A new study corrects an important error in mathematical 3D 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 your eye distinguishes one color from another. The research has the potential to enhance scientific data visualizations, improve television sets and recalibrate the textile and paint industries.
“The supposed shape of color space requires a paradigm shift,” said Roxana Bojak, a computer scientist with a background in mathematics who created science visualizations at Los Alamos National Laboratory. Bujack is the lead author of the paper prepared by the Los Alamos team at Proceedings of the National Academy of Sciences In the mathematics of color perception.
“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 one wrong is very much a scientist’s dream,” Bojak said.
“Our original idea was to develop algorithms to automatically improve color maps for data visualization, to make it easier to understand and interpret,” Bojak said. So the team was surprised to find that they were the first to decide that the long-term application of Riemann’s geometry, which allows straight lines to be generalized to curved surfaces, did not work.
To create industry standards, accurate mathematical model of the envision color space And there is a need. The first attempts used Euclidean spaces – the familiar geometry taught in many high schools; More advanced models used Riemannian geometry. Models paint red, green, and blue in 3D space. These are the colors that are powerfully recorded by the cones that detect light on our retina, and not surprisingly – the colors that blend to create all the RGB images on a computer screen.
In the study, which mixes psychology, biology, and mathematics, Bojak and her colleagues discovered that using Riemannian geometry exaggerates the perception of large differences in color. This is because people realize that a large difference in color is less than the amount you would get if you added small color differences between two widely separated colors.
Riemannian geometry cannot explain this effect.
“We didn’t expect this, and we don’t know exactly Engineering Who is this new? the color “Space yet,” Bojack said. “We might be able to think of it normally but with an extra hydration or weight function that pulls long distances, making it shorter. But we can’t prove that yet.”
Roxana Bojak et al., The Non-Rymantine nature of the perceptual color space, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.211975311
Los Alamos National Laboratory
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