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Mininimum face size
The face detector can discover very small faces, however these may be unclear for proper comparison. A general rule in neural networks, if the human can't recognize it, don't expect better results. If the face is very small, a human take additional information (hair, his clothes, who is it with, where was the photograph taken, etc.), and can easily infer who the person is.
Note that I said the hair, because this is not part of the face, and our detector does not take it into account. Let's see an example:
If you ever saw The Big Bang Theory you will easily recognize that this character is Sheldon Cooper. The rectangle shows the face detected by our default detector. As you can see, the photo has good quality, and the face a good size, 283x283. But what happens if we cut the face?
Surely you will still recognize the character, but observe how as you shrink your face, more information is lost. Many details in the eyes, the nose, are lost.
Up to 125px (13.36% in my tests with real photos.) probably has enough detail to speak of a quality comparison. Up to 60px (2.32% in my tests), you can still recognize it, and our recognition model will still work well, but you will notice the lack of detail. If you have similar people, there are possibilities that start to get confused.