No, 'one of him' does not mean a picture that belongs to him. 'One of him' has nothing to do with possession - it means a photograph of his face. Compare the structure with this:
I admired Jane's flowers and took a photo of them. ( a photograph of the flowers).
When I graduated, a professional photographer took a formal picture of me. ( a portrait of me)
If you are talking about things that belong to people, you need to use the possessive pronouns:
A photo of mine/yours/his/hers/ours/theirs = These photos belong to these people
If you are talking about photos, pictures, portraits, etc in which these people feature, you use the object pronouns:
A photo of me/you/him/her/us/them = You can see these people in these photos
I hope this makes sense.