I agree that trying to determine the distribution of these drawings is hard because it isn't a simple floating point number in its current form.

But maybe you could covert it to a linear monotonic measure?

You could pass it to an image recognition model and see record the degree to which it thinks it is an:

animal horse unicorn

Basically if it fails to be a unicorn, see if it is a horse and if it fails to be a horse check if it is an animal. This gives you some type of linear measure if you place these three measures along the same axis adjacently. Then you can transform each image to a floating point number and then characterize the distribution.