Every face you're familiar with, whether friend or celebrity, has a distinctive shape and proportion. But familiar faces also have a set of characteristic movements. Those movements, scientists say, are stored in your memory, and play a crucial role in face recognition.
This effect is understood by actors who are masters of impressions. Watch as Kevin Spacey does a series of impressions (Link to YouTube). Before he even gets into doing the voice, he concentrates on the characteristic movement and posture of his subject.
The same is true with these "nano-impressions" by Ross Marquand. The movement is a bigger part of his impressions than the voice. For the impression to work, the movement, voice, words, and timing combined have to be powerful enough to override the contrary impression given by the impersonator's face metrics (Link to YouTube)
Psychology professors Karen Lander and Lewis Chuang of the University of Manchester showed in a research project that moving faces are much easier to recognize, especially when the person is moving in a distinctive way. An expressionless face simply rotating doesn't offer much. They write that the "distinctiveness of the observed motions may be important, with the beneficial effect becoming more pronounced as the face moves in a more "characteristic'' or distinctive manner."
This is why I don't mind if a portrait subject is moving. In fact, I like it more if they're moving. It gives me a better sense of their character, and helps me decide the best pose and expression.
Portraits in the Wild: Painting People in Real Settings
Why are Moving Faces Easier to Recognize? (free PDF of the study) by Karen Lander and Lewis Chuang
Eyebrows and Face Recognition
Disrupting Face Recognition Technology