This visualization captures the 3D mathematical space used to map the human perception of color. A new mathematical representation has found that line segments representing the distance between widely separated colors do not add correctly using previously accepted geometry. The research contradicts 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 could result in more vibrant 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 the 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 boost scientific data visualizations, improve televisions, and recalibrate the textile and paint industries.
“The assumed shape of the 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 the lead author of the paper on the mathematics of color perception by a team from Los Alamos. 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 incorrect. That model was suggested by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger, all giants in mathematics and physics, and show that one of they are wrong is practically a scientist’s dream.”
Modeling of the human perception of color enables automation of image processing, computer graphics, and display tasks.
A Los Alamos team corrects the mathematics that scientists, including Nobel Prize-winning physicist Erwin Schrödinger, have used to describe how the 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,” said Bujack. So the research team was surprised when they found 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 needed 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 plot red, green, and blue in 3D space. Those are the colors registered most strongly by the light-sensing cones in our retinas, and, unsurprisingly, the colors that combine to create all the images on your RGB computer screen.
In the study, which combines psychology, biology and mathematics, Bujack and his colleagues found that the use of Riemannian geometry overestimates the perception of large color differences. This is because humans perceive a large color difference to be less than the sum we would get if we added up the small color differences between two widely separated hues.
Riemannian geometry cannot explain this effect.
“We didn’t expect this and we still don’t know the exact geometry of this new color space,” said Bujack. “We could think of it normally, but with an additional damping or weighing function that pulls in long distances, 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.
DOI: 10.1073/pnas.2119753119
Financing: Laboratory-Directed Research and Development Program of the Los Alamos National Laboratory.
