An invisible matte painting is one where it looks just like reality - no Hudson River school stuff, nothing overly dramatic, just an attempt to recreate reality.
Takachiho-jo (Takachiho Castle) Note: There is no Takachiho-jo in real life. Takachiho is the name of the town about 45km from Nobeoka where the background for this painting was shot. The castle is Shuri-jo in Okinawa.
If you're curious about the source plate, here it is:
Source plate