MyCarta

A blog about Technology, Geoscience, Visualization, Data Science

Busting bad colormaps with Python and Panel

Posted on September 17, 2020 by matteomycarta

I have not done much work with, or written here on the blog about colormaps and perception in quite some time.

Last spring, however, I decided to build a web-based app to show the effects of using a bad colormaps. This stemmed from two needs: first, to further my understanding of Panel, after working through the awesome tutorial by James Bednar, Panel: Dashboards (at PyData Austin 2019); and second, to enable people to explore interactively the effects of bad colormaps on their perception, and consequently the ability to on interpret faults on a 3D seismic horizon.

I introduced the app at the Transform 2020 virtual subsurface conference, organized by Software Underground last June. Please watch the recording of my lightning talk as it explains in detail the machinery behind it.

I am writing this post in part to discuss some changes to the app. Here’s how it looks right now:

The most notable change is the switch from one drop-down selector to two-drop-down selectors, in order to support both the Matplotlib collection and the Colorcet collection of colormaps. Additionally, the app has since been featured in the resource list on the Awesome Panel site, an achievement I am really proud of.

You can try the app yourself by either running the notebook interactively with Binder, by clicking on the button below:

or, by copying and pasting this address into your browser:

https://mybinder.org/v2/gh/mycarta/Colormap-distorsions-Panel-app/master?urlpath=%2Fpanel%2FDemonstrate_colormap_distortions_interactive_Panel

Let’s look at a couple of examples of insights I gained from using the app. For those that jumped straight to this example, the top row shows:

the horizon, plotted using the benchmark grayscale colormap, on the left
the horizon intensity, derived using skimage.color.rgb2gray, in the middle
the Sobel edges detected on the intensity, on the right

and the bottom row, shows:

the horizon, plotted using the Matplotlib gist_rainbow colormap, on the left
the intensity of the colormapped, in the middle. This is possible thanks to a function that makes a figure (but does not display it), plots the horizon with the specified colormap, then saves plot in the canvas to an RGB numpy array
the Sobel edges detected on the colormapped intensity, on the right

I think the effects of this colormaps are already apparent when comparing the bottom left plot to the top left plot. However, simulating perception can be quite revealing for those that have not considered these effects before. The intensity in the bottom middle plot is very washed out in the areas corresponding to green color in the bottom left, and as a result, many of the faults are not visible any more, or only with much difficulty, which is demonstrated by the Sobel edges in the bottom right.

And if you are not quite convinced yet, I have created these hill-shaded maps, using Matt Hall”s delightful function from this notebook (and check his blog post):

Below is another example, using the Colocrcet cet_rainbow which is is one of Peter Kovesi’s perceptually uniform colormaps. I use many of Peter’s colormaps, but never used this one, because I use my own perceptual rainbow, which does not have a fully saturated yellow, or a fully saturated red. I think the app demonstrate, that even though they are more subtle , this rainbow still is introducing some artifacts. The yellow colour creates narrow flat bands, visible in the intensity and Sobel plots, and indicated by yellow arrows; the red colour is also bad as usual, causing an artificial decrease in intensity(magenta arrows).

How to fix rainbows and other bad colormaps using Python

Posted on September 26, 2018 by matteomycarta

Yep, colormaps again!

In my 2014 tutorial on The Leading Edge I showed how to Evaluate and compare colormaps (Jupyter notebook here). The article followed an extended series of posts (The rainbow is dead…long live the rainbow!) and then some more articles on rainbow-like colormap artifacts (for example here and here).

Last year, in a post titled Unweaving the rainbow, Matt Hall described our joint attempt to make a Python tool for recovering digital data from scientific images (and seismic sections in particular), without any prior knowledge of the colormap. Please check our GitHub repository for the code and slides, and watch Matt’s talk (very insightful and very entertaining) from the 2017 Calgary Geoconvention below:

One way to use the app is to get an image with unknown, possibly awful colormap, get the data, and re-plot it with a good one.

Matt followed up on colormaps with a more recent post titled No more rainbows! where he relentlessly demonstrates the superiority of perceptual colormaps for subsurface data. Check his wonderful Jupyter notebook.

So it might come as a surprise to some, but this post is a lifesaver for those that really do like rainbow-like colormaps. I discuss a Python method to equalize colormaps so as to render them perceptual. The method is based in part on ideas from Peter Kovesi’s must-read paper – Good Colour Maps: How to Design Them – and the Matlab function equalisecolormap, and in part on ideas from some old experiments of mine, described here, and a Matlab prototype code (more details in the notebook for this post).

