Researchers in the US have finally completed the missing mathematical pieces of theoretical physicist Erwin Schrödinger’s century-old color theory, based on his geometric model describing how humans perceive color.
In the 1920s, the Austrian-Irish scientist proposed a mathematical model of color perception based on visual response. He suggested that the full range of human-visible colors could be mapped as a three-dimensional geometric shape defined by cone-cell responses.
Now, a team of researchers led by Roxana Bujack, PhD, a computer scientist at Los Alamos National Laboratory (LANL), used advanced geometry to show that saturation, hue, and lightness aren’t shaped by culture or experience.
The scientists finalized Schrödinger’s model and showed that these attributes are built directly into the mathematical structure of human vision, and not just “in the eye of the beholder.”
“What we conclude is that these color qualities don’t emerge from additional external constructs such as cultural or learned experiences but reflect the intrinsic properties of the color metric itself,” Bujack stated. She said the metric describes color differences as measurable geometric distances.
Schrödinger’s color puzzle
Human vision depends on trichromacy, meaning that it uses three types of cone cells (photoreceptors) in the retina – red, green, and blue – to detect wavelengths and produce color vision. In the 19th century, German mathematician Bernhard Riemann first proposed that these perceptual spaces are not straight, but curved.
In the 1920s, Schrödinger defined the perceptual attributes of hue, saturation, and lightness. He suggested these qualities arise from a metric of color perception in his Riemannian framework. His definitions provided a century-long framework for understanding color attributes.
However, while working on algorithms for scientific visualization, the researchers detected shortcomings in Schrödinger’s mathematical foundations. This opened the door to further refining the mathematical understanding of color perception.
The team found that the neutral axis, the line of gray tones that runs from black to white, was a major problem. They realized that Schrödinger had never actually defined the axis mathematically, even though his definitions rely on how colors are positioned relative to it.
Fixing the gap
To define the neutral axis, the team worked outside of the Riemannian model. It marked a significant breakthrough in the mathematics of visualization. They also corrected two additional effects.
They also addressed the Bezold- Brücke effect, in which increasing brightness can make a color appear to shift in hue. The team did this by using the shortest path, instead of a straight line, in their geometric model of color perception.
The scientists also used the shortest path in a non-Riemannian space to address the phenomenon of diminishing returns in color perception. “Understanding color perception is an important component of visualization science, a critical capability that informs many useful endeavors,” they concluded in a statement.
Their work, presented at the Eurographics Conference on Visualization, represents a culmination of a project on color perception. The same project also delivered a pioneering study in the Proceedings of the National Academy of Sciences in 2022.
Their current paper has been published in the Computer Graphics Forum, the official journal of the Eurographics Association.