Tangled Bank #72

The newest Tangled Bank is up and running. It’s already number 72 – and counting. This time featured by Chris at his blog Ouroboros (research in the biology of aging).

Tangled Bank #72 is called: What’s in a name? and listens a whole lot of interesting articles about “science and medicine, broadly defined”.

There are even a few other posts around the topic color – broadly defined:

See you next time at Tangled Bank #73.

Confusion Lines of the CIE 1931 Color Space

This is the second of three parts on the color blindness test based on the confusion lines of the CIE 1931 color space. In this part of the trilogy I would like to introduce you the confusion lines of the CIE 1931 color space, which was introduced in part one.

The CIE 1931 color space, which is two-dimensional, reflects only hue and saturation, which make up together chromaticity. The third dimension – lightness – is not shown in the diagram. But this doesn’t really matter, because many considerations of colors don’t need lightness. When looking at confusion lines we also don’t need the third dimension and therefore, they can be shown very nicely on the chromaticity diagram.

Let us have a look at some historical facts about confusion lines:

  • In 1855 J. C. Maxwell said: “Find two for a colorblind undistinguishable colors. Mark them on the CIE diagram and draw a line through them. This line will connect all colors which can’t be told apart by the colorblind person. You then can find more lines and all of those lines are either parallel or meet in a single point.”
  • A. König analyzed in 1892 the confusion lines and the so-called intersection point (also called co-punctal point) on three persons affected by color blindness.
  • In the year 1935 F. H. G. Pitt did some further research and found the confusion lines and corresponding intersection points for protanopic and deuteranopic persons.
  • D. Farnsworth (1955) and L. C. Thomson & W. D. Wright (1953) completed the work by adding the results for tritanopic persons.

Many studies followed and up to today these confusion lines are the main source while constructing tests on color blindness.

Confusion Lines - Protanopia
Confusion Lines – Protanopia

If you have a look at the diagram on the right side you can see the confusion lines associated to protanopic (red-blind) persons. The colors connected by one line can’t be distinguished by a protanope. If you would draw another line through the co-punctal point (intersection point), all colors on that line would look the same to a red-blind person too.

You can also see that there is a line going through a point called W. This is the so called white-point. Of course white can be told apart from red, even by a colorblind. But we have to take into account that the chromaticity diagram doesn’t include lightness. This means all colors along a line need the correct lightness adjustment to be undistinguishable by each other. Otherwise a colorblind can see a difference evenso it would be only a difference in brightness and not a different color perception.

Confusion Lines - Deuteranopia
Confusion Lines – Deuteranopia

The diagram of lines for deuteranopes (green-blind) looks quite the same as for protanopes. Both types of color blindness share a strong confusion on red and green colors, therefore the name red-green color blindness.

You can also see, that the lines are not exactly the same. Especially the intersection point is outside the range of the visible colors.

Confusion Lines - Tritanopia
Confusion Lines – Tritanopia

The last diagram looks totally different. The shown lines are connecting undistinguishable colors for tritanopes (blue-blind). Because the intersection point is at the blue end of the color spectrum, the color perception is completely different to the ones of red- or green-blind persons.

When you have a close look at all three diagrams you can also see, that the count of confusion lines differs. This is due to the following fact: Each line shows the smallest difference between distinguishable colors. This means not only the colors on one line, but all the colors between two lines are undistinguishable by persons affected by a certain type of color blindness.

In numbers:

  • People with normal vision can differentiate 150 wavelengths of colors.
  • Red-blind persons can see around 17 different wavelenghts.
  • Green-blind persons are able to distinguish around 27 wavelengths.
  • Blue-blind persons have an even more restricted visual field in the color spectrum.

By the way: Confusion lines are also called isochromatic lines, because they show lines of the same color (to the colorblind). A more accurate term would be pseudo-isochromatic lines, which is often used in academical papers.

In part three of this series, which will be the last part, we will have a look at the color blindness test based on these lines

Further readings:
Fundamental Studies Of Color Vision from 1860 To 1960
The Perception of Color

This is the second part about the color blindness test based on confusion lines of the CIE 1931 color space. The first part can be found at: CIE 1931 Color Space and the last part at: Color Blindness Test based on Confusion Lines of the CIE 1931 Color Space.

CIE 1931 Color Space

I would like to introduce a color blindness test based on the confusion lines of the CIE 1931 color space (also known as CIE XYZ color space). Because the topic is not the easiest one and needs some explanation I would like to split it into three parts. In this first of three parts I will introduce the CIE 1931 color space. In part two and three which will follow next week I will talk about the confusion lines of the CIE 1931 color space and last but not least the color blindness test based on the CIE 1931 color space confusion lines.

