With this post I would like to introduce my new, perceptually balanced rainbow color palette. I used the palette for the first time in How to assess a colourmap, an essay I wrote for 52 Things You Should Know About Geophysics, edited by Matt Hall and Evan Bianco of Agile Geoscience.
In my essay I started with the analysis of the spectrum color palette, the default in some seismic interpretation softwares, using my Lightness L* profile plot and Great Pyramid of Giza test surface (see this post for background on the tests and to download the Matlab code). The profile and the pyramid are shown in the top left image and top right image in Figure 1, from the essay.
In the plot the value of L* varies with the color of each sample in the spectrum, and the line is colored accordingly. This erratic profile highlights several issues with spectrum: firstly, the change in lightness is not monotonic. For example it increases from black (L*=0) to magenta [M] then drops from magenta to blue [B], then increases again and so on. This is troublesome if spectrum is used to map elevation because it will interfere with the correct perception of relief, particularly if shading is added. Additionally, the curve gradient changes many times, indicating a nonuniform perceptual distance between samples. There are also plateaus of nearly flat L*, creating bands of constant color (a small one at the blue, and a large one at the green [G]).
The Great Pyramid has monotonically increasing elevation (in feet – easier to code) so there should be no discontinuities in the surface if the color palette is perceptual. However, clearly using the spectrum we have introduced many artificial discontinuities that are not present in the data. For the bottom row in FIgure 1 I used my new color palette, which has a nice, monotonic, compressive Lightness profile (bottom left). Using this palette the pyramid surface (bottom right) is smoothly colored, without any perceptual artifact.
This is how I created the palette: I started with RGB triplets for magenta, blue, cyan, green, and yellow (no red), which I converted to L*a*b* triplets using Colorspace transformations, a Matlab function available on the Matlab File Exchange. I modified the new L* values by fitting them to an approximately cube law L* function (this is consistent with Stevens’ power law of perception), and adjusted a* and b* values using Lab charts like the one in Figure 2 (from CIELab Color Space – Gernot Hoffmann, Department of Mechanical Engineering, University of Emden) to get 5 colors moving up the L* axis along an imaginary spiral (I actually used tracing paper). Then I interpolated to 256 samples using the same ~cube law, and finally reconverted to RGB .
There was quite a bit of trial and error involved, but I am very happy with the results. In the animations below I compare the spectrum and the new palette, which I call cubeYF, as seen in CIELab color space. I generated these animations with the method described in this post, using the 3D color inspector plugin in ImageJ:
I also added Matlab’s default Jet rainbow – a reminder that defaults may be a necessity, but in many instances not the ideal choice:
OK, the new palette looks promising, insofar as modelling is concerned. But how would it fare using some real data? To answer this question I used a residual gravity map from my unpublished thesis in Geology at the University of Rome. I introduced this map and discussed the geological context and objectives of the geophysical study in a previous post, so please refer to that if you are curious about it. In this post I will go straight to the comparison of the color palettes; if you are unfamiliar with gravity data, try to imagine negative residuals as elevation below sea level, and positive residuals as elevation above seal level – you won’t miss out on anything.
In Figures 3 to 6 I colored the data using the above three color palettes, and grayscale as benchmark. I generated these figures using Matlab code I shared in my post Visualization tips for geoscientists: Matlab, and I presented three of them (grayscale, Spectrum, and cubeYF) at the 2012 convention of the Canadian Society of Exploration Geophysicists in Calgary (the extended abstract, which I co-authored with Steve Lynch of 3rd Science, is available here).
In Figure 3, the benchmark for the following figures, I use grayscale to represent the data, assigning increasing intensity from most negative gravity residuals in black to most positive residuals in white (as labeled next to the colorbar). Then, I used terrain slope to create shading: the higher the slope, the darker the shading that is assigned, which results in a pseudo-3D display that is very effective (please refer to Visualization tips for geoscientists: Surfer, for an explanation of the method, and Visualization tips for geoscientists: Matlab for code).
In Figure 4 I color the pseudo-3D surface with the cubeYF rainbow. Using this color palette instead of grayscale allows viewers to appreciate smaller changes, more quickly assess differences, or conversely identify areas of similar anomaly, while at the same time preserving the peudo-3D effect. Now compare Figure 4 with Figure 5, where we use the spectrum to color the surface: this palette introduces several artefacts (sharp edges and bands of constant hue) which confuse the display and interfere with the perception of pseudo-relief, all but eliminating the effect. For Figure 6 I used Matlab’s default Jet color palette, which is better that the spectrum, and yet the relief effect is somewhat lost (due mainly to a sharp yellow edge and cyan band).
It looks like both spectrum and jet are poor choices when used for color representation of a surface, with the new color palette a far superior alternative. In the CSEG convention paper mentioned above (available here) Steve and I went further by showing that the spectrum not only has these perceptual artifacts and edges, but it is also very confusing for viewers with deficient color vision, a condition that occurs in about 8% of Caucasian males. We did that using computer software  to simulate how viewers with two types of deficient color vision, Deuteranopia and Tritanopia, would see the two colored surfaces, and we compare the results. In other words, we are now able to see the images as they would see them. Please refer to the paper for a full discussion on these simulation.
In here, I show in Figures 7 to 9 the Deuteranope simulations for cubeYF, spectrum, and jet, respectively. In all three simulations the hue discrimination has decreased, but while the spectrum and jet are now even more confusing, the cubeYF has preserved the relief effect.
That’s it for today. In my next post, to be published very shortly, you will get the palette, and a lot more.
A more perceptual color palette for structure maps, CSEG/CSPG 2012 convention, Calgary
How to assess a colourmap, in 52 Things You Should Know About Geophysics
 An alternative to the method I used would be to start directly in CIELab color space, and use a some kind of spiral *L lightness profile programmatically. For example:
- Using 3D helical curves from: http://www.mathworks.com/matlabcentral/fileexchange/25177-3d-curves
- Using Archimedes spiral
- Expanding on code by Steve Eddins at Mathworks (A path through L*a*b* color space) in this article , one could create a spiral cube lightness with something like:
%% this creates best-fit pure power law function % Inspired by wikipedia - http://en.wikipedia.org/wiki/Lightness l2=linspace(1,power(100,0.42),256); L2=(power(l2,1/0.42))'; %% this makes cielab real cube function spiral radius = 50; theta = linspace(0.6*pi, 2*pi, 256).'; a = radius * sin(theta); b = radius * cos(theta); Lab1 = [L2, a, b]; RGB_realcube=colorspace('RGB<-Lab',(Lab1));
 The simulations are created using ImageJ, an open source image manipulation program, and the Vischeck plug-in. I later discovered Dichromacy, anther ImageJ plug-in for these simulations, which has the advantage of being an open source plugin. They can also be performed on the fly (no upload needed) using the online tool Color Oracle.