Let’s get started. Below is a time structure map for a horizon in the Penobscot 3D survey (offshore Nova Scotia, licensed CC-BY-SA by dGB Earth Sciences and The Government of Nova Scotia). Can you clearly identify the discontinuities in the southern portion of the map? No?

OK, let me help you. Below I am showing the map resulting from running a Sobel filter on the horizon.

This is much better, right? But the truth is that the discontinuities are right there in the original data; some, however, are very hard to see because of the colormap used (nipy spectral, one of the many Matplotlib cmaps), which introduces perceptual artifacts, most notably in the green-to-cyan portion.

In the figure below, in the first panel (from the top) I show a plot of the colormap’s Lightness value (obtained converting a 256-sample nipy spectral colormap from RGB to Lab) for each sample; the line is coloured by the original RGB colour. This erratic Lightness profile highlights the issue with this colormap: the curve gradient changes magnitude several times, indicating a nonuniform perceptual distance between samples.

In the second panel, I show a plot of the cumulative sample-to-sample Lightness contrast differences, again coloured by the original RGB colours in the colormap. This is the best plot to look at because flat spots in the cumulative curve correspond to perceptual flat spots in the map, which is where the discontinuities become hard to see. Notice how the green-to-cyan portion of this curve is virtually horizontal!

That’s it, it is simply a matter of very low, artificially induced perceptual contrast.

Solutions to this problem: the obvious one is to Other NOT use this type of colormaps (you can learn much about which are good perceptually, and which are not, in here); a possible alternative is to fix them. This can be done by re-sampling the cumulative curve so as to give it constant slope (or constant perceptual contrast). The irregularly spaced dots at the bottom (in the same second panel) show the re-sampling locations, which are much farther apart in the perceptually flat areas and much closer in the more dipping areas.

The third panel shows the resulting constant (and regularly sampled) cumulative Lightness contrast differences, and the forth and last the final Lightness profile which is now composed of segments with equal Lightness gradient (in absolute value).

Here is the structure map for the Penobscot horizon using the nipy spectum before and after equalization on top of each other, to facilitate comparison. I think this method works rather well, and it will allow continued use of their favourite rainbow and rainbow-like colormaps by hard core aficionados.

If you want the code to try the equalization, get the noteboook on GitHub.

Logarithmic spiral, nautilus, and rainbow

Posted on November 28, 2014 by matteomycarta

The other day I stumbled into an interesting article on The Guardian online: The medieval bishop who helped to unweave the rainbow. In the article I learned for the first time of Robert Grosseteste, a 13th century British scholar (with an interesting Italian last name: Grosse teste = big heads) who was also the Bishop of Lincoln.

The Bishops’ interests and investigations covered diverse topics, making him a pre-renaissance polymath; however, it is his 1225 treatise on colour, the De Colore, that is receiving much attention.

In a recent commentary on Nature Physics (All the colours of the rainbow), and reference therein (A three-dimensional color space from the 13th century), Smithson et al. (who also recently published a new critical edition/translation of the treatise with analysis and critical commentaries) analyze the 3D colorspace devised by Grosseteste, who claimed it allows the generation of all possible colours and to describe the variations of colours among different rainbows.

As we learn from Smithson et al., Grosseteste’s colorpsace had three dimensions, quantified by physical properties of the incident light and the medium: these are the scattering angle (which produces variation of hue within a rainbow), the purity of the scattering medium (which produces variation between different rainbows and is linked to the size of the water droplets in the rainbow), and the altitude of the sun (which produces variation in the light incident on a rainbow). The authors were able to model this colorspace and also to show that the locus of rainbow colours generated in that colorspace forms a spiral surface (a family of spiral curves, each form a specific rainbow) in the perceptual CIELab colorspace.

I found this not only fascinating – a three-dimensional, perceptual colorspace from the 13th century!! – but also a source of renewed interest in creating the perfect perceptual colormaps by spiralling through CIELab.

My first attempt of colormap spiralling in CIELab, CubicYF, came to life by selecting hand-picked colours on CIELab colour charts at fixed lightness values (found in this document by Gernot Hoffmann). The process was described in this post, and you can see an animation of the spiral curve in CIELab space (created with the 3D color inspector plugin in ImageJ) in the video below:

Some time later, after reading this post by Rob Simmon (in particular the section on the NASA Ames Color Tool), and after an email exchange with Rob, I started tinkering with the idea of creating perceptual rainbow colormaps in CIELab programmatically, by using a helix curve or an Archimedean spiral, but reading Smithson et al. got me to try the logarithmic spiral.

