How does Latin handle "picture nouns"?

Question

"Picture nouns" are nouns like that have their own content such as, picture, story. In English this characteristics results in ambiguity. When we say "my photo" it may mean:

1. A photo that I am in its content. (i.e I am in the picture)
2. I own the photo (regardless of its content)

In Latin we might use the genitive case (or even the dative of possession) as well as the possessive adj. My question is how they are applied correctly. In other words:

is fabula mea to be taken on the first/second/both of the meanings above? and the same question for fabula mei.

Answer 1

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' in English)

You must also bear in mind that the genitive of the personal pronouns, mei, tui, nostri, etc. were not usually used for denoting possession, as there were possessive adjectives for that exact purpose.

So combining the two you'd have something like:

Statua mea Caesaris: My statue of Caesar

Even something confusing in English, like "his statue of himself" (i.e. if Caesar owned a statue of himself) would be clearer in the Latin

Statua sua sui

So, in other words, possessive adjectives are for possessing, genitives are for describing here.