A 100-year-old idea about colour has just had a major repair job.

Researchers at Los Alamos National Laboratory say they have resolved a key problem in Erwin Schrödinger’s theory of colour, using geometry to build a mathematical definition of colour perception based on hue, saturation and lightness.

Their findings were presented at the Eurographics Conference on Visualization and formalise Schrödinger’s model of colour, showing those familiar colour qualities are built into the structure of colour perception itself.

“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,” Los Alamos scientist Roxana Bujack said.

“This metric geometrically encodes the perceived color distance, that is, how different two colors appear to an observer.”

The work fills what researchers described as a missing piece in Schrödinger’s long-standing goal of a closed mathematical model of colour.

That goal was to define hue, saturation and lightness using only the geometric property of highest colour similarity.

Human colour vision is based on three types of cone cells, centred around red, blue and green. That gives colour spaces three dimensions, which lets scientists organise and compare colours mathematically.

In the 19th century, mathematician Bernhard Riemann proposed that perceptual colour spaces are curved, not flat or straight.

In the 1920s, Schrödinger built on that idea by defining hue, saturation and lightness within a Riemannian model of colour perception, using a metric that describes how people perceive colour differences.

The Los Alamos team said Schrödinger’s definitions have shaped colour science for about 100 years, but they found important weaknesses in the mathematics while developing algorithms for scientific visualisation.

The biggest problem involved the neutral axis, the line of greys running from black to white.

Schrödinger’s definitions of hue, saturation and lightness depend on where a colour sits in relation to that axis, but he never formally defined the axis itself.

The researchers said that left the construction formally incomplete.

They said their most important advance was finding a way to define the neutral axis using only the geometry of the colour metric.

To do that, the team moved beyond the traditional Riemannian model, which they described as a major mathematical advance for visualisation science.

The researchers also addressed two other problems in the older framework.

One was the Bezold-Brücke effect, where changing light intensity can make a colour appear to shift in hue.

They addressed that by using the shortest path in their geometric model of colour perception instead of a simple straight line.

They also used the shortest path in a non-Riemannian space to account for diminishing returns in colour perception, another effect the older approach had not fully captured.

Los Alamos said a more precise model of colour perception could be useful in photography, video, visualisation and related technologies. It could also improve how scientists create and interpret visual data.

The work builds on a broader Los Alamos project on colour perception, which also produced a 2022 paper in the Proceedings of the National Academy of Sciences.

The study, “The Geometry of Color in the Light of a Non‐Riemannian Space,” was published in Computer Graphics Forum.

Read more from Science Daily.