They can bring the pictures to the hospital. And some police departments that are technology-advanced will sometimes use phones with picture storing capabilities or laptops.
Do they have a booking picture, which can be from an earlier arrest? Non-booking photos are harder to create an array from, because background, like "Danger" signs, can impact the reaction. Further, if this is very early in the investigation, an individual picture might be used as a preliminary means of ID. Subsequently, you need an array or an actual lineup. In addition, confirmation of an ID of a suspect from a video of the crime scene or immediately around it can be used.
The best practices that Mark would recommend to the police as a prosecutor are not always followed. And some of what Mark would recommend as appropriate would get a motion to suppress out of me as defense attorney. There's a lot of litigation in this area, and a whole lot of cases where how the ID was obtained doesn't matter one iota to the case. In other words, the police might have botched it, but there's so much evidence, who cares.
Best of luck,
Jim Clark-Dawe