Researchers have finally completed Erwin Schrödinger’s nearly century-old theory of color perception by mathematically defining how humans experience hue, saturation, and lightness. The breakthrough, led by Roxana Bujack at Los Alamos National Laboratory, strengthens the geometric foundation of Schrödinger’s framework and corrects long-standing mathematical gaps.
Schrödinger, better known for his work in quantum physics, proposed in the 1920s that color perception could be described within a curved mathematical space. Building on ideas from 19th-century mathematician Bernhard Riemann, he argued that qualities like hue, saturation, and lightness were not arbitrary or purely cultural constructs, but instead emerged from the internal geometry of a perceptual color system, according to new research reported by ScienceDaily.
For decades, his definitions influenced how scientists modeled color. However, while developing advanced visualization algorithms, Bujack and her colleagues discovered weaknesses in the original mathematical structure. One of the most significant issues involved the neutral axis, the line of gray tones stretching from black to white. Schrödinger’s model relied on this axis, yet he never formally defined it. Without a rigorous definition, the framework remained incomplete.
The team’s key achievement was deriving the neutral axis directly from the geometry of the color metric itself. In doing so, they moved beyond the traditional Riemannian framework and into a non-Riemannian mathematical space. This shift allowed them to correct structural flaws and make the model self-contained, fulfilling Schrödinger’s original goal.
The researchers also addressed perceptual phenomena such as the Bezold-Brücke effect, where increasing brightness can subtly shift perceived hue. Instead of assuming color changes along straight lines, they calculated the shortest paths within curved geometric space. This approach also accounted for diminishing perceptual returns, where increasingly large physical color differences produce smaller noticeable changes to the human eye.
The findings, published here, were presented at the Eurographics Conference on Visualization and build on earlier work published in 2022 in the Proceedings of the National Academy of Sciences. Accurate color modeling is critical for visualization science, influencing everything from photography and video processing to complex data simulations used in national security research.
By grounding hue, saturation, and lightness firmly in geometry, the team has provided a stronger mathematical basis for understanding how we perceive color. Nearly 100 years later, Schrödinger’s vision of a fully geometric color theory may finally be complete.
