Researchers have refined and mathematically perfected the theory of color perception proposed by physicist Erwin Schrödinger nearly a century ago. The research team, led by scientist Roxanne Bujak at Los Alamos National Laboratory, demonstrated that hue, saturation, and brightness can be derived from the geometric structure of the color space. The work was published in the journal Proceedings of the National Academy of Sciences (PNAS).
Schrödinger's theory, developed in the 1920s, is based on the idea that the space of perceived colors can be curved, in the spirit of Bernhard Riemann's geometry. Because human vision is based on three types of cone cells that are sensitive to red, green, and blue light, color is described in three dimensions. Schrödinger argued that the basic characteristics of color – hue, saturation and brightness – are determined by the internal geometry of this space.
However, mathematical flaws remain in his model. In particular, the so-called neutral axis is not officially defined – a gray line from black to white, corresponding to the positions of other colors is indicated. Without a clear definition of this axis, the entire structure remains incomplete.
The Los Alamos team was able to derive the neutral axis solely from the geometric properties of the colorimeter, a system that describes how two different colors are perceived.
“We conclude that hue, saturation, and brightness are not external constructs—cultural or learned. They reflect internal properties of the color measure itself,” notes Roxana Buzhak.
In addition, the researchers also addressed two additional known limitations of the classical model. They took into account the Bezold-Brücke effect, in which a change in brightness can lead to a change in color. Instead of assuming a linear color change, the scientists calculated the shortest path in curved space. The same approach can explain the effect of “diminishing returns” – a situation in which increasing differences between colors are perceived as less and less noticeable.
To solve these problems, researchers must go beyond traditional Riemannian geometry and use a more general mathematical model. They say this is an important step toward perfecting Schrödinger's concept.
An accurate mathematical model of color perception is of great practical importance. It is essential for scientific visualization, from photography and video technology to big data analysis and computer modeling. Improved color models enable more accurate interpretation of complex data and create more powerful visualization tools, including those used in national security research.
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