Really?Once I asked a British person:
1. This is the car of mine.
2. This is the car of me.
He told me that number 1 (mine) is correct.
Because the subject of the second sentence is "you" and thus it requires a reflexive pronoun. Just like you would say "I have a picture of myself" because "I" requires a reflexive pronoun. "This" does not require a reflexive pronoun and thus you can say "This is a picture of me" or "That was a picture of you". And just like you would not need a reflexive pronoun if the person who had/seen (or any other verb) the picture was not the person in the picture, i.e. "Does she have a picture of you?" or "Have you seen that new picture of him?"Hullo, Lon and Ania.
Maybe it's the cold spell that's invaded Northern Italy, but I cannnot see why, if, say, "This is a picture of me" is correct, sb's #3 sentence "Do you have a picture of you?" should be considered wrong.