In Evaluate and compare colormaps, I have shown how to extract and display the lightness profile of a colormap using Python. I do this routinely with colormaps, but I realize it takes an effort, and not all users may feel comfortable using code to test whether a colormap is perceptual or not.
This got me thinking that there is perhaps a need for a user-friendly, interactive tool to help identify colormap artifacts, and wondering how it would look like.
In a previous post, Comparing color palettes, I plotted the elevation for the South American continent from the Global Land One-km Base Elevation Project using four different color palettes. In Figure 1 below I plot again 3 of those: rainbow, linear lightness rainbow, and grayscale, respectively, from left to right. In maps like these some artifacts are very evident. For example there’s a classic film negative effect in the map on the left, where the Guiana Highlands and the Brazilian Highlands, both in blue, seem to stand lower than the Amazon basin, in violet. This is due to the much lower lightness (or alternatively intensity) of the colour blue compared to the violet.
However, other artifacts are more subtle, like the inversion of the highest peaks in the Andes, which are coloured in red, relative to their surroundings, in particular the Altipiano, an endorheic basin that includes Lake Titicaca.
My idea for this tool is simple, and consists of two windows. The first is a basemap window which can display either a demo dataset or user data loaded from an ASCII grid file. In this window the user would interactively select a profile by building a polyline with point-and-click, like the one in Figure 2 in white.
The second window would show the elevation profile with the colour fill assigned based on the colormap, like in Figure 3 at the bottom (with colormap to the right), and with a profile of the corresponding colour intensities (on a scale 1-255) at the top.
In this view it is immediately evident that, for example, the two highest peaks near the center, coloured in red, are relative intensity lows. Another anomaly is the absolute intensity low on the right side, corresponding to the colour blue, where the elevation profile varies smoothly.
I created this concept prototype using a combination of Matlab, Python, and Surfer. I welcome suggestions for possible additional features, and would like to hear form folks interested in collaboration on a web app (ideally in Python).
For getting maps and art together, I thought it could not be topped. Then today, I stumbled into NASA’s Perpetual Ocean animation: beautiful!
From the original Source: This is an animation of ocean surface currents from June 2005 to December 2007 from NASA satellites. Watch how bigger currents like the Gulf Stream in the Atlantic Ocean and the Kuroshio in the Pacific carry warm waters across thousands of miles at speeds greater than four miles per hour (six kilometers per hour); how coastal currents like the Agulhas in the Southern Hemisphere move equatorial waters toward Earth’s poles; and how thousands of other ocean currents are confined to particular regions and form slow-moving, circular pools called eddies. Credit: NASA/SVS
More media options, including a 20 minute version at 30 fps can be found here
Perceptual rainbow palette – Matlab function and ASCII files
In my last post I introduced cubeYF, my custom-made perceptual lightness rainbow palette. As promised there, I am sharing the palette with today’s post. For the Matlab users, cube YF, along with the other palettes I introduced in the series, is part of the Matlab File Exchange submission Perceptually improved colormaps.
For the non-Matlab users, please download the cubeYF here (RGB, 256 samples). You may also be interested in cube1, which has a slightly superior visual hue contrast, due to the addition of a red-like color at the high lightness end but at the cost of a modest deviation from 100% perceptual. I used cube 1 in my Visualization tips for geoscientists series.
Perceptual rainbow palette – preformatted in various software formats
The palettes are also formatted for a number of platforms and software products: Geosoft, Hampson-Russell, SMT Kingdom, Landmark Decision Space Geoscience, Madagascar, OpendTect, Python/Matplotlib, Schlumberger Petrel, Seisware, Golden Software Surfer, Paradigm Voxelgeo. Please download them from my Color Palettes page and follow instructions therein.
Comparison of South America maps using, from left to right: ROYGBIV (from this post) , classic rainbow, cubeYF, and grayscale
Again, there is little doubt in my mind that cubeYF does a superior job compared to the other two rainbow palettes as it is free of artefacts  and more similar to grayscale (with the additional benefit of color).
The ROYGBIV and cubeYF map have been included in Marek Kultys’ excellent tutorial Visual Alpha-Beta-Gamma: Rudiments of Visual Design for Data Explorers, recently published on Parsons Journal for information mapping, Volume V, Issue 1.
An online palette testing tool
Both cubeYF and cube1 feature in the colormap evaluation tool by the Data Analysis and Assessment Center at the Engineer Research and Development Center. If you want to quickly evaluate a number of palettes, this is the right tool. The tool has a collection of many palettes, organized by categories, which can be used on 5 different test image, and examined in terms of RGB components and human perception. Below here is an example using cube YF.
