In Japanese, they're called "igyou-atama" (異形頭) or, literally, "strange-looking heads." They are oddly wonderful.
This trend is directly connected to a series of anti-piracy public service announcements that play in Japanese movie theatres.
Over the past few years, cosplayers would sometimes dress as these anti-piracy characters. There was also the inevitable fan art.
Igyou-atama, which are also called heteromorphic heads, are not a new phenomena per se. Going back further, we can see examples in video games (Pyramid Head from Silent Hill, for example) and Japanese pop culture.
Even going back further, there does seem to be a connection between these strange-looking heads and the yokai known tsukumogami or "haunted relics."
It's easy to see the appeal. Igyou-atama do look cute.
Last Halloween, some people in Japan dressed up in igyou-atama outfits.
There seems to be more fan art, too.
But at Halloween parades this month in Japan, there appear to be more costumes of them than ever. (Please be aware that while the number of costumes has increased, this is still very much a geek subculture trend and this isn't mainstream as most Japanese wear more typical costumes.)
Here, have a look for yourself:
Of course, Boba Fett is a traditional costume. But that other outfit is igyou-atama.