Beauty is in the eye of the beholder, but not color, researchers at Los Alamos National Laboratory report in a new study, suggesting that the perception of color properties is intrinsic.
Research shows that despite differences in how we label color, and quirks like the 2015 online debate over skirt color, our basic knowledge of color distinctions is not driven by external factors such as culture or experience.
The research builds on the work of physicist Erwin Schrödinger, famous for his “Schrödinger’s Cat” thought experiment, who studied color perception, among other biological phenomena.
The authors of the new study combined results from studies of color perception within a geometric framework and found that Schrödinger’s mathematical definitions of hue, saturation and brightness were flawed. Beyond merely building on his work, they resolved these ambiguities and helped complete his work more than a century later.
“We concluded that these color qualities do not result from additional external constructs such as culture or learning experience, but reflect intrinsic properties of the color measure itself,” said lead author and data scientist Roxana Bujack.
“This metric geometrically encodes the perceived color distance, that is, how different two colors are seen by an observer,” adds Bujack.
Humans have trichromatic vision, which relies on three color-sensing cones in the retina. The sensitivity of each type of photoreceptor cell peaks at a different wavelength, and we use the combination of signal intensities produced by these cells to sense the color spectrum.
This process gives us the three dimensions of color space or color organization. These perceptual spaces are like mental realms, where we process sensory perceptions into representations of the world around us.
In the 19th century, mathematician Bernhard Riemann proposed the idea that the space in which we perceive colors is curved rather than straight, a concept rooted in his branch of differential geometry of the same name.
While it is well known that a straight line is the shortest distance between two points in Euclidean space, Riemannian geometry usually focuses on curved surfaces where the local shortest path (geodesic) between two points is not straight.
Physicist Hermann von Helmholtz proposed that individual color properties could be defined geometrically based only on their closest similarity in the Riemannian metric, a mathematical tool used to study higher-dimensional analogs of certain manifolds or surfaces.
In the 1920s, Schrödinger used the Riemannian model of color perception to define the perceptual properties of hue, brightness, and saturation. His definition is based on the color’s position relative to the neutral axis, or the gray gradient between black and white.
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These definitions became widely accepted over the next century, providing a framework for our understanding of color properties. However, when the authors of the new study worked on algorithms for scientific visualization, they discovered problems with Schrödinger’s work.
“Despite some criticism, Schrödinger’s geometric formulation of color properties survives in spirit to this day, although it also conflicts with some phenomena observed in experiments,” they wrote.
They point out that Schrödinger never formally defined the neutral axis, although his definition of color properties was based on the color’s position relative to it.
Recognizing the opportunity to advance the mathematics of color perception, researchers attempted to complete Schrödinger’s work more than a century later.
They explain that they succeeded in defining the neutral axis based on the geometry of the color metric, which required working outside the Riemannian model.
The researchers also made other important corrections. Schrödinger’s idea could not explain the Bezold-Bruck effect, for example, the phenomenon whereby changing light intensity causes a change in perceived hue.
Bujack and her colleagues corrected this by replacing the straight-line definition of stimulus mass between color and black with the shortest geodesic in perceptual color space.
They also explain diminishing returns in color perception, which refers to our tendency to perceive large color differences as less than the sum of small color differences.
In a related 2022 paper, many researchers argued that this effect “does not exist in Riemannian geometry,” citing the need for improved color difference modeling methods.
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With this new research, they outline a novel framework for modeling color in non-Riemannian space.
“Overall, our solution is the first comprehensive realization of Helmholtz’s vision: formal geometric definitions of hue, saturation, and brightness derived entirely from measures of perceptual similarity and independent of external constructs,” the researchers write.
The research was published in Computer Graphics Forum.