Then I wondered: what if I used this to tell me something about a color palette’s mood? The circular histogram of colors reminded me of the Harmonic templates  on the hue wheel from this paper And so I created fat colorbars using the three palettes I used in the last post, saved them as images, and run the monitor with them. Here below are the results for Matlab jet, Industry Spectrum, and cubeYF. Looking at these palettes in terms of harmony I would say that jet is not very harmonic (too large a portion of the hue circle; the T template, which is the largest, spans 180 degrees), and that the spectrum is terrible.
CubeYF is also exceeding a bit 180 degrees, but looks very close to a T template rotated by 180 degrees (rotations are allowed). So perhaps I could trim it a bit? But to me it looks a lot nicer and gives me a vibe of really good mood, and reminds me of one of those beautiful central american headdresses, like Moctezuma’s crown.
 Looking at the intensity of the colorbars may help in the assessment: the third and fourth colorbars are very similar and both look perceptually linear, whereas the first and second do not.
 Quoted from Richard’s blog post: “… in the middle is a circular histogram of the colours (spectral shades) in the image, and gives an idea of how much of each colour there is. Up the left is a histogram of image brightness (lightness of colour), and up the right is a histogram of colour saturation (vibrancy)”.
 Quoted from the paper’s abstract: “Harmonic colors are sets of colors that are aesthetically pleasing in terms of human visual perception. If you are interested in this idea there is a set of slides and a video on the author’s website
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 by 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:
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).
Figure 3 – Grayscale benchmark
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).
Figure 4 – cube YF rainbow
Figure 5 – Industry spectrum
Figure 6 – Matlab Jet
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.
Deuteranope Simulation of cube YF
Deuteranope Simulation of Industry spectrum
Deuteranope Simulation of Matlab Jet
That’s it for today. In my next post, to be published very shortly, you will get the palette, and a lot more.
 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
%% 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.
Based on visual inspection I argued that linear L* colored map compares more favourably with the grayscale – my perceptual benchmark – on the right – than the first and second, which use my ROYGBIV rainbow palette (from this post) and a classic rainbow palette, respectively. I noted that looking at the intensity of the colorbars may help in the assessment: the third and fourth colorbars are very similar and both look perceptually linear, whereas the first and second do not.
So it seems that among the three color palettes the third ones is the best, but…..
… prove it!
All the above is fine and reasonable, and yet it is still very much subjective. How can I prove it, convince myself this is indeed the case?
Well, of course one way is to use my L* profile and Great Pyramid tests with Matlab code from the first post of this series. Look at the two figures below: comparison of the lightness L* plots clearly shows the linear L* palette is far more perceptual than the ROYGBIV.
One disadvantage of this method is that you have to use Matlab, which is neither free nor cheap, and have to be comfortable with some code and ASCII file manipulation.
Just recently I had an idea for an open source alternative with ImageJ and the 3D color inspector plugin. The only preparatory step required is to save a palette colorbar as a raster image. Then open the image in ImageJ, run the plugin and display the colorbar in Lab space in a 3D view. There are many options to change the scale of the plot, the perspective, and how the colors are displayed (e.g. frequency weighted, median cut, etcetera). The view can be rotated manually, and also automatically. Below I am showing the rotating animations for the same two palettes.
The whole process, including the recording of the animations using the Quicktime screencast feature, took me less than 10 minutes, and it leaves no doubt as to which one is the best color palette. Let me know what you think.
A few observations: in 3D the ROYGBIV palette is even more strikingly and obviously non-monotonic. The lightness gradient varies in magnitude, resulting in non-uniform contrast. Compare for example the portion between blue and green to that between green and yellow: these have approximately the same number of samples but very different change in lightness value between the extremes. The gradient sign also changes, producing perceptual inversions, for example with the yellow to red section following the blue to yellow. These inversions may result in perceived elevation inversions, for example, if using this palette to display elevation data. On the other hand, the linear L* palette nicely spirals upwards with L* changing monotonically from 0 to 100.
Today I’d like to share a color palette that I really like:
It is one of the palettes introduced in a paper by Kindlmann et al. . The authors created their palettes with a technique they call luminance controlled interpolation. They explain it in this online presentation. However they used different palettes (their isoluminant rainbow, and their heated body) so if you find it confusing I recommend you look at the paper first. Indeed, this is a good read if you are interested in colormap generation techniques; it is one of the papers that encouraged me to develop the methodology for my cube law rainbow, which I will introduce in an upcoming post.
