Thanks, @priort. Interesting links. Definitions (like standards) are great because there are so many to choose from.
There is, of course, a difference between the reflectivity of a red ball, and the light emitted from a red ball (which also depends on the illumination), and the perceived colour of the red ball. When we are dealing with images, we care about the pixels, which depends only on the light that hits the sensor.
The CIE originated in concepts of illumination rather than images, and still retains that perspective.
The Hasler and Susstrunk paper quantifies “overall colourfulness” of a picture, rather than of a single colour. A picture might be a solid colour, so standard deviations are zero, whch simplies the calculation. So we can compute the coloufulness of each pixel in an image.
All commands use ImageMagick in Windows BAT scripts.
magick ^
%SRC% ^
-channel RGB -separate +channel ^
( -clone 0,1 ^
-compose MinusSrc -composite ^
-evaluate Pow 2 ^
) ^
( -clone 0-2 ^
-poly "0.5,1,0.5,1,-1,1" ^
-evaluate Pow 2 ^
) ^
-delete 0-2 ^
-compose Plus -composite ^
-evaluate Pow 0.5 ^
hs.jpg

From Colorfulness, Saturation, Chrominance and Other Ways of Understanding Color
magick ^
%SRC% ^
-channel RGB -separate +channel ^
( -clone 0-2 -evaluate-sequence Max +write mpr:MAX +delete ) ^
( -clone 0-2 -evaluate-sequence Min +write mpr:MIN +delete ) ^
-delete 0-2 ^
( mpr:MAX mpr:MIN -compose Plus -composite ) ^
( mpr:MAX mpr:MIN -compose MinusSrc -composite ) ^
-compose Multiply -composite ^
mpr:MAX -compose DivideSrc -composite ^
mm.jpg

This isn’t a million miles away from the previous result.
Let’s try 2 * Saturation * Lightness:
magick ^
%SRC% ^
-colorspace HSL ^
-channel 1,2 -separate +channel ^
-compose Multiply -composite ^
-evaluate Multiply 2 ^
sl.jpg

This is very different. Ah, well.