Category Archives: Tutorial

The rainbow is dead…long live the rainbow! – The rainbow is dead…long live the rainbow! – Perceptual palettes, part 3

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Inroduction

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!

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The rainbow is dead…long live the rainbow! – series outline

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The rainbow is dead…long live the rainbow! – Part 1

The rainbow is dead…long live the rainbow! – Part 2: a rainbow puzzle

The rainbow is dead…long live the rainbow! – Part 3

The rainbow is dead…long live the rainbow! – Part 4 – CIE Lab heated body

The rainbow is dead…long live the rainbow! – Part 5 – CIE Lab linear L* rainbow

The rainbow is dead series – Part 6 -Comparing color palettes

The rainbow is dead series – Part 7 – Perceptual rainbow palette – the method

The rainbow is dead series – Part 7 – Perceptual rainbow palette – the godies

The rainbow is dead…long live the rainbow! – The rainbow is dead…long live the rainbow! – Perceptual palettes, part 2: a rainbow puzzle

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ROYGBIV or YOGRVIB?

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:

INT = (0.2989 * RGB(:,1) + 0.5870* RGB(:,2) + 0.1140 * RGB(:,3))';

Give it a try, then hover with your mouse over the image to read the intensity values.

roygbiv_intensityroygbiv_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!

ROYGBIV puzzle

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:

1=Y
2=?
3=?
4=?
5=?
6=?
7=?

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.

roygbiv_random_deuteranoperoygbiv_random

Conclusion

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.

Related posts (MyCarta)

The rainbow is dead…long live the rainbow! – the full series

What is a colour space? reblogged from Colour Chat

Color Use Guidelines for Mapping and Visualization

A rainbow for everyone

Is Indigo really a colour of the rainbow?

Why is the hue circle circular at all?

A good divergent color palette for Matlab

Related topics (external)

Color in scientific visualization

The dangers of default disdain

Color tools

How to avoid equidistant HSV colors

Non-uniform gradient creator

Colormap tool

Color Oracle – color vision deficiency simulation – stand alone (Window, Mac and Linux)

Dichromacy –  color vision deficiency simulation – open source plugin for ImageJ

Vischeck – color vision deficiency simulation – plugin for ImageJ and Photoshop (Windows and Linux)

For teachers

NASA’s teaching resources for grades 6-9: What’s the Frequency, Roy G. Biv?

The rainbow is dead…long live the rainbow! – Perceptual palettes, part 1

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Introduction

This is the first  post in a series on the rainbow and similar color palettes. My goal is to demonstrate it is not a good idea to use these palettes to display scientific data, and then answer these two questions: (1) is there anything we can do to “fix” the rainbow, and (2) if not, can we design a new one from scratch.

The rainbow is dead…some examples

In a previous post I showed a pseudo-3D rendering of my left hand x-ray using intensity (which is a measure of bone thickness) as the elevation. I mapped the rendering to both grayscale and rainbow color palettes, and here I reproduced the two images side by side:


I used this example to argue (briefly) that the rainbow obscures some details and confuses images by introducing artifacts. Notice that in this case it clearly reduces the effectiveness of the pseudo-3D rendering in general. It also introduces inversions in the perception of elevation. The thick part in the head of the radius bone, indicated by the arrow, looks like a depression, whereas it is clearly (and correctly) a high in the grayscale version.

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Visualization tips for geoscientists: Matlab, part II

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Introduction

In my previous post on this topic I left two loose ends: one in the main text about shading in 3D, and one in the comment section to follow-up on a couple of points in Evan’s feedback. I finally managed to go back and spend some time on those and that is what I am posting about today.

Part 1 – apply shading with transparency in 3D with the surf command

I was trying to write some code to apply the shading with transparency and the surf command. In fact, I’ve been trying, and asking around in the Matlab community for more than one year. But to no avail. I think it is not possible to create the shading directly that way. But I did find a workaround. The breakthrough came when I asked myself this question: can I find a way to capture in a variable the color and the shading associated with each pixel in one of the final 2D maps from the previous post? If I could do that, then it would be possible to assign the colors and shading in that variable using this syntax for the surf command:

surf(data,c);

where data is the gravity matrix and c is the color and shading matrix. To do it in practice I started from a suggestion by Walter Robertson on the Matlab community in his answer to my question on this topic.

