New Research Upturns 100 Years of Color Perception

3D Mathematical Space Used To Map Human Color Perception
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3D Mathematical Space Used to Map Human Color Perception

This visualization captures the 3D mathematical space used to map human color perception. A new mathematical representation has found that line segments representing the distance between widely separated colors are not correctly summed using previously accepted geometry. The research contradicts long-held assumptions and will develop a variety of practical applications of color theory. Credit: Los Alamos National Laboratory

A paradigm that moves away from the 3D mathematical definition developed by Schrödinger and others to explain how we see colors could result in more vibrant computer screens, TVs, textiles, printed materials, and more.

The new research corrects a key error in 3-dimensional mathematical space developed by Nobel Prize-winning physicist Erwin Schrödinger and others to explain how your eye distinguishes one color from another. This false model has been used by scientists and industry for over 100 years. The work has the potential to increase scientific data visualizations, improve television and recalibrate the textile and dye industries.

“The default shape of 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 the Los Alamos team. was published in the magazine. Proceedings of the National Academy of Sciences.

“Our research shows that the current mathematical model of how the eye perceives color differences is wrong. This model was proposed by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – all giants in mathematics and physics – and proving either one wrong is almost a scientist’s dream. .

It enables the automation of modeling human color perception, image processing, computer graphics and visualization tasks.

The Los Alamos team refines the math used by scientists, including Nobel Prize-winning physicist Erwin Schrödinger, to explain how your eye distinguishes one color from another.

“Our original idea was to develop algorithms that would automatically improve color maps for data visualization, making them easier to understand and interpret,” Bujack said. Said. That’s why the research team was surprised to discover that they were the first to discover that the longstanding application of Riemannian geometry, which allows the generalization of straight lines to curved surfaces, doesn’t work.

A precise mathematical model of the perceived color space is needed to establish industry standards. Early attempts used Euclidean spaces, the familiar geometry taught in many high schools. Later, more advanced models used Riemann geometry. Models draw red, green, and blue in 3D space. These are the colors most strongly recorded by the light-sensing cones in our retinas, and – not surprisingly – the colors that mix to create all the images on your RGB computer screen.

In the study, which combined psychology, biology and mathematics, Bujack and colleagues discovered that using Riemann geometry exaggerates 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.

Riemannian geometry cannot explain this effect.

“We didn’t expect this, and we don’t know the exact geometry of this new color space yet,” Bujack said. “We might think of it as normal, but with an additional damping or weighing function that pulls long distances and shortens them. But we can’t prove it yet.”

Reference: “Non-Riemannian nature of perceptual color space” by Roxana Bujack, Emily Teti, Jonah Miller, Elektra Caffrey, and Terece L. Turton, April 29, 2022. Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2119753119

Funding: Los Alamos National Laboratory Laboratory Directed Research and Development Program.

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