Deducing the hour based on RA
Will you know the date and location from where the image is taken?
If you are sucessfully using the big dipper already you probably using this info.
There is a "degeneracy" between date and time.  The sky rotates once a siderial day (23hrs 56 min) and once a siderial year (which is 20min longer than tropical year: sun to same position). So the sky tonight at say 20:00 is the same as the sky at 20:04 the previous day. In two weeks that's 1 hour. So you need the date.

At the same time (say Universal Time == London time) at each longitude the observer is facing a different direction. So 15 deg long is equivalent to 1 hour in time. So you need longitude. Others have alluded to latitude. You see stars diffrently at different latitudes.   For example at the equator the pole star is on the northern horizon, and invisible in the sothern hemisphere. 

The core relationships is between right ascension (like "longitude" for stars), siderial time and hour angle. The hour angle is the angle between the meridial and position of star. Or the siderial time is the right ascension of stars crossing the meridian. You could work this out from an wide field image using a service like https://nova.astrometry.net/ and then convert "siderial time to local time". There's a stack overflow answer plus others.