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.

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.

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.

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.

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.

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.

Projection

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.

Red-green color blindness is split into two different types: Whereas people affected by protan color blindness are less sensitive to red light, deuteranopia or deuteranomly (the second type of red-green color blindness) is related to sensitiveness on green light.

Protans have either defective long-wavelength cones (L-cones) or the L-cones are missing at all. If they are missing it is called protanopia or sometimes red-dichromacy. Affected persons are dichromats because they have only two working cone types, short- and medium-wavelength, compared to persons with normal vision with three different cone types.

If the L-cones are defective they appear in different intensities. This results in either a stronger or a weaker color blindness. If L-cones are not missing but defective it is called protanomaly. People suffering from this kind of color blindness are called anomalous trichromats.

Protans have difficulties to distinguish between blue and green colors and also between red and green colors. When comparing the two spectrums you can see that there are different colors and shades of colors which are hard to distinguish for a protanopic person. So those persons are not only blind on red and green colors but a lot more. This means the well known term red-green color blindness is actually misleading and gives a wrong impression of protan color blindness (and also deutan color blindness).

Protanopia and protanomaly both are congenital color vision deficiencies. Their cause is an unequal recombination in the gene array which is passed on thereafter from parents to their children.

The genes encoding the L-cone photopigments are located on the X chromosome. This chromosome is also called the sex-chromosome, because women have two X’s compared to men with only one X combined with Y chromosome. If something is encoded on the X chromosome it is called sex linked. Sex linked traits are more often observed on men than women because a woman always has a second X chromosome which can compensate the deficiency. This unbalance between men and women can be seen in the table above showing the ratios of each kind of protan color blindness.

There are a number of studies which show that color vision deficiencies are a serious risk factor in driving. Particularly protan color blindness reduces substantially the ability to see red lights, regardless of the severity of the defect. Tests showed that protans were very much over-represented in an accident causing group of drivers mostly involving either signal lights or brake lights. Some scientists estimate that being a protan has associated with it a level of risk of road accident that is equivalent to having a blood alcohol level of between 0.05 and 0.08 per cent. Because of that for example in Australia you can’t get hold of a commercial drivers licence since 1994 if you are suffering from protanopia or protanomaly.

Read more about Tritanopia and Deuteranopia—the other two types of color blindness.

Further reading:
Opsin Genes, Cone Photopigments, Color Vision, and Color Blindness
Protan Colour Vision Deficiency and Road Accidents
Wikipedia: Color Blindness

Related articles:
The Biology Behind Red-Green Color Blindness
Colorblind Population
At The Traffic Light