So I started my experiments with a warm-up and tried to replicate a Nautilus using a logarithmic spiral with a growth ratio equal to 0.1759. You may have read that the rate at which a Nautilus shell grows can be described by the golden ratio phi, but in fact the golden spiral constructed from a golden rectangle is not a Nautilus Spiral (as an aside, as I was playing with the code I recalled reading some time ago Golden spiral, a nice blog post (with lots of code) by Cleve Moler, creator of the first version of Matlab, who simulated a golden spiral using a continuously expanding sequence of golden rectangles and inscribed quarter circles).

My nautilus-like spiral, plotted in Figure 1, has a growth ratio of 0.1759 instead of the golden ratio of 1.618.

Figure 1: nautilus-like spiral with growth ratio = 0.1759

And here’s the colormap (I called it logspiral) I came up with after a couple of hours of hacking: as hue cycles from 360 to 90 degrees, chroma spirals outwardly (I used a logarithmic spiral with polar equation c1*exp(c2*h) with a growth ratio c2 of 0.3 and a constant c1 of 20), and lightness increases linearly from 30 to 90.

Figure 2 shows the trajectory in the 2D CIELab a-b plane; the colours shown are the final RGB colours. In Figure 3 the trajectory is shown in 3D CIELab space. The coloured lightness profiles were made using the Colormapline submission from the Matlab File Exchange.

Figure 2: logspiral colormap trajectory in CIELab a-b plane

Figure 3: logspiral colormap in CIELab 3D space

N.B. In creating logspiral, I was inspired by Figure 2 in the Nature Physics paper, but there are important differences in terms of colorspace, lightness profile and perception: I am not certain their polar coordinates are equivalent to Lightness, Chroma, and Hue, although they could; and, more importantly, the three-dimensional spirals based on Grosseteste’s colorpsace go from low lightness at low scattering angles to much higher values at mid scattering angles, and then drop again at high scattering angle (remember that these spirals describe real world rainbows), whereas lightness in logspiral lightness is strictly monotonically increasing.

In my next post I will share the Matlab code to generate a full set of logspiral colormaps sweeping the hue circle from different staring colours (and end colors) and also the slower-growing logarithmic spirals to make a set of monochromatic colormaps (similar to those in Figure 2 in the Nature Physics paper).

Spectral lightness rainbow colormap

Posted on November 18, 2014 by matteomycarta

Spectral lightness rainbow

Quick post to share my replica of Ethan Montag ‘s Spectral lightness colormap from this paper. My version has a linear Lightness profile (Figure 1) that increases monotonically from 0 (black) to 100 (white) while Hue cycles from 180 to 360 degrees and then wraps around and continues from 0 to 270.

You can download the colormap files (comma separated in MS Word .doc format) with RGB values in 0-1 range and 0-255 range.

Figure 1

Figure 2

Matlab code

To run this code you will need Colorspace, a free function from Matlab File Exchange, for the color space transformations.

%% generate Chroma, Lightness, Hue components
h2=linspace(0,270,60*2.56);
h1=linspace(180,360,103);
h=horzcat(h1,h2);
c=ones(1,256)*25;
l=linspace(0,100,256);

%% merge together
lch = vertcat(l,c,h)';

%% convert to RGB
rgb = colorspace('LCH->rgb',lch);

%% Plot color-coded lightness profile
figure;
h=colormapline(1:1:256,lch(:,1),[],rgb);
set(h,'linewidth',2.8);
title('Montag Spectral L* lightness plot ','Color','k','FontSize',12,'FontWeight','demi');

%%  Pyramid test data
PY=zeros(241,241);
for i = 1:241
    temp=(0:1:i-1);
      PY(i,1:i)=temp(:);
end
test=PY.';
test=test-1;
test(test==-1)=0;
test1=test([2:1:end,1],:);
PY1=PY+test1;
PY2=fliplr(PY1);
PY3= flipud(PY1);
PY4=fliplr(PY3);
GIZA=[PY1,PY2;PY3,PY4].*2;
x=linspace(1,756,size(GIZA,1));
y=x;
[X,Y]=meshgrid(x,y);
clear i test test1 PY PY1 PY2 PY3 PY4 temp;

%% display Pyramid surface
fig1=figure;
surf(X,Y,GIZA,GIZA,'FaceColor','interp','EdgeColor','none');
view(-35,70);
colormap(rgb);
axis off;
grid off;
colorbar;
% set(fig1,'Position',[720 400 950 708]);
% set(fig1,'OuterPosition',[716 396 958 790]);
title('Montag Spectral L*','Color','k','FontSize',12,'FontWeight','demi');

Aknowledgements

The coloured lightness profiles were made using the Colormapline submission from the Matlab File Exchange.

New rainbow colormap: sawthoot-shaped lightness profile

Posted on November 13, 2014 by matteomycarta

Why another rainbow

In the comment section of my last post Steve Eddins from Mathworks reported that some Matlab users prefer Jet to Parula, the new default perceptual colormap in Matlab, because within certain ranges Jet affords a greater contrast, intended as the rate of change in lightness.

My counter-argument to that is that yes, some data may benefit from being displayed using Jet (in terms of contrast, and hence the power to resolve smaller anomalies) because of those areas of very steep rate of change of lightness, like the blue to cyan and yellow to red portions (see Figure 1). But the price one has to pay is that there is an area of very low gradient (a greenish band between cyan and yellow) where there’s nearly no contrast, which would obfuscate subtle anomalies in the data. On top of that there’s no control of where each of those areas are located, so a lot of effort has to go into trying to fit those regions of artificially high contrast to the portion of data of interest.

Figure 1

Because of their high lightness, the yellow and cyan artificial edges also cause problems. In his latest blog post Steve uses a test pattern do demonstrate how they make the interpretation of trivial structures more difficult. He also explains why they occurr in some locations and not others in the first place. I wonder if the resulting regions of high lightness juxtaposed to regions of low lightness could be chromatic Mach bands.

Additionally, as Steve points out, the low-contrast juxtaposition of dark red and dark blue bands creates the visual illusion of depth (Chromostereopsis) in other positions of the test pattern, creating further confusion.

But I have some good news for the hardcore fans of Jet, and rainbow colormaps in general. I created a rainbow with a sawtooth-shaped lightness profile made up of 5 ramps, each with the same rate of change in lightness and total lightness change of 60, and alternatively negative and positive signs. This is shown in Figure 2, and replaces the lightness profile of a basic 6-color rainbow (magenta-blue-cyan-green-yellow-red) shown in Figure 3.

Figure 2

Figure 3

With this rainbow users have the ability to apply greater contrast to their data to boost small anomalies, but in a more controlled way. The colormap is available with my File Exchange function, Perceptually improved colormaps. Below is the Matlab code I used to generate the new rainbow.

Matlab code

To run this code you will need Colorspace, a free function from Matlab File Exchange, for the color space transformations.

%% basic 6-colour rainbow
% create RGB components
m = [1, 0, 1]; % magenta
b = [0, 0, 1]; % blue
c = [0, 1, 1]; % cyan
g = [0, 1, 0]; % green
y = [1, 1, 0]; % yellow
r = [1, 0, 0]; % red
% concatenate components
rgb = vertcat(m,b,c,g,y,r);
% interpolate to 256 colours
rainbow=interp1(linspace(1, 256, 6),rgb,[1:1:256]);

%% calculate Lab components
% convert from RGB to Lab colour space
% requires this function: Colorspace transforamtions
% www.mathworks.com/matlabcentral/fileexchange/28790-colorspace-transformations
lab = colorspace('RGB->Lab',rainbow);

%% replace random lightness profile with sawtooth-shaped profile
% contrast (magnitude of lightness change) between
% each pair of adjeacent colors set to 60
L1 = [90, 30, 90, 30, 90, 30];
% interpolate to 256 lightness values
L1int = interp1(linspace(1, 256, 6),L1,[1:1:256])';
% replace
lab1 = horzcat(L1int,lab(:,2),lab(:,3));

%% new rainbow
% convert back from Lab to RGB colour space
swtth = colorspace('RGB<-Lab',lab1);

Test results

Figures 4, 5, and 6 show the three colormaps used with my Pyramid test surface (notice in Figure 5 that the green band artifact with this rainbow is even more pronounced than with jet). I welcome feedback.

Figure 4

Figure 5

Figure 6

Aknowledgements

The coloured lightness profiles were made using the Colormapline submission from the Matlab File Exchange.

What your brain does with colours when you are not “looking” – part 2

Posted on November 3, 2014 by matteomycarta

In What your brain does with colours when you are not “looking”, part 1, I displayed some audio spectrogram data (courtesy of Giuliano Bernardi at the University of Leuven) using 5 different colormaps to render the amplitude values: Jet (until recently Matlab’s standard colormap), grayscale, linear lightness rainbow, modified heated body, and cube lightness rainbow. I then asked readers to cast a vote for what they thought was the best colormap to visualize this dataset.

I was curious to see how all these colormaps fared, but my expectation was that Jet would sink to the bottom. I was really surprised to see it came on top, one vote ahead of the linear lightness rainbow (21 and 20 votes out of 62, respectively). The modified heated body followed with 11 votes.

My surprise comes from the fact that Jet carries perceptual artifacts within the progression of colours (see for example this post). One way to demonstrate these artifacts is to convert the 2D map into a 3D surface where again we use Jet to colour amplitude values, but we use the intensities from the 2D map for the elevation. This can be done for example using the Interactive 3D Surface Plot plugin for ImageJ (as in my previous post Lending you a hand with image processing – introduction to ImageJ). The resulting surface is shown in Figure 1. This is almost exactly what your brain would do when you look at the 2D map colored with Jet in the previous post.

Figure 1

In Figure 2 the same data is now displayed as a surface where amplitude values were used for the elevation, with a very light sun shading to help a bit with the perception of relief, but no colormap at all. to When comparing Figure 1 with Figure 2 one of the artifacts is immediately recognized: the highest values in Figure 2, which honours the data, become a relative low in Figure 1. This is because red has lower intensity than yellow and therefore data colored in red in 2D are plotted at a lower elevation than data colored in yellow, even though the amplitudes of the latter were lowest.

Figure 2

For these reasons, I did not expect Jet to be the top pick. On the other hand, I think Jet is perhaps favoured because with consistent use, our brain, learns in part to accommodate for these non-perceptual artifacts in 2D maps, and because it has at least two regions of higher contrast (higher magnitude gradient) than other colormaps. Unfortunately, as I wrote in a recently published tutorial, these regions are randomly placed in the colormap, and the gradients are variable, so we gain on contrast but lose on faithfulness in representing the data structure.

Matt Hall wrote a great comment following the previous post, really making an argument for switching between multiple colormaps in the interpretation stage to explore and highlight features in both the signal and the noise in the data, and that perhaps no single colormap is best overall. I agree 100% on almost everything Matt said, except perhaps on the best overall: looking at the 2D maps, at least with this dataset, I feel the heated body could be the best overall colormap, even if marginally. In Figure 3, Figure 4, Figure 5, and Figure 6 I show the 3D displays obtained by converting the 2D grayscale, linear lightness rainbow, modified heated body, and cube llightness rainbow, respectively. Looking at the 3D displays altogether gives me a confirmation of that feeling.

What do you think?

Figure 3

Figure 4

Figure 5

Figure 6

Geophysical tutorial – How to evaluate and compare colormaps in Python

Posted on November 3, 2014 by matteomycarta

These below are two copies of a seismic horizon from the open source Penobscot 3D seismic survey coloured using two different colormaps (data from Hall, 2014).

Figure 1

Do you think either of them is ‘better’? If yes, can you explain why? If you are unsure and you want to learn how to answer such questions using perceptual principles and open source Python code, you can read my tutorial Evaluate and compare colormaps (Niccoli, 2014), one of the awesome Geophysical Tutorials from The Leading Edge. In the process you will learn many things, including how to calculate an RGB colormap’s intensity using a simple formula:

import numpy as np
ntnst = 0.2989 * rgb[:,0] + 0.5870 * rgb[:,1] + 0.1140 * rgb[:,2] # get the intensity
intensity = np.rint(ntnst) # rounds up to nearest integer

…and how to display the colormap as a colorbar with an overlay plot of the intensity as in Figure 2.

Figure 2

Reference

Hall, M. (2014) Smoothing surfaces and attributes. The Leading Edge 33, no. 2, 128–129. Open access at: https://github.com/seg/tutorials#february-2014

Niccoli, M. (2014) Evaluate and compare colormaps. The Leading Edge 33, no. 8., 910–912. Open access at: https://github.com/seg/tutorials#august-2014

New Matlab isoluminant colormap for azimuth data

Posted on October 30, 2014 by matteomycarta

I recently added to my Matlab File Exchange function, Perceptually improved colormaps, a colormap for periodic data like azimuth or phase. I am going to briefly showcase it using data from my degree thesis in geology, which I used before, for example in Visualization tips for geoscientists – Matlab. Figure 1, from that post, shows residual gravity anomalies in milligals.

Figure 1

Often we’re interested in characterizing these anomalies by calculating the direction of maximum dip at each point on the surface, and for that direction display the azimuth, or dip azimuth. I’ve done this for the surface of residual anomalies from Figure 1 and displayed the azimuth in Figure 2. Azimuth from 0 to 360 degrees are color-coded using Jet, Matlab’s standard colormap (until recently). Typically I do not trust azimuth values when the dip is close to zero because it is often contaminated by noise so I would use shading to de-saturate the colors where dip has the lowest values, but for ease of discussion I haven’t done so in this case.

Figure 2. Azimuth values color-coded with Jet.

There are two problems with Figure 2. First, the well-known problems with the jet colormap. For example, blue is too dark and blue areas appear as bands of constant colour. Yellow is much lighter than any other colour so we see artificial yellow edges that are not really present in the data. But there is an additional issue in Figure 2 because azimuths close in value to 0 and 360 degrees are colored with blue and red, respectively, instead of a single color as they should, causing an additional artificial edge.

In Figure 3 I recolored the map using a colormap that replicates those used in many geophysical software tools to display azimuth or phase data. This is better because it wraps around at 360 degrees but the perceptual issues are unresolved: in this case red, yellow and blue all appear as sharp perceptual edges.

Figure 3. Azimuth values color-coded with generic azimuth colormap.

Figure 4. Azimuth values color-coded with isoluminant azimuth colormap.

In Figure 4 I used my new colormap, called isoAZ (for isoluminant azimuth). This colormap is much better because not only does it wraps around at 360 degrees, but also lightness is held constant for all colors, which eliminates the perceptual anomalies. All the artificial yellow, red, and blue edges are gone, only real edges are left. This can be more easily appreciated in the figure below: if you hover with your mouse over it you are able to switch back and forth between Figure 3 and Figure 4.

From an interpretation point of view, azimuths 180 degrees apart are of opposing colours, which is ideal for dip azimuth data because it allows us to easily recognize folds where dips of opposite direction are juxtaposed at an edge. One example is the sharp edge in the northwest quadrant of Figure 4, where magenta is juxtaposed to green. If you look at Figure 1 you see that there’s a relative high in this area (the edge in Figure 4) with dips of opposite direction on either side (East and West, or 0 and 360 degrees).

The colormap was created in the Lightness-Chroma-Hue color space, a polar transform of the Lab color space, where lightness is the vertical axis and at each value of lightness, chroma is the radial coordinate and hue the polar angle. One limitation of this approach is that due to theirregular shape of the color gamut section at each lightness value, we can never exceed chroma values of about 38-40 (at lightness = 65 in Matlab; in Python, with extensive trial and error, I have not been able to go past 36 using the Scikit-image Color module), which make the resulting colors pale, pastely.

it creates For those that want to experiment with it further, I used just a few lines of code similar to the ones below:

radius = 38; % chroma
theta = linspace(0, 2*pi, 256)'; % hue
a = radius * cos(theta);
b = radius * sin(theta);
L = (ones(1, 256)*65)'; % lightness
Lab = [L, a, b];
RGB=colorspace('RGB<-Lab',Lab(end:-1:1,:));

This code is a modification from an example by Steve Eddins on a post on his Matlab Central blog. In Steve’s example the colormap cycles through the hues as lightness increases monotonically (which by the way is an excellent way to generate a perceptual rainbow). In this case lightness is kept constant and hue cycles through the entire 360 degrees and wraps around. Also, instead of using the Image Processing Toolbox, I used Colorspace, a free function from Matlab File Exchange, for the color space transformations.

For data like fracture orientation where azimuths 180 degrees apart are equivalent it is better to stack two of these isoluminant colormaps in a row. In this way we place opposing colors 90 degrees apart, whereas color 180 degrees apart are the same. You can do it using Matlab commands repmat or vertcat, as below:

radius = 38; % chroma
theta = linspace(0, 2*pi, 128)'; % hue
a = radius * cos(theta);
b = radius * sin(theta);
L = (ones(1, 128)*65)'; % lightness
Lab = [L, a, b];
rgb=colorspace('RGB<-Lab',Lab(end:-1:1,:));
RGB=vertcat(rgb,rgb);

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Spectral lightness rainbow

You can download the colormap files (comma separated in MS Word .doc format) with RGB values in 0-1 range and 0-255 range.

Matlab code

Aknowledgements

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Why another rainbow

Matlab code

Test results

Aknowledgements

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Reference

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