot explain this effect.

“We weren’t expecting this and we don’t know the exact geometry of this new color space yet,” said Bujack. “We might think of it normally, but with an added hydration or weight function that travels long distances, making it shorter. But we can’t prove that yet.”