The full code to do that is below here, followed by an explanation including 3 figures. As for the other post, since the data set I use is from my unpublished thesis in Geology, I am not able to share it, and you will have to use your own data, but the Matlab code is simply adapted.

%% cell 1
figure;
shadedpcolor(x,y,data,(1-normalise(slope)),[-5.9834 2.9969],[0 1],0.45,cube1,0);
axis equal; axis off; axis tight
shadedcolorbar([-5.9834 2.9969],0.55,cube1);

In cell 1 using again shadedpcolor.m, normalise.m, and cube1 color palette I create the 2D shaded image, which I show here in Figure 1.

Figure 1



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Visualization tips for geoscientists – Matlab

			
						

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Introduction


In my last post I described how to create a powerful, nondirectional shading for a geophysical surface using the slope of the data to assign the shading intensity (i.e. areas of greater slope are assigned darker shading). Today I will show hot to create a similar effect in Matlab.


Since the data set I use is from my unpublished thesis in Geology, I am not able to share it, and you will have to use your own data, but the Matlab code is simply adapted. The code snippets below assume you have a geophysical surface already imported in the workspace and stored in a variable called “data”, as well as the derivative in a variable called “data_slope”.


Method 1 – with a slope mask and transparency


Some time ago I read this interesting Image Processing blog post by Steve Eddins at Mathworks on overlaying images using transparency. I encourage readers to take a look at this and other posts by Steve, he’s great! That particular blog post gave me the idea to use transparency and the slope to create my favorite shading in Matlab.


In addition to the code below you will need normalise.m from Peter Kovesi‘s website, and to import the color palette cube1.


%% alpha transparency code snippet
black = cat(3, zeros(size(data)), zeros(size(data)), ...
    zeros(size(data)));             % make a truecolor all-black image
gray=black+0.2;                     % make a truecolor all-gray image
alphaI=normalise(data_slope);       % create transparency weight matrix
                                    % using data_slope

imagesc(data);colormap(cube1);      % display data
hold on
h = imagesc(gray);                  % overlay gray image on data
hold off
set(h, 'AlphaData', alphaI);        % set transparency of gray layer using
axis equal;                         % weight matrix
axis tight;
axis off;


And here is the result in Figure 1 below – not bad!




Figure 1. Shaded using transparency


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Lending you a hand with impage processing – introduction to ImageJ

			
						

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In a previous post I used an x-ray of my left hand to showcase some basic image visualization techniques in Matlab.


If you are interested in learning image processing and analysis on your own (just like I did) but are not too interested in the programming side of things or would rather find a noncommercial alternative I’d recommend ImageJ. I just stumbled into it a few weeks ago and was immediately drawn to it.


ImageJ is a completely free, open source, Java-based image processing environment. It allows users to display, edit, analyze, process, and filter images, and its capabilities are greatly increased by hundreds of plugins on the official webpage and elsewhere.


It is used extensively by biomedical and medical image processing professionals (check this fantastic tutorial by the Montpellier RIO imaging lab), but is popular in many fields, from A-stronomy (you can read a brief review in here) to Z-oology (check this site).


I decided to give it a try right away. Within an hour of installing it on my iMac I had added the Interactive 3D SurfacePlot plugin, loaded the hand x-ray image, displayed it and adjusted the z scale, smoothing, lighting, and intensity thresholds to what (preliminarily) seemed optimal.


For each discrete adjustment I saved a screen capture, then I reimported as an image sequence in ImageJ and easily saved the sequence as an AVI movie, which is here below. I’m hoping this will give you a sense of how I iteratively converged to a good result.




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Lending you a hand with image processing – basic techniques 2

			
						

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In my last post I illustrated some simple techniques to enhance and visualize a hand x-ray image. I showed how to use intensity values as if they were elevation to display the hand in pseudo-relief. I did this in 2 ways using the Matlab command surf: once keeping the elevation range of [0-255] obtained from intensity, and a second time creating a different elevation range (through trial and error) to try to further enhance the relief effect. In the case of the hand x-ray the relief was indeed enhanced but with that also unimportant details that are distracting possibly from the task (for the hypothetical specialist commissioning our image enhancement work) of interpreting the x-ray. Today I want to show you a case in which it would be useful to enhance dramatically the smaller details in an image. Below is a beautiful coin of the Roman Emperor Augustus I found here.









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