Riemann, Helmholtz, Schrödinger. If you’ve studied math or physics at college – or are just a fan of paradoxical cats – you’ve almost certainly heard these names before: they’re all legends in the field.
“Proving one of them wrong is pretty much the dream of a scientist,” said Roxana Bujack, a computer scientist with a background in mathematics who creates scientific visualizations at Los Alamos National Laboratory in a statement.
But that’s what she and her colleagues have done – not for one, but all three of those big names. In a recent paper published in the Proceedings of the National Academy of Sciences, Bujak and her co-authors have corrected a mathematical error underpinning how we understand color perception.
“Our research shows that the current mathematical model of how the eye perceives color differences is incorrect,” Bujak said. “That model was suggested by Bernhard Riemann and developed by Hermann von Helmholtz and Erwin Schrödinger – all giants in mathematics and physics.”
It’s a mistake that was made more than 100 years ago, but the consequences are far-reaching in today’s world. That’s because the way we model color space underpins modern computer graphics, image processing, and visualization tasks – if you’ve ever wondered just why we refer to “RGB” color, it’s because of this model.
The first step in the standard model of color perception starts with plotting red, green, and blue – the three colors picked up most easily by human retinas – in three-dimensional space.
Technically, it’s in what’s known as Riemannian space – kind of a generalization of the Euclidean space we’re used to dealing with in grade school, and very useful when you’re dealing with something whose appearance depends on the scale you see it at. That may sound strange, but a good example is the planet Earth: from far away, it’s a sphere, but from where you’re sitting right now, it’s pretty flat.
The good thing about Riemann spaces, though, is that they’re usually well-behaved. Specifically, it’s pretty easy to measure distances between point A and point Z – and extra importantly, if you add up the distances between points A, B, C, D, and so on, all the way up to point Z, you’ll get the same result.
That may sound like a given for any space, but in fact, it’s not always true. And as it turns out, one of the places it isn’t true is in color modeling.
“We didn't expect this,” Bujack said, “and we don't know the exact geometry of this new color space yet.” But it’s certainly not Riemannian, for one major reason: the principle of diminishing returns.
Put simply, the human brain is pretty bad at figuring out “scales” of color, and we tend to see big differences between two colors as being smaller than the sum of all the smaller differences making them up.
“The assumed shape of color space requires a paradigm shift,” Bujack explained – but exactly what that shift will be is yet to be discovered.
“We might be able to think of it normally but with an added dampening or weighing function that pulls long distances in, making them shorter,” she said. “But we can't prove it yet.”