Is there any way to make beautiful squircle-icons as defined here from any square bitmap image without going through a drag- and click- and resize-orgy in a GUI-driven application?

What I want is something like
where iconmake.sh would make sure the image is square (cut otherwise), resizes it and then applies all the magic (masks, highlights,...) necessary.

There as to be a way because this is basically what happens to the website-icon on the fly when you "bookmark" it.

Is this a service on the device itself that the browser uses and that I could invoke from a shell script as well?
If not: Would it possible to do this from the command line on my Ubuntu box, using, say, imagemagick? I used imagemagick a while back for other purposes and found it quite powerful, but I don't know if it can handle layers, masks etc.