This is cool, but I wonder why most of the demo images - and a lot of the images I uploaded - seem to have their colors aligned in a single plane.
In the example images, the sand in the sand+sky picture is the only thing this is really true for.
Now imagine you rolled the card into a cylinder. The result would depend on the lighting, but most likely you'd be able to see some shading across the object, so that there are some darker and lighter pixels. In, the HSV colour space you'd now have a line - all the H and S values for those pixels would be the same, but there would be a range of values for V.
Now imagine you replaced the matt card with a shiny piece. You might see a whitish specular highlights where the object reflects a light source or the sky. The added whiteness would have made some pixels have a lower saturation (S). So now you have variation in S and V, but not H. That would form a plane in the HSV plot.
http://beneast.com/wp-content/uploads/2017/09/fahrelnissa-ze...
Well, not that flat actually, the way the image were processed also makes them flatter than they really are see
https://uploads2.wikiart.org/images/vincent-van-gogh/the-sta...
for example.
Another way to explain why a cylinder is only good for representing two dimensions is simply that a circle asserts that length(x) == width(y) leaving only 2 values represented by a cylinder: (x,y) and z.
https://bainbridgecode.wordpress.com/2012/04/24/beating-png-...
and
https://bainbridgecode.wordpress.com/2012/05/07/beating-png-...
There are plots at the end of part 3 showing the image channels separately for YCrCb and my custom PCA derived space. They clearly show that there's a lot less duplication of data between channels with the latter. And that in turn is obviously good for compression.