Briefly looking on PHI, I've found a simple genitive of description does the trick.
Pictura canis: A picture of a dog
Statua Caesaris: A statue of Caesar
As far as using the possessive adjective, it wouldn't denote the same possible meaning as it does in English.
pictura mea: My picture (that I own)
pictura mei: A picture of me (commonly said as 'my picture' ...