A new study has uncovered a mathematical error in Erwin Schrödinger’s century-old theory explaining how eyes distinguish one color from another, and takes the first steps to correct the famous physicist’s work. A research team at Los Alamos National Laboratory has prepared a paper that shows that the longstanding “current mathematical model of how the eye perceives color differences” is wrong.
The new mathematical notation found that line segments representing the distance between widely separated colors do not correctly match human color perception when using previously accepted geometry. The new discovery could have the potential to create more vibrant monitors and displays, as well as printed materials and textiles.
“Our research shows that the current mathematical model of how the eye perceives color differences is inaccurate,” said Roxana Bujack, a computer scientist with a background in mathematics and designing scientific visualizations.
“This model was proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – each of the giants in mathematics and physics,” the lab’s website says. It’s almost every scientist’s dream to prove one of them wrong.”
It enables the automation of modeling human color perception, image processing, computer graphics and visualization tasks. “Our original idea was to develop algorithms that would automatically improve color maps for data visualization, making them easier to understand and interpret,” says Bujack.
But the team didn’t expect to discover that the longstanding application of Riemann geometry, which allowed straight lines to be generalized to curved surfaces, was flawed. Models using Riemann geometry plot red, green, and blue in 3D space, the colors most strongly recorded by a human’s retina and used in RGB computer screens.
Bujack and his colleagues discovered that Riemannian geometry overestimated the perception of large color differences. This is because people perceive a large color difference to be less than the sum you would get if you added up the small color differences between two very different hues. And 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,” says Bujack.
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