Thanks to new research into how humans perceive color differences, Erwin Schrödinger’s century-old ideas have taken a major step forward.
A team led by Los Alamos scientist Roxana Bujak used geometry to construct a mathematical definition of color perception based on hue, saturation, and brightness. Their results, presented at the Visualization Science Conference, formalize Schrödinger’s model of color and show that these familiar color properties are built into the structure of color perception itself.
“Our conclusion is that these color properties do not emerge from additional external constructs such as culture or learning experiences, but rather reflect intrinsic properties of the color metrics themselves,” Bujak said. “This metric geometrically encodes perceived color distance, or how different two colors appear to the observer.”
Complete Schrödinger’s Color Puzzle
By defining these perceptual attributes more precisely, the researchers provided the missing piece in Schrödinger’s long-standing vision of a closed mathematical model of color. The goal was to define hue, saturation, and lightness using only the geometric properties of highest color similarity.
Human color vision is based on three types of cone cells: red, blue, and green. This makes the color space three-dimensional, allowing scientists to organize and compare colors mathematically.
In the 19th century, mathematician Bernhard Riemann proposed that perceptual color space is neither flat nor straight, but curved. In the 1920s, Schrödinger built on the idea by defining hue, saturation, and lightness within the Riemann model of color perception, using metrics to describe how people perceive differences in color.
Fixing a century-long mathematical gap
Schrödinger’s definition has shaped color science for nearly 100 years. But while developing an algorithm for scientific visualization, the team at Los Alamos noticed a significant weakness in the mathematics behind the model.
The biggest problem had to do with the neutral axis, which is the gray line going from black to white. Schrödinger’s definitions of hue, saturation, and lightness depend on where a color lies relative to that axis, but he never formally defined the axes themselves.
This omission created a serious gap. Without a precise definition of the neutral axis, the entire structure was formally incomplete. The team’s most important advance was finding a way to define the neutral axis using only color metric geometry.
To accomplish that, researchers needed to move beyond the traditional Riemann model. This change represents a major mathematical advance in visualization science.
A better model of color change
The team also fixed two other important issues in the old framework.
One concerns the Bezold-Brücke effect, a phenomenon in which colors appear to change in hue as the intensity of light changes. The researchers addressed this problem by using shortest paths in a geometric model of color perception, rather than relying on simple straight lines.
They also used shortest paths in non-Riemannian space to account for diminishing returns in color perception. This is another effect that was not fully captured by older approaches.
Why color perception matters
This research was presented at the Eurographics Conference on Visualization and builds on the broader Los Alamos project on color perception. The project also produced a landmark paper in 2022. Proceedings of the National Academy of Sciences.
More accurate models of color perception could have widespread value in fields that rely on accurate color, such as photography, video, visualization, and related technologies. It could also improve the way scientists create and interpret visual data.
Scientific visualization plays an important role in helping researchers understand complex information. Better color models can support more effective analysis across many fields, including national security science.
The team’s research is currently providing the basis for future color modeling in non-Riemannian spaces.
Funding: This research was supported by Los Alamos’ Institute-Directed Research and Development Program and the National Nuclear Security Administration’s Advanced Simulation and Computing Program.
