If we have one photo of an object, there exists infinitely possiblities for "What is object's real 3D geometric shape". In mathematics there is no way to figure out the 3D shape from a single 2D picture.
We - people - are jailed by our thinking practices and learnings. If we see a well taken portrait, we very soon figure out who that person is, if somebody who we remember, fits. Even, if the portrait is taken straight from the front, we easily imagine how he looks out sideways and that happens even if we never have seen him. But the portrait can in reality be taken of a flat photo or of some other person, who happens to look out same from camera's direction. That other person can have much longer nose, but the straight onto face portrait tells nothing about it. The portrait even can be taken of a concave (=a negative mask) that is appropriately coloured inside.
Our limitations quide us to say, for example: "That's John Doe!". When we are told "No, this photo is taken of his portrait which is flat, John Doe weights 100 kilograms" , we justify our hasty decision by saying "Who in the hell takes a photo of a photo!"
Evolution or God has made us to take actions which are based on sparse information. The probability of choosing right has stayed high enough to keep us alive. So, sparse information can be sufficient. Thats why there is not any theoretical obstacle in front of developing a computer program that, like us, chooses a plausible 3D face model from the infinite set of possiblities, which becomes available, when somebody inputs one 2D portrait.
If we Google "single photo face modelling", there pops out at least as much to choose from as if somebody fatally ill tries to find the magic snake oil or the miraculous healer, who takes his cancer off.
Some of the face modelling suites are only frameworks, where the user makes all decisions. The framework only give the tools to input those decisions and to see their results instantly.
Some face modelling suites really have some knowledge about faces. There exists some general bacic face types to choose from. The user must point or draw feature by feature, which part in his photo corresponds a feature in the basic model. When the feature list has been walked through, the program outputs the model that the user can fine tune.
Some of "face model from a single photo" suites are claimed to be automatic and there are available demo videos that look out very respectable. I really like to know, if those demos are more than the one that an alchemist shows to the monarch to get still a little more gold to be finally able to make wagon loads of gold.
In theory automatic single photo face modelling can be more than alchemy presuming that they really are made to take into the account "what is probable in reality". It means the ability to do proper reasoning - artificial intelligence - at least, when the talking is about the faces.