Do directors have a voice in choosing movie posters, or is it always a producer or external choice? Even for different movie posters in different countries, do directors ever decide to use a specific image for their movies?
I'd say that directors do not have much input into designing the poster, since they are usually made by third-party design studios, with more then one of these usually competing to make the best and be chosen by the marketing staff of the movie studio.
This entertaining YouTube video reveals the psychology behind why movie posters look the way they do. It argues directors may not have much of a say.