More than a century after Erwin Schrödinger sketched the foundations of a mathematical theory of color perception, scientists at Los Alamos have finally completed what he began—filling in a critical gap that had left his elegant model unfinished for nearly 100 years.
The work matters because how we see color shapes everything from the photographs we take to the way scientists interpret complex visual data. Yet until now, the mathematics describing something so fundamental to human experience remained incomplete. A team led by Los Alamos scientist Roxana Bujack set out to solve that problem by using geometry to build a rigorous definition of color perception based on three qualities we experience intuitively: hue, saturation, and lightness.
Schrödinger's original insight drew on work by 19th-century mathematician Bernhard Riemann, who proposed that color spaces aren't flat but curved. Building on this idea in the 1920s, Schrödinger created a mathematical model that explained how people perceive differences between colors. His framework shaped color science for roughly a century. But when the Los Alamos team was developing algorithms for scientific visualization, they discovered a major weakness in the mathematics behind the model: Schrödinger had never formally defined the neutral axis—the line of grays that runs from black to white—even though his entire system depended on it.
That omission created a serious gap. Without a precise definition of the neutral axis, the construction was formally incomplete. Bujack and her team found a way to define it using only the geometry of the color metric itself, a breakthrough that required moving beyond the traditional Riemannian model entirely. "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 said. Their results, presented at the Eurographics Conference on Visualization, show that hue, saturation, and lightness are built into the fundamental structure of how humans perceive color, not layered on top of it.
The team addressed two other important issues in Schrödinger's framework as well. One involved the Bezold-Brücke effect, a phenomenon where changing light intensity can make a color appear to shift in hue. Rather than relying on a simple straight line, the researchers used the shortest path in their geometric model of color perception to account for this. They also used shortest-path calculations in a non-Riemannian space to capture diminishing returns in color perception—a subtlety that Schrödinger's model had not fully captured.
The implications ripple outward quickly. Photography, video, visualization, and related technologies all depend on accurate color modeling. A more precise understanding of how humans perceive color could improve the way scientists create and interpret visual data across fields ranging from national security sciences to medical imaging. The work was supported by the Laboratory Directed Research and Development program at Los Alamos and the National Nuclear Security Administration's Advanced Simulation and Computing program, and builds on a broader Los Alamos project on color perception that produced a groundbreaking paper in the Proceedings of the National Academy of Sciences in 2022.
The completion of Schrödinger's vision now provides a foundation for future color modeling in non-Riemannian space—a mathematical landscape that opens new doors for understanding not just how we see, but how to represent what we see with greater precision and fidelity.