This is how I understand their method to create the palette: they mapped six pure-hue rainbow colors (magenta, blue, cyan, green, yellow, and red) in HSL space, and adjusted the Luminance by changing the HSL Lightness value to ‘match’ that of six control points evenly spaced along the gray scale palette. After that, they interpolated linearly along the L axis between 0 and 1 using the equation presented in the paper.
CIE Lab linear L* rainbow palette
For this post I will try to create a similar palette. In fact, initially I was thinking of just replicating it, so I imported the palette as a screen capture image into Matlab, reduced it to a 256×3 RGB colormap matrix, and converted RGB values to Lab to check its linearity in lightness. Below I am showing the lightness profile, colored by value of L*, and the Great Pyramid of Giza – my usual test surface – also colored by L* (notice I changed the X axis of both L* plots from sample number to Pyramid elevation to facilitate comparison of the two figures).
Clearly, although the original palette was constructed to be perceptually linear, it is not linear following my import. Notice in particular the notch in the profile in the blue area, at approximately 100 m elevation. This artifact is also visible as a flat-looking blue band in the pyramid.
I have to confess I am not too sure why the palette has this peculiar lightness profile. I suspect this may be because their palette is by construction device dependent (see the paper) so that when I took the screen capture on my monitor I introduced the artifacts.
The only way to know for sure would be to use their software to create the palette, or alternatively write the equation from the paper into Matlab code and create a palette calibrated on my monitor, then compare it to the screen captured one. Perhaps one day I will find the time to do it but having developed my own method to create a perceptual palette my interest in this one became just practical: I wanted to get on with it and use it.
Fixing and testing the palette
Regardless of what the cause might be for this nonlinear L* profile, I decide to fix it and I did it by simply replacing the original profile with a new one, linearly changing between 0.0 and 1.0. Below I am showing the L* plot for this adjusted palette, and the Great Pyramid of Giza, both again colored by value of L*.
The pyramid with the adjusted palette seems better: the blue band is gone, and it looks great. I am ready to try it on a more complex surface. For that I have chosen the digital elevation data for South America available online through the Global Land One-km Base Elevation Project at the National Geophysical Data Center. To load and display the data in Matlab I used the first code snippet in Steve Eddin’s post on the US continental divide (modified for South America data tiles). Below is the data mapped using the adjusted palette. I really like the result: it’s smooth and it looks right.
But how do I know, really? I mean, once I move away from my perfectly flat pyramid surface, how do I know what to expect, or not expect? In other words, how would I know if an edge I see on the map above is an artifact, or worse, that the palette is not obscuring real edges?
In some cases the answer is simple. Let’s take a look at the four versions of the map in my last figure. The first on the left was generated using th ROYGBIV palette I described in this post. It would be obvious to me, even if I never looked at the L* profile, that the blue areas are darker than the purple areas, giving the map a sort of inverted image look.
But how about the second map from the left? For this I used the default rainbow from a popular mapping program. This does not look too bad at first sight. Yes, the yellow is perceived as a bright, sharp edge, and we now know why that is, but other than that it would be hard to tell if there are artifacts. After a second look the whole area away from the Andes is a bit too uniform.
A good way to assess these maps is to use grayscale, which we know is a good perceptual option, as a benchmark. This is the last map on the right. The third map of South America was coloured using my adjusted linear L* palette. This maps looks more similar to our grayscale benchmark. Comparison of the colorbars will also help: the third and fourth are very similar and both look perceptually linear, whereas the third does show flatness in the blue and green areas.
Let me know what you think of these examples. And as usual, you are welcome to use the palette in your work. You can download it here.
With my following post, Comparing color palettes, I introduced my new method to compare palettes with ImageJ and the 3D color inspector plugin. Here below are the recorded 3D animations of the initial and adjusted palettes respectively. In 3D it is easier to see there is an area of flat L* between the dark purple and dark blue in the initial color palette. The adjusted color palette instead monotonically spirals upwards.
I find the Color Use Guidelines by Cynthia Brewer (of Color Brewer fame) very well done and extremely useful. Below is a screen captures of the main page. To see an explanation of and example for each color scheme visit the interactive guidelines.
The perfect lead into my series on perceptual color palettes. Great post!
The original article on the Guardian is here. And here is the conversation that lead to improved map, as put together on Storify.
I thought it’d be interesting to run a simulation of what the map would actually look lie to viewers with the 3 types of color deficient vision. Below are my results for the first map. It is obvious from this simulation that while the map is OK for Tritanope viewers, the green and red areas are very confusing for Protanope and Deuteranope viewers.