Under UK law, the starting point is s4 of the Copyright, Designs and Patents Act 1988 which defines a photograph as "a recording of light or other radiation on any medium on which an image is produced or from which an image may by any means be produced". Legally, x-rays and other medical radiographic imagery ought to be treated the same as a photograph taken with a camera.
Whether a copyright exists at all when you face is basically scanned in a machine is a debatable point. The current test under European law whether there is an "intellectual creation" is from the Infopaq case. The British courts helpfully explicated the test in SAS v World Programming:
"The essence of the term is that the person in question has exercised expressive and creative choices in producing the work. The more restricted the choices, the less likely it is that the product will be the intellectual creation (or the expression of the intellectual creation) of the person who produced it."
Has there been expressive and creative choices? It is certainly arguable that putting someone's head in a big machine and flicking a switch doesn't quite amount to an "expressive and creative choice". Traditional radiography generally does involve some choices based on skill: often an x-ray technician may have to spend some time getting a person to be positioned in exactly the right way to photograph their particular injury, but the machine depicted above seems to have solved that problem for the dental case—you put your head in the position that the design of the machine indicates and then the machine does the rest. Ultimately, we don't really know whether copyright exists on this until a court gives us a determination on it.
If copyright does exist, it'll belong to the dentist, not the patient. It isn't work-for-hire or anything like that.
The US is an interesting contrast: the US Copyright Office's Copyright Compendium states that "the Office will not register works produced by a machine or mere mechanical process that operates randomly or automatically without any creative input or intervention from a human author", and specifically notes that they believe this category includes "medical imaging produced by x-rays, ultrasounds, magnetic resonance imaging, or other diagnostic equipment".
(That's an agency determination though and hasn't been tested in court, and so rests on Chevron deference, which may not be around for much longer since the newest Supreme Court justices don't seem so keen on the idea.)