Possibly a caliber 18'''L 15P dating to about 1904.
The dial is vitreous enamel with Omega "Paris" style Arabic numerals and blued steel "Poire" hands.
The movement is decorated which was often done for movements intended for export to North America.
It is housed in an American made case, I can't see the makers mark but it's rolled gold and the "Imperial" is possibly the grade of rolled gold, which is guