A new study corrects a critical error in a 3D mathematical space developed by Nobel laureate physicist Erwin Schrödinger and others and used by scientists and industry for more than 100 years to describe how your eyes can tell the difference between a color and another color. The research has the potential to advance scientific data visualization, improve television and recalibrate the textile and coatings industry.
“The hypothetical shape of color space requires a paradigm shift,” said Roxana Bujack, a computer scientist with a mathematics background who creates scientific visualizations at Los Alamos National Laboratory. Bujack is lead author of the Los Alamos team’s paper Proceedings of the National Academy of Sciences The mathematics of color perception.
“Our research shows that the current mathematical model of how the eye perceives color differences is incorrect. The model proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger (all the giants of mathematics and physics), proves that one of the It’s almost a scientist’s dream to be wrong,” Bujak said.
Modeling human color perception enables automation of image processing, computer graphics, and visualization tasks.
“Our original idea was to develop algorithms to automatically improve colormaps for data visualizations, making them easier to understand and interpret,” Bujack said. So the team was surprised when they found that they were the first to determine that a long-standing application of Riemannian geometry (allowing the generalization of straight lines to surfaces) didn’t work.
In order to create an industry standard, an accurate mathematical model of the perceived color space is required. The first attempt uses Euclidean space – a familiar geometry taught in many high schools; more advanced models use Riemannian geometry. The model draws red, green, and blue in 3D space. These are the most intense colors recorded by the light-detecting cones on our retinas, and – unsurprisingly – these colors mix together to create all the images on your RGB computer screen.
In the study, which blended psychology, biology and mathematics, Bujack and her colleagues found that using Riemannian geometry overestimated the perception of large color differences. This is because large differences in color are thought to be smaller than the sum of the small differences in color between two shades located far apart.
Riemannian geometry cannot explain this effect.
“We didn’t expect this, and we didn’t know the exact geometry of this new color space,” Bujack said. “We might be able to think of it normally, but adding damping or weighing to lengthen the distances and make them shorter. But we can’t prove it yet.”
Colorful graphics distort public perception of scientific results
Roxana Bujack et al., Non-Riemannian properties of perceptual color spaces, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.211975311
Courtesy of Los Alamos National Laboratory
Citation: Math Errors: A New Study Overturns a 100-Year-Old Understanding of Color Perception (10 Aug 2022) Retrieved 10 Aug 2022 from https://phys.org/news/2022-08 -math-error-overturns-year-old-perception.html
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