The mistake that changes how we see color — The Blueprint

Meet the woman who disproved Riemann, Helmholtz and Schrödinger.
Alice Cooke
A math error could change how we see color.
  • Researchers have identified a key math error in the theory of color perception.
  • The theory was developed by famous scientists, including Erwin Schrödinger.
  • Correcting the error could lead to major improvements in a huge range of industries.

This story first appeared in our subscriber-only weekly Blueprint newsletter. Receive exclusive interviews and analyses like this, direct to your inbox every Sunday, by subscribing to IE+.

Being able to accurately model human color perception has a massive impact on automating image processing, computer graphics, and visualization.

To come up with a concrete mathematical model of perceived color space, red, green, and blue are plotted in 3D space. These colors are chosen because they’re the ones that are most strongly registered by light-detecting cones in our retinas.

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Bujack’s team set out to develop algorithms that would automatically enhance the color maps commonly used in data visualization to make it easier to read them – and that’s when they happened across the mistake.

The resultant paper, which was published in the Proceedings of the National Academy of Science, is the work of lead author and computer scientist Roxana Bujack and a research team from the Los Alamos National Laboratory (LANL).

Bujack, who creates scientific visualizations at LANL, claimed the current mathematical models used for color perceptions were incorrect and in need of a “paradigm shift.” So in that spirit, we caught with her to find out how she did it, and what differences that paradigm shift might make.

The mistake that changes how we see color — The Blueprint
A key math error could change color perception.

Interesting Engineering: What prompted this research in the first place?

Roxana Bujack: The original goal of the work was to automatically optimize color maps. We need them to help application scientists at LANL understand their data.

Our minds have trouble digging meaning out of arrays of digits, but we can quickly spot patterns and trends when those numbers are converted to pictures, with colors representing different values in the data.

Our visualizations help physicists, climate modelers, space weather researchers and many others make sense of vast data streams that might otherwise bury their revelations beneath seemingly endless spreadsheet columns.

Did you achieve what you set out to achieve?

No, we completely lost track of our original goal. Now, we don't have funding anymore.

Are there any other aims to the work that you have yet to achieve?

Yes! So far, we just know that the old model does not work. We want to find out what geometry the space really has. Also, we want to see if similar phenomena occur in other human senses: if a second order Weber-Fechner law exists.

The Weber-Fechner laws relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell.

What implications does this discovery have going forward?

For now: We know that we have to use experiments with large color differences to map out perceptual color space. Once we have a model that might have many more implications, for example, for automatic image and video processing.

How long do you think it might take for that to happen?

Not sure. Maybe 20 years?

Having made this discovery, do you think it's plausible that there are other such errors that have yet to be discovered?

Definitely! This is what science is all about!

But error is maybe too strong a word. As more experimental evidence shows up, science is always on the move and improving. Schroedinger's work was extraordinary and changed the way people thought about color back then, probably more than our work does today. And we are now just waiting for someone to tell us what we did wrong.

Why do you think this error persisted for so long without correction?

If I had to guess, I would say that maybe the color researchers thought about the Riemannian (curved) space somehow as the ‘opposite’ of the Euclidean (straight) space and ignored that it is a pretty regulated construct itself.

Ok, so what kind of geometry might your team use to describe perceptual color space going forward?

We’re investigating this, but if we’re lucky, a Riemannian space with a scaling function could do the trick, but more experiments are needed to see if that works.

A path-connected metric space would be a good model. But of course, you have to allow for some perceptual 'noise' like in the theory of Thurstone.

Louis Leon Thurstone proposed the theory that intelligence is composed of several different factors. The seven primary mental abilities in Thurstone's model were verbal comprehension, word fluency, number facility, spatial visualization, associative memory, perceptual speed and reasoning.

Without the stochastical component, it would violate the most fundamental metric property: the identity of indiscernibles, i.e., that zero is only returned if both inputs are identical. You can present two very close colors to an observer between which he will not see a difference even though they are not 100% identical.

What are you and the team working on now, as a result of these findings?

This project has now ended, so we are mostly wrapping up experiments that look into other regions of color space to see if the phenomenon of diminishing returns exists homogeneously or differs over different regions.

Quickfire questions

What or who inspires you?

I have always been inspired by the search for meaning, for somehow making an impact, or leaving a trace at least. And that led me to science. To me, being able to contribute to the overall knowledge of mankind is the most inspiring and motivating thought.

What gets you out of bed in the morning?

If I don't get my kids to the daycare by 8am, they don't get breakfast.

What makes you smile?

This video of a kitten touching a cactus.

What is your greatest achievement to date?

The paper about color space being non-Riemannian is probably my greatest achievement of all past and future times. I mean seriously, how often do you get the chance to disprove Riemann, Helmholtz, and Schrödinger?

What is your biggest regret?

I wish I could have saved my mom.

What would you say to someone wanting to follow in your footsteps?

Awesome! I have always wanted someone to want to follow in my footsteps.

What advice would you give your younger self?

1. You are pretty!

2. Being pretty gets you nothing relevant!

3. You will love your children more than you can imagine. Just to get you in the ballpark: it absolutely overshadows the love that you have felt for your parents, partners and pets combined. And that makes you very vulnerable.

It would require an extraordinary level of human greatness on the side of your partner to not exploit that.

This story first appeared in our subscriber-only weekly Blueprint newsletter. Receive exclusive interviews and analyses like this, direct to your inbox every Sunday, by subscribing to IE+.