A new study corrects a major error in 3D mathematical space developed by Nobel Prize-winning physicist Erwin Schrödinger and others, and used by scientists and industry for more than 100 years to describe how the eye distinguishes one color from another. The research has the potential to drive 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 a paper from a Los Alamos team in the Proceedings of the National Academy of Sciences on the mathematics of color perception.
“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’re wrong is more or less a scientist’s dream,” Bujack said.
Modeling of human color perception enables automation of image processinginfographic and display Chores.
“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 team was surprised when they discovered that they were the first to determine that the old application of Riemannian geometry, which allows straight lines to be generalized to curved surfaces, did not work.
To create industry standards, an accurate mathematical model of perception color space needed Early attempts used Euclidean spaces, the familiar geometry taught in many high schools; the most advanced models used Riemannian geometry. The models plot red, green, and blue in 3D space. Those are the colors recorded most intensely 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 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 widely separated hues.
Riemannian geometry cannot explain this effect.
“We didn’t expect this, and we don’t know exactly geometry of this new color space still,” Bujack said. “We could think of it normally, but with an added damping or weighing function that pulls in long distances, making them shorter. But we can’t prove it yet.”
Roxana Bujack et al, The Non-Riemannian Nature of Perceptual Color Space, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.211975311
Los Alamos National Laboratory
Citation: Math Error: New Study Overturns 100-Year Color Perception Understanding (Aug 10, 2022) Retrieved Aug 10, 2022 from https://phys.org/news/2022-08-math-error -overturns-year-old-perception.html
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