There is some ambiguity between using the helping verb "have" for the perfect tense, and using it as an imperative. Nevertheless, there are certain conventions.
He has taken a picture
means that he took the picture himself.
He has his picture taken
means that someone takes a picture of him. However,
The picture he has taken.
by itself, suggests that he is the one who took the picture. If he asked or paid someone else to take a picture of him, it would be more natural to use the past perfect.
The picture he had taken
This is still somewhat ambiguous, so for clarity you should add more detail to define the subject of the picture:
The picture he had taken of himself became popular
Note that it's became popular, not become popular, as the action happens in the past, relative to the current moment.