In my last post I discussed the two main issues with the rainbow color palette from the point of view of human color vision, and concluded one of these issues is insurmountable.
But before I move to presenting alternative color palettes, let me give you one last example of how bad the rainbow is. It was sent to me by Antony Price, a member of the LinkedIn group Worldwide Geophysicists. Antony created a grayscale and a rainbow-colored version – using the same data range and number of intervals – of the satellite altimeter derived free-air gravity map of the world . I am showing the two maps below.
Following the first post in this series, Steve commented:
Matteo, so would I be correct in assuming that the false structures that we see in the rainbow palette are caused by inflection points in the brightness? I always assumed that the lineations we pick out are caused by our flawed color perception but it looks from your examples that they are occurring where brightness changes slope. Interesting.
As I mention in my brief reply to the reader’s comment, I’ve done some reading and more experiments to try to understand better the reasons behind the artifacts in the rainbow, and I am happy to share my conclusions. This is also a perfect lead into the rest of the series.
Human vision vs. the rainbow – issue number 1
I think there are two issues that make us see the rainbow the way we see it; they are connected but more easily examined separately. The first one is that we humans perceive some colors as lighter (for example green) and some as darker (for example blue) at a given light level, which is because of the difference in the fundamental color response of the human eye for red, green, and blue (the curves describing the responses are called discrimination curves).
There is a well written explanation for the phenomenon on this website (and you can find here color matching functions similar to those used there to create the diagram). The difference in the sensitivity of our cones explains why in the ROYGBIV color palette (from the second post in this series) the violet and blue appear to us darker than red, and red in turn darker than green and yellow. The principle … applies also to mixes involving the various cones (colours), hence the natural brightness of yellow which stimulates the two most reactive sets of cones in the eye. We could call this a flaw in color perception (I am not certain of what the evolutionary advantage might be), which is responsible for the erratic appearance of the lightness (L*) plot for the palette shown below (If you would like to know more about this plot and get the code to make it to evaluate color palettes, please read the first post in this series).
So to answer Steve, I think yes, the lineations we pick in the rainbow are caused by inflection points in the lightness profile, but those in turn are caused by the differences in color responses of our cones. But there’s more!
If you are interested in the topic of color palettes for scientific data, and the rainbow in particular, I would say you ought to read this 2007 IEEE visualization paper by Borland and Taylor: Rainbow Color Map (Still) Considered Harmful. It clearly and elegantly illustrates why the rainbow palette should be avoided when displaying scientific data. I like Figure 1 in the paper in particular. The illustration shows how it is easy to order perceptually a set of 4 paint chips of different gray intensity, but not at all easy to order 4 paint chips colored red, green, yellow, and blue. The author’s argument is that the rainbow colors are certainly ordered, from shorter to longer wavelengths, but they are not perceptually ordered. In this post I wanted to extend the chips example to all 7 colors in the rainbow and try to demonstrate the point in a quantitative way.
Here below is a 256-sample rainbow palette I created interpolating between the RGB values for the seven colors of the rainbow red, orange, yellow, green, blue, indigo, and violet (ROY G BIV):
On this palette I see a number of perceptual artifacts, the most notable ones being a sharp edge at the yellow and a flat zone at the green. The existence of these edges I tried to explain quantitatively in the first post of this series.
Now, to go back to the experiment, from the original RGB values for the non interpolated colors I created the 7 color chips below . Question: can you order them based on their perceived intensity?
I think if you have full color vision (more on the topic of rainbow and impaired color vision in the next section of this post) eventually you will be able to order them as I did.If not, try now below. In this new image I converted the color chips to gray chips using the values obtained in Matlab with this formula:
Give it a try, then hover with your mouse over the image to read the intensity values.
Not surprisingly, the values are not in any particular order. This reinforces the notion that although the rainbow colors are ordered by increasing wavelength (or decreasing in this case) , they are not perceptually ordered. (See this comment to my previous post). Below I rearranged the gray chips by increasing intensity.
And now I reconverted from gray to RGB colors and adjusted the distance between each pair of chips so that it is proportional to the intensity difference between the chips in the pair (I actually had to artificially change the value for green and orange so they would not overlap). That was an epiphany for me. And the name is funny too, BIV R GOY, or YOG R VIB…
I said that it was an epiphany because I realize the implications of trying to create a palette by interpolating through these colors with those distances. So I did it, and I am showing it below in the top color palette. We jumped out of the frying pan, into the fire! We went from perceptual artifacts that are inherent to the rainbow (reproduced in reverse order from blue to red to facilitate comparison as the bottom palette) to interpolation artifacts in the intensity ordered rainbow. Hopeless!
As if what I have shown in the previous section wasn’t scary enough, I took 7 squares and colored them using the same RGB values for Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Then I used the Dichromacy plug-in in ImageJ to simulate how these colors would be seen by a viewer with Deuteranopia (the more common form of color vision deficiency). I then shuffled the squares in random order on a square canvas, and numbered them 1-7 in clockwise order.
Puzzle: can you pair the squares numbered 1 through 7 with the colors R though V? I will give away the obvious one, which is the yellow:
Cannot do it? For the solution just hover over the image with your mouse. If you like the animation and would like to use it on your blog, twitter, Facebook, get the GIF file version here. Please be kind enough to link it back to this post.
When I tried myself I could not solve the puzzle, and that finally convinced me that trying to fix the rainbow was a hopeless cause. Even if we could, it would still confuse a good number of people (about 8% of male have one form or the other of color vision deficiency). From the next post on I will show what I got when I tried to create a better, more perceptual rainbow from scratch.