Daltonism

Machin stamps are colour-coded according to their denomination. The coding scheme is somewhat ad hoc. But what if we wanted to be more systematic?

There are surprising few existing systems for encoding numbers as colours. One is the old system used for electronic components:

The digits zero to nine are represented by ten colours. My favourite mnemonic is:

Black Bananas Really Offend Your Girlfriend, But Violets Get Welcomed

In the past, colour-blind people were allegedly discouraged from becoming electricians because of the possibility of confusing earth (green), live (red) and neutral (black) in the pre-1977 UK domestic mains cabling colour scheme.

In an ideal world, the mapping of colours to numeric values would be fairly immune to any colour vision deficiency (CVD) experienced by the viewer. This led me to an investigation into colour-blindness: what used to be called "Daltonism" in the UK.

There are plenty of resources on the web explaining the various forms of colour blindness, but I wanted to be able to objectively assess how "good" a palette of colours was for:

1. People with no colour deficiency (I'll call them "trichromats"),
2. People with protanopia, deuteranopia or tritanopia ("dichromats"), and
3. People with monochrome vision ("monochromats").

One metric of how well a palette of colours "fills" a colour space is to measure the minimum "distance" between any two entries. I chose the CIELAB colour space and the CIEDE2000 metric because they were close-at-hand as part of my previous Goldenrod project.

I defined lambda as the minimum distance (ΔE2000) between colours in the palette as seen by trichromats; also known as minD(normal). The greater this number, the less likely that two entries within the palette will be confused by trichromats.

I then used a corrected version of Color.Vision.Simulate from HCIRN to simulate the four colour deficiencies and produce four "confused" palettes from the original:

1. protanope
2. deuteranope
3. tritanope
4. achromatope

Each of the confused palettes will have a minimum distance between colours within them; call these minimum distances minD(protanope), etc.

I defined beta as the minimum of minD(protanope), minD(deuteranope) and minD(tritanope). The greater this number, the less likely that two entries within the original palette will be confused by dichromats. I appreciate that there are far fewer sufferers of tritanopia in the general population than of the other two forms of dichromatism, but I haven't scaled the three distance metrics accordingly; I'm running under the premise of "none left behind".

I defined alpha to be minD(achromatope). The greater this number, the less likely that two entries within the original palette will be confused by monochromats.

Finally, I defined omega to be the minimum distance between two adjacent CIELChab hues from the original palette, measured in degrees. This number measures hue separation perceived by trichromats.

In summary:

• Lambda, λ, is "min ΔE2000" for the original, trichromatic palette. It measures how different the colours in the palette seem to a viewer with no colour vision deficiency. Larger values indicate greater variation.
• Beta, β, is the least "min ΔE2000" for the dichromatic remappings of the palette. It measures how different the colours in the palette seem to a viewer with one of those colour vision deficiencies. Larger values indicate greater variation.
• Alpha, α, is "min ΔE2000" for the achromatic remapping of the palette. It measures how different the colours in the palette seem to a viewer with achromatopsia, when rendered in greyscale or in some low-light conditions. Larger values indicate greater variation.
• Omega, ω, is "min Δhab" for the original, trichromatic palette. It measures the perceived hue separation (measured in degrees) experienced by a viewer with no colour vision deficiency. Larger values indicate greater separation.

Unfortunately, as the number of entries in a palette increases, we expect the λ, β, α and ω scores to decrease, so we cannot easily compare palettes with differing numbers of entries. Perhaps the scores could be scaled depending on the palette size, but I haven't tried to work out the factor; I suspect it's not linear.

In general, for our purposes, a "good" palette is one with high λ, β and/or α scores. Maximising λ is appropriate for about 92% of the population; β for about 8%; and α for less than 0.01%.

The accompanying web page computes the scores for existing and novel palettes.

If we take "Chilliant Pale/Deep 19" from that page and re-order the palette into hue order, we get a colour-blind-friendly scheme with which to encode the digits zero to nine:

This could be the basis for a new colour-coding of stamp denominations...