Lets say you are in public, and the Police approach you. You do not wish to speak to them and want to walk away. They detain you for the purpose of taking a photo of you but you have not committed a crime and they won't state whether you are the suspect of a crime.
In general in the US, anyone may photograph anyone else if they are all in a public place, although in some states such a photo may not be used commercially without permission, which must often be paid for and may be refused.
It is unusual for police to photograph people on the street, but they might want to document who was present at a particular place and time. They can do so, but I am not at all sure that they can prevent a person from covering his or her face, or turning his or her back, or charge a person who does so with obstruction. I don't think so.
Under some circumstances in the US police may ask a person for identification, and may charge a person who refuses to provide it. This varied from one state to another, and usually depends on the specific circumstances. (If a person is driving an automobile, police may demand to see a driver's license, for example.)
Unless a police officer puts a person under arrest, the officer has no general right to control that person's actions, beyond instructing the person not to interfere with ongoing police work. I do not think an obstruction charge would hold up for covering one's face or turning away in the absence of an arrest.
Generally the police may only detain you if they've met a cetain burden of proof that you likely comitted a crime (whether or not you actually did committ a crime is a matter for trial, not arrest or detainment.). They can take your picture at this point and lawfully request identification (and failure to do so is non-compliance). Asking a random person on the street to have their picture taken is a violation of this if the person refuses to consent to such evidence gathering AND the police do not have the evidence to meet the burden of proof for arrest.
However, in public, police may use any survallence footage available to them and given with consent of the owner of the recording if the footage is likely to reveal a person or persons involved with a crime. So long as the individuals in the camera's view do not have a reasonable expectation of privacy or are notified of the cameras, they are not a violation of any right to privacy.
In the case of traffic cameras (red light or speed cameras) the tickets issued by them are typically not criminal charges but civil charges (Had a cop pulled you over in either case, there's a criminal charge for the break in law). This is a double-edge sword in who it favors as Civil Cases have a proponderance of evidence standard for conviction, rather than a beyond reasonable doubt standard, but to the defendant, the charge is less severe (you will only pay the fine, with no points put on your liscense because the nature of the cameras will be unable to prove that it was infact you in the drivers seat... but it can prove you owned the vehicle and thus in part responsible for its safe operation. If your brother was driving, you're responsibility is letting a person who drives like crazy behind the wheel of your car.). One of the few reliable defenses here is if the car was reported stolen at the time of the camera infraction.
