A century old idea from Erwin Schrödinger has taken a significant step forward, due to latest research into how humans perceive differences between colours.
A team led by Los Alamos scientist Roxana Bujack used geometry to construct a mathematical definition of color perception based on hue, saturation, and lightness. Their results, presented at a visualization science conference, formalize Schrödinger’s model of color and show that these familiar color qualities are built into the structure of color perception itself.
“What we conclude is that these color qualities don’t emerge from additional external constructs akin to cultural or learned experiences but reflect the intrinsic properties of the colour metric itself,” Bujack said. “This metric geometrically encodes the perceived color distance — that’s, how different two colours appear to an observer.”
Completing Schrödinger’s Color Puzzle
By defining these perceptual attributes more rigorously, the researchers have supplied a missing piece in Schrödinger’s long standing vision for a closed mathematical model of color. The goal was to define hue, saturation, and lightness using only the geometric property of highest color similarity.
Human color vision relies on three varieties of cone cells, that are centered around red, blue, and green. That offers color spaces three dimensions, allowing scientists to prepare and compare colours mathematically.
Within the nineteenth century, mathematician Bernhard Riemann proposed that perceptual color spaces should not flat or straight, but curved. Within the Nineteen Twenties, Schrödinger built on that concept by defining hue, saturation, and lightness inside a Riemannian model of color perception, using a metric that describes how people perceive color differences.
Fixing a Century Old Mathematical Gap
Schrödinger’s definitions have shaped color science for roughly 100 years. But while the Los Alamos team was developing algorithms for scientific visualization, they found that the mathematics behind the model had necessary weaknesses.
The largest problem involved the neutral axis, the road of grays that runs from black to white. Schrödinger’s definitions of hue, saturation, and lightness depend upon where a color sits in relation to that axis, yet he never formally defined the axis itself.
That omission created a serious gap. With out a precise definition of the neutral axis, all the construction was formally incomplete. The team’s most significant advance was finding a technique to define the neutral axis using only the geometry of the colour metric.
To perform that, the researchers had to maneuver beyond the standard Riemannian model. That shift represents a significant mathematical advance for visualization science.
A Higher Model of How Colours Change
The team also corrected two other necessary issues within the older framework.
One involved the Bezold- Brücke effect, a phenomenon by which changing light intensity could make a color appear to shift in hue. The researchers addressed this through the use of the shortest path of their geometric model of color perception slightly than counting on a straightforward straight line.
In addition they used the shortest path in a non-Riemannian space to account for diminishing returns in color perception, one other effect that had not been fully captured by the older approach.
Why Color Perception Matters
The research was presented on the Eurographics Conference on Visualization and builds on a broader Los Alamos project on color perception. That project also produced a groundbreaking 2022 paper within the Proceedings of the National Academy of Sciences.
A more precise model of color perception could have wide value in fields that depend upon accurate color, including photography, video, visualization, and related technologies. It could also improve the way in which scientists create and interpret visual data.
Scientific visualization plays a vital role in helping researchers understand complex information. Higher color models can support simpler evaluation across many areas, including national security sciences.
The team’s work now provides a foundation for future color modeling in non-Riemannian space.
Funding: This work was supported by the Laboratory Directed Research and Development program at Los Alamos and by the National Nuclear Security Administration’s Advanced Simulation and Computing program.