CIE 1931 Color Space
CIE 1931 Color Space

The acronym CIE stands for International Commission on Illumination which is the international authority on light, illumination, color, and color spaces. And 1931 is the year of birth of this specific color space.

Where it all began

Let us go back into history and have a look at where it all began. Based on the research on wavelengths and colors of Thomas Young at the turn of the 19th century, Hermann von Helmholtz developed around fifty years later a color theory. He stated, that the human eye has three different types of color receptors (cones) and that every color we perceive is a mixture of signals of those three types of cones, which roughly reflect the three different colors red, green and blue.

In the roaring twenties of the last century two scientists (W. David Wright, John Guild) took up this theory and independently made some experiments. To find out more about the three-color-theory a setup with four colored lights on two different sides was used.

  • On the left side a test color was projected by a light source.
  • On the right side the observer had three adjustable light sources (red, green and blue).

Now each observer (also called CIE standard observer) had the task to adjust the three lights accordingly, that the color on the right hand side was exactly the same as the test color on the other side. After many tests with a lot of test persons the results were mathematically analyzed. This produced three different curves of intensity for each light source to mix all colors of the color spectrum.

Funnily enough not every color could be matched and sometimes some red had to be added to the test color to get a correct match. This was also taken into account of the mathematical equations and resulted in a red curve including negative values. These three curves were standardized and are called the CIE RGB color matching functions r, g and b.

CIE RGB to CIE 1931

Because mathematicians don’t like negative numbers if they can change it, the commission changed it. Based on the CIE RGB functions and their corresponding values, new functions were calculated. Those new functions called x, y and z had to fulfill a list of conditions. Some of them were:

  • The new functions must be everywhere greater or equal to zero.
  • The y function describes only the luminosity.
  • The white point is, where x = y = z = 1/3.

All this put together produced the well known CIE XYZ color space which is also known as CIE 1931 color space. This color space aims to describe all visible colors to the human eye and can be shown as a three dimensional cube.


Because three dimensional objects can’t be illustrated very well a two dimensional representation had to be found. The Y parameter of the so-called tristimulus values X, Y and Z is a measure of the brightness. This helped to easily calculate the new chromaticity values x and y by the following rules:

  • x = X / (X + Y + Z)
  • y = Y / (X + Y + Z)

The corresponding chromaticity diagram is shown in the above picture. The outer curved line is called spectral locus and corresponds to the well known color spectrum, shown with corresponding wavelengths. The straight line on the lower part between blue and red is called purple line. This line relates to all colors which can only be mixed up by blue and red which are not part of the color spectrum.

In the next part I will talk about the confusion lines of the CIE 1931 color spectrum. And this leads us to the final part about the color blindness test based on those confusion lines.

Color Blindness is not ‘Color Blindness’

Most people connect the term color blindness to blindness and color, which tells them, that if you are colorblind you can see only black and white or maybe grayscale pictures. Only when they talk to somebody who really is colorblind or read something about color blindness, they find out, that they are wrong.

Color blindness is just the most common term for describing all different types of vision conditions which relate to a less broader color spectrum. If you are affected by color blindness you can see less colors than a “normal” human being but not none.

If we have a look at the terminology there are three different well known terms to describe this disability:

  • Color Vision Deficiency: This is the most accurate term. It is mostly used in scientific papers or from doctors. It describes the actual handicap to the point but it is not well known in common speech.
  • Daltonism: This term is derived from the 18th century researcher John Dalton. Himself colorblind he did some investigations and described the phenomenon for the first time in a scientific paper. The naming is still used in some languages and is also related to all types of color vision deficiency.
  • Color Blindness: This is the most common term although it is misleading. Maybe it made the run in common speech because it’s just easier to say “he is colorblind” than “he has a color vision deficiency”.

All three terms relate to the same phenomenon: People or animals who can’t see colors as “normal” human beings can see colors.

Maybe we need to have a quick look at how a “normal” human being actually can see. If you are not suffering from a color vision deficiency, you have three different cone types inside your eyes. Each of this has a special color spectrum it relates to and sends signals to the visual system. All three signals, which can be stronger or weaker, are mixed up to one distinct color inside your visual system.

If you are colorblind usually there is something wrong with one of those different cone types. Either they are faulty or missing at all. This means you still can see colors but less. Maybe less diverse, less shades, less colors and definitely less colorful. But not to be mixed up with a black&white picture. Those are only grayscale pictures or looked at it differently – brightness pictures.

Colorblind people can see colors. They can see blue and violet, green and yellow, red and orange and a lot more. Maybe just a bit less colorful here and a bit less colorful there, which makes them having bigger problems to distinguish colors. But anyway, they definitely can see colors.