Here’s what you’ll learn when you read this story:
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Because our eyes perceive color using cones coded primarily for red, green, and blue, photoreception of color can be modeled using three-dimensional geometry.
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While scientists have tried to accurately portray this perception over the centuries, the most modern conception still can’t explain certain visual phenomena.
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This new study takes a step outside of what’s known as Riemannian model, creating what might be the most accurate mathematical representation of photoreception ever created.
The way we perceive color may seem obvious, but for more than a century, scientists have been trying to mathematically work out how humans perceive color as it relates to hue, lightness, and saturation. Now, a new study published in the journal Color Graphics Forum—led by scientists at the Los Alamos National Laboratory (LANL)—has highlighted three shortcomings in Schrödinger’s color theory (science’s most modern understanding of color perception) and confirmed that the perception of color is intrinsic, rather than a phenomenon formed outside of physics and biology.
“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,” Roxana Bujack, lead author of the study from LANL, said in a press statement. “This metric geometrically encodes the perceived color distance—that is, how different two colors appear to an observer.”
At the heart of this breakthrough lies the physical way our eyes perceive colors—three cones with specific sensitivities red, green, and blue. This makes our eyes trichromatic (some people are actually tetrachromatic, but that’s a discussion for another day). Trichromatic eyes allow color to be perceived in three-dimensional color spaces, and it’s taken centuries of work to perfectly capture how our photoreceptors interpret color using mathematics and geometry.
The Austrian-Irish theoretical physicist Erwin Schrödinger may be best known for his eponymous thought experiment involving box-bound felines and quantum superposition, but the famous scientist also studied color theory. In the 1920s, he built his theory on centuries of work in the field, dating all the way back to Isaac Newton’s Optiks treatise from 1704. Modern perceptions of color theory began to take shape in the early-to-mid 1800s, when German mathematician Georg Friedrich Bernhard Riemann showed that these spaces were not straight (Euclidian), but curved.
“In a Euclidean space, the shortest path between two points is a straight line. However, in Riemannian geometry, the concept of a straight line does not play the same role because of the nonzero curvature of the space in the general case,” the authors wrote in the study. “The analogous concept in Riemannian geometry is a geodesic, the path connecting two points that is locally shortest.”
Decades later, German physicist Hermann von Helmholtz discovered that individual colors could be geometrically defined based only on closest similarity in the Riemannian metric, according to Science Alert. And in the 1920s, Schrödinger essentially rescued these ideas from obscurity when he defined attributes of hue, saturation, and lightness based on a somewhat-undefined neutral axis (basically gradients of grays between black and white) within Riemannian geometry.
While Schrödinger’s work (building on centuries of color theory) certainly advanced mathematical modeling of color perception, it wasn’t perfect. As the authors note, this modern conception of color theory, for instance, couldn’t explain the Bezold-Brücke effect, which describes how light intensity changes our perception of a hue. It also couldn’t explain the phenomenon of diminishing returns in color perception, where large color differences appear less intense than the summation of small color differences.
In this new study, the LANL authors successfully defined this neutral axis by working outside of the Riemannian model. They also resolved both the problem of the Bezold-Brücke effect (by applying a “geodesic path in perceptual color space” between a color and black) and the principle of diminishing returns (by using the shortest path in non-Riemannian space).
By plugging these experimental holes, the researchers were able to produce a paper that represents the most accurate mathematical representation of how our eyes see color yet—the culmination of more than three centuries of science.
“This results in the first complete solution to what Helmholtz had envisioned: formal geometric definitions of hue, saturation, and lightness that are fully derived from the perception of closest similarity and nothing else,” the authors wrote.
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