under the clear sky When the sun rises high, the normal human eye can see almost the entire visible color spectrum. If you remove direct sunlight, you only get a small portion of the rainbow due to reflections. But even though the darkness distorts our reference point, we can still judge the color of the shadow. Many factors influence the hues we detect, including our eyes, our brains, the air, objects that reflect light, the shape of the Earth, and even our visual memory.
Trying to reproduce that range of color and sensitivity on computer monitors and printers is both an engineer’s nightmare and a dream. And that’s exactly the problem Roxana Bujak, a staff scientist with a large data science team at New Mexico’s Los Alamos National Laboratory, is trying to solve computationally. There’s math behind “everything that happens in Photoshop,” she says Bujack. “It’s all just matrices and operations, but it’s easy to see what the math does.”
Any answer to this question will be very different from the color wheels of art classes or the way most computer screens and printers work today. His digital work relies on his RGB (red, green, blue) model, using the monitor’s light source to adjust the brightness of these three of his colors, creating pigment within the pixels. His CMY (cyan, magenta, yellow) model of printer, on the other hand, is subtractive, removing color from a white base. When printing yellow on cardboard, the printer combines his CMY inks to change the light background to varying degrees to achieve the desired color.
These color models were last updated a century ago. Erwin Schrödinger, famous for his quantitative research, improved RGB along with mathematician Bernhard Riemann and physicist Hermann von Helmholtz. For example, they realized that they could not measure the distance between a rosy red and a dull green in a straight line, so they looked for a more flexible model. They moved from representing colors in the familiar physical space known as Euclidean geometry to the distorted world of Riemannian geometry.
Bujack likens the interpretation to an airline service map. The route is not a straight line, but a half-moon that reflects the curvature of the Earth. “Suppose you select two colors and choose the one that is on the shortest path between them. For example, magenta in the center, purple on the right, and pink on the left. Then from magenta to purple, and from magenta to “Measure your path to pink,” she says. “The sum of these two path segments equals the length of the entire path drawn from magenta to pink, and these represent the perceived difference between the two colors. This is from Seattle via Reykjavik. It should be about the same distance as the flight to Amsterdam.”
Schrödinger’s 3D model has been the basis of color theory for over 100 years. Scientists and developers apply this when trying to perfect the digital representation of colors on a machine’s screen. This helps translate into pixels how the human eye distinguishes between different shades, such as how this text can be perceived as black and the background as white without being blurred.
For Bujak, the contours of this space are familiar. She studied Mathematics at the University of Leipzig in Germany, where she took a course in Image Processing and came to learn some of that field. There she became fascinated with the mathematics that powers various programs, including Photoshop and her processor-intensive video games. She graduated with her PhD in computer science in 2014, and then arrived at the Alamos Institute in Los Angeles, where she was based for her project in Manhattan.
So in 2021, her team launched a project with a modest purpose. It’s about designing color maps and building algorithms that streamline the conversion of pigments into numbers and dates, Bujack says. Illustrators who use Photoshop, Final Cut, and similar programs will benefit. The same goes for climate scientists, physicists, and weather researchers who use colors to represent numerical data.
But they discovered a contradiction that upends a century of understanding of the field. “Schrödinger’s work was very sophisticated, and he realized that to describe color space you need a curved space, and that this stupid Euclidean space just wouldn’t work,” says Bujak. But Schrödinger and his collaborators “didn’t realize they needed a more robust model.”
Schrödinger’s mathematics didn’t work, Bujak and her team found, because it couldn’t predict the correct hue between two colors. For example, on a flight path between Seattle and Reykjavik, you can calculate the remaining time on your itinerary. However, at the midpoint between purple and red, the expected color is not obtained. The old 3D approach overestimated how different we perceive one shade of her from another. The Los Alamos team published their findings in the journal April 2022. Proceedings of the National Academy of Sciences. “As a scientist, I’ve always dreamed of proving famous people wrong,” says Bujak. “But this level of fame is beyond even my wildest dreams.”
However, the revelation did not bring a clear solution. “The current model is not accurate,” he says. “[But] That doesn’t mean there’s an off-the-shelf model to replace it. ” Mapping the new space is “much more labor intensive” than Schrödinger’s calculations, so any mathematical updates will be “years and years into the future.”
However, the impact of this discovery could reach our computers sooner. Nick Spiker, a color engineer working on her IDT Maker, a proprietary digital relighting system, consulted Bujack after her research was published. He subsequently filed a patent for a product that helps video producers and photographers change the apparent time of videos and photos.
Although we don’t have a replacement model yet, Bujack’s insights could help us build a better one. For example, “if you’re watching Netflix or other visual content and want accurate colors,” Spiker says. He added, “This makes images look more realistic than ever before.”
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