In one of the three chapter I submitted for this book, Prototype colourmaps for fault interpretation, I talk about building a widget for interactive generation of grayscale colourmaps with sigmoid lightness. The whole process is well described in the chapter and showcased in the accompanying GitHub repo.
This post is an opportunity for me to reflect on how revisiting old projects is very important. Indeed, I consider it an essential part of how I approach scientific computing, and a practical way to incorporate new insights, and changes (hopefully betterments) in your coding abilities.
In the fist version of the Jupyter notebook, submitted in 2017, all the calculations and all the plotting commands where packed inside a single monster function that was passed to ipywidgets.interact. Quite frankly, as time passed this approach seemed less and less Phytonic (aka mature) and no longer representative of my programming skills and style, and increased understanding of widget objects.
After a significant hiatus (2 years) I restructured the whole project in several ways:
– Converted Python 2 code to Python 3
– Created separate helper functions for each calculation and moved them to the top to improve on both clarity and reusability of the code.
– Improved and standardized function docstrings
– Optimized and reduced the number of parameters
– Switched from interact to interactive to enable access to the colormaparray in later cells (for printing, further plotting, and exporting).
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 repositoryfor the code and slides, andwatch 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.
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.
Another old model brought back to life. This is the Click on the image below to see the model in action. This is the ternary system quartz – nepheline – kalsilite, also called petrogeny’s residua system, which is used to describe the composition of many cooled residual magmas and the genesis of very under saturated alkaline rocks.
More on this classification, used for cooled residual magmas, on Alessandro Da Mommio’s website, for example his page on Tracheite.
I just tried Sketchfab today at lunch. In less than five minutes I was able to bring back from the dead my defunct AutoCAD 3D model of the Yoder-Tilley tetrahedron for basalt classification. Click on the image below to see the model in action. If you want to learn more about basalt classification, check on Alessandro Da Mommio’s awesome website.
My top two favorite 3D geology models from today’s browsing:
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.
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];
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];