If a portrait photograph is an intellectual creation i.e. was taken by a person (and not in an automatic photo booth) and has an individual character, i.e. the photographer has not simply snapped the person in the portrait in any particular way but rather with sufficient creative means and leeway (choice of lens, filter, moment of shooting the image, etc.), it is considered to be a protected work. Simply said, you can ask whether another person in the same situation would have taken the same or a very similar picture. In this case, you would have to deny that it has copyright character.
In case of doubt, it is advisable to assume that the work in question is protected by copyright.
UPDATE 2020: As a result of the new Swiss Copyright Act, a photographic portrait has to be considered as a protected work just because it is an intellectual creation, that means, there was a human being that snapped the shot, even if that photograph doesn’t have individual character.