A recent study led by Los Alamos National Laboratory in the United States claims to have solved the flawed color perception theory proposed by physicist Erwin Schrödinger nearly a century ago, providing a complete mathematical description of the geometric nature of how humans perceive color. The research team used geometric methods to describe the human eye's experience of hue, saturation and brightness, proving that these perceptual dimensions are the basic properties of the color system itself, rather than the result of acquired culture or learning experience.
The work, led by Los Alamos National Laboratory scientist Roxana Bujack, has been reported at major conferences in the field of visualization science and published in the journal Computer Graphics Forum, filling in a key missing link in Schrödinger's vision of a complete color model. The research shows that under the new mathematical framework, hue, saturation and lightness can be completely defined by the geometric relationship between colors, thus conceptually closing this long-pending theoretical system.
Human color vision relies on three types of cone cells in the retina that are sensitive to red, green, and blue bands. Together, they form a three-dimensional "color space" that is used to organize and distinguish various colors. As early as the 19th century, the mathematician Riemann proposed that the space perceived by humans may not be "straight", but has curvature. In the 1920s, Schrödinger gave the mathematical definitions of hue, saturation and lightness under the framework of Riemannian geometry, laying the foundation for subsequent color science.
However, in the process of developing scientific visualization algorithms, the Los Alamos team discovered that Schrödinger's theory has obvious weaknesses in its mathematical structure, making it difficult to support certain precise applications. This discovery prompted them to conduct a systematic reflection on the traditional model, and finally proposed a revised and expanded geometric framework to make the theory more consistent with the measured data.
In the research, a key problem to be overcome is the so-called "neutral axis", which is the gray axis from black to white. Schrödinger's definition was highly dependent on the position of color near this axis, but he never gave a strict mathematical characterization of this axis, resulting in the entire model lacking a complete formal basis. The breakthrough of the Los Alamos team was that for the first time, the neutral axis was strictly mathematically defined solely based on the geometric properties of the color measurement itself, and in the process it broke through the limitations of the traditional Riemannian framework.
The researchers embedded the results of a large number of previous color experiments into standard color spaces such as CIERGB and found that people subjectively feel that the isochromatic surface formed by colors with "the same hue" does not move along a straight line toward a certain vertex. This shows that the assumptions about the geometric structure of color space in the classical model are too ideal, and more complex non-straight structures are needed to depict the real perceptual differences of humans.
In the process of patching the theoretical flaws, the team also corrected two other long-standing problems. One of these involves the Bezold–Brugge effect, whereby changes in light intensity alter people's subjective perception of hue. The researchers abandoned the original geometric description based on straight lines and instead used the "shortest path" (geodesic) in the perceptual color space to describe the distance between colors, thereby more accurately reflecting the hue shift that occurs with changes in brightness.
The same "shortest path" idea has also been introduced into a non-Riemannian color space to explain the so-called "diminishing returns of perception" phenomenon: when the color difference becomes larger and larger, the human eye's sensitivity to the difference no longer increases linearly, and even tends to saturation. The new model can provide quantitative explanations under a unified framework, making the theory more consistent with psychophysical experimental results.
Bujak said the team concluded that traditional color attributes such as hue, saturation and lightness are not labels attached to colors that rely on cultural background or learning experience, but are intrinsic properties encoded in the geometric structure of the color measurement itself. In her opinion, the new model defines "color distance" geometrically, which is how far apart observers subjectively feel two colors are. It provides Schrödinger's original idea with a mathematical cornerstone that has been missing for nearly a hundred years.
The research, presented at this year's Eurographics Visualization Conference, is one of the first steps in a long-term color vision project at Los Alamos National Laboratory. This project has published an important paper in the Proceedings of the National Academy of Sciences (PNAS) as early as 2022. On this basis, this work further advances non-Riemannian color space modeling and lays the foundation for more sophisticated visual computing research in the future.
A more accurate color perception model is believed to have broad application prospects in many fields. From photography and video technology to scientific imaging and data visualization, the accuracy of color models directly affects the clarity and reliability of information presentation. The research team pointed out that accurately simulating the "color distance" in human eyes will help scientists and engineers make more reliable visual designs and judgments when faced with complex data, thereby serving many key fields from high-performance simulation to national security science.
The paper "The Geometry of Color in the Light of a Non-Riemannian Space" was completed by Bujak and collaborators Emily N. Stark, Terece L. Turton, Jonah M. Miller and David H. Rogers, and will be officially published in May 2025. The project received funding from the Los Alamos National Laboratory Directed Research and Development Program and the National Nuclear Security Administration's Advanced Simulation and Computing Program.