A 2022 study identifies an important error in the 3D mathematical color space developed by the Nobel Prize-winning physicist Erwin Schrödinger and others, For more 100 years we used this mathematical space to describe how the eye distinguishes one color from another, and to build electronic color reproduction accordingly. Now it seems the underlying model may be faulty. On the bright side, the research has the potential to boost scientific data visualizations, recalibrate the textile and paint industries, and improve (or completely disrupt) how displays are made. If–science can figure out what the color space is, now that we know it’s not what we thought.
This visualization above captures the 3D mathematical space used to map human color perception. A new mathematical representation has found that the line segments representing the distance between widely separated colors don’t add up correctly using the previously accepted geometry. The research contradicts long-held assumptions and will improve a variety of practical applications of color theory. Credit: Los Alamos National Laboratory
“The assumed 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 lead author of the paper by 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 proving one of them wrong is pretty much the dream of a scientist,” said Bujack.
“Our original idea was to develop algorithms to automatically improve color maps for data visualization, to make them easier to understand and interpret,” Bujack said. So the team was surprised when they discovered they were the first to determine that the longstanding application of Riemannian geometry, which allows generalizing straight lines to curved surfaces, didn’t work.
Say what now?
To create the industry standards that video professionals have depended on for everything, a precise mathematical model of perceived color space is needed. If you recall, Riemannian geometry plots red, green and blue in the 3D space. Those are the colors registered most strongly by light-detecting cones on our retinas–the all important RGB spectrum.
In the new study published the online journal PNAS; phys.org describes it as blending psychology, biology and mathematics, Bujack and her colleagues discovered that Riemannian geometry overestimates our perception of large color differences. People perceive a big difference in color to be less than the sum of the incremental differences that lie between two widely separated shades–a principle of diminishing returns. Color-driven painters like Kandisky understood this subjectivity and the relativity of perception. Not surprisingly that didn’t make it into the science that drives digital video; Riemannian geometry cannot account for it
“We didn’t expect this, and we don’t know the exact geometry of this new color space yet,” Bujack said. “We might be able to think of it normally but with an added dampening or weighing function that pulls long distances in, making them shorter. But we can’t prove it yet.”
No matter how subtle the necessary adjustments will need to be, in the world of color pixels the effect of a changed color space will be anything but subtle.
More information: Roxana Bujack et al, The non-Riemannian nature of perceptual color space, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2119753119
Journal information: Proceedings of the National Academy of Sciences