A paradigm shift away from the 3D mathematical description developed by Schrödinger and others to describe how we see color could result in more vibrant computer screens, TVs, textiles, printed materials and more.
New research corrects a significant flaw 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 over 100 years. The study has the potential to drive scientific data visualizations, improve televisions and recalibrate the textile and dye industry.
“The assumed shape of color space requires a paradigm shift,” said Roxana Bujack, a computer scientist with a background in mathematics who creates scientific visualizations at Los Alamos National Laboratory. Bujack is lead author of the paper on the mathematics of color perception by a Los Alamos team. It was published in the Proceedings of the National Academy of Sciences.
“Our research shows that the current mathematical model of how the eye perceives color differences is wrong. That 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 automation of image processing, computer graphics, and visualization tasks.
A team from Los Alamos is correcting math 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 so that they are easier to understand and interpret,” says Bujack. So the research team was surprised to find that they were the first to discover that the long-standing application of Riemann geometry, which can generalize straight lines to curved surfaces, didn’t work.
An accurate mathematical model of perceived color space is needed to create industry standards. The first attempts made use of Euclidean spaces – the familiar geometry taught in many high schools. Later, more advanced models used the Riemann geometry. The models plot red, green and blue in 3D space. Those are the colors most strongly detected by light-detecting cones on our retina, and – unsurprisingly – the colors that blend together to 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 Riemann geometry overestimated the perception of large color differences. This is because people consider a large color difference to be less than the sum you would get when you add up small color differences that are between two widely separated shades.
The Riemann geometry cannot explain this effect.
“We weren’t expecting this and we don’t know the exact geometry of this new color space yet,” Bujack said. “We might think about it normally, but with an added damping or weighting function that pulls long distances in, making them shorter. But we can’t prove it yet.”
Reference: “The non-Riemannian nature of perceptual color space” by Roxana Bujack, Emily Teti, Jonah Miller, Elektra Caffrey and Terece L. Turton, Apr 29, 2022, Proceedings of the National Academy of Sciences.
Funding: Los Alamos National Laboratory’s lab-driven research and development program.