The museum houses all kinds of jinmenseki, or rock with a human face, including celebrity lookalikes like Elvis Presley. And according to this post from Kotaku from 2013, there are also movie and video game character rocks E.T., Donkey Kong and Nemo.
According to the Sankei, the museum is currently run by Yoshiko Hayama, the wife of the original owner who passed away in 2010. But it was his rock collection that started it all. An avid collector, the late Shozo Hayama spent 50 years collecting rocks that looked like faces. His only requirement was that nature be the only artist.