18 hours ago
Beauty may lie in the eye of the beholder, but color does not, according to researchers from Los Alamos National Laboratory in the US. Their new study suggests that the perception of color attributes is intrinsic rather than influenced by external factors.
Despite differences in how we label colors—and phenomena like the 2015 internet debate about the color of a dress—our basic perception of color distinctions is not driven by culture or experience, the study indicates.
The research builds on the work of Erwin Schrödinger, the physicist famous for his "Schrödinger's cat" thought experiment, who also studied biological phenomena including color perception.
By combining results from color-perception studies within a geometric framework, the authors identified shortcomings in Schrödinger's mathematical definitions of hue, saturation, and lightness. Beyond extending his work, they resolved these ambiguities and completed his theory more than a century later.
"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," says lead author and data scientist Roxana Bujack.
"This metric geometrically encodes the perceived color distance—that is, how different two colors appear to an observer," Bujack adds.
Humans have trichromatic color vision, relying on three types of cone cells in the retina. Each photoreceptor type peaks in sensitivity at a different wavelength, and the brain interprets the combination of signals to perceive the color spectrum.
This process creates three-dimensional color spaces—organized perceptual spaces where sensory perceptions are processed into representations of the world around us.
In the 19th century, mathematician Bernhard Riemann introduced the idea that perceptual spaces for color are curved rather than flat, a concept rooted in Riemannian geometry.
While a straight line is the shortest distance between two points in Euclidean space, Riemannian geometry studies curved surfaces where the shortest path, called a geodesic, may not be straight.
Physicist Hermann von Helmholtz proposed that individual color attributes could be defined geometrically based on closest similarity within the Riemannian metric—a mathematical tool for studying manifolds, or higher-dimensional surfaces.
In the 1920s, Schrödinger applied the Riemannian model of color perception to define hue, lightness, and saturation based on a color's position relative to the neutral axis—the gradient of grays between black and white.
These definitions were widely accepted for the following century, forming the foundation of our understanding of color attributes. However, while developing algorithms for scientific visualizations, the new study's authors found issues with Schrödinger's work.
"With a little criticism, Schrödinger's geometric formulation of the color attributes has, in spirit, survived until today even though it, too, is in conflict with some phenomena observed in experiments," they write.
Notably, Schrödinger never formally defined the neutral axis, despite basing his color attribute definitions on colors' positions relative to it.
Seeing an opportunity to advance the mathematics of color perception, the researchers aimed to complete Schrödinger's work over a century later.
They succeeded by defining the neutral axis based on the geometry of the color metric, which required moving beyond the Riemannian model.
The team also addressed other important issues. For example, Schrödinger's framework could not explain the Bezold-Brücke effect, where changes in light intensity cause perceived shifts in hue.
Bujack and colleagues corrected this by replacing the straight-line definition of stimulus quality between a color and black with the shortest geodesic path in perceptual color space.
They also accounted for diminishing returns in color perception—the tendency to perceive large color differences as less than the sum of smaller differences.
In a related 2022 paper, many of the same researchers argued that this effect "cannot exist in a Riemannian geometry," highlighting the need for improved models of color differences.
Related: Scientists Say They Found a New Color Humans Have Never Seen Before
The new study outlines a novel framework for modeling color in non-Riemannian space.
"Collectively, our solutions provide the first comprehensive realization of Helmholtz's vision: formal geometric definitions of hue, saturation, and lightness derived entirely from the metric of perceptual similarity, without reliance on external constructs," the researchers write.
The study was published in the Computer Graphics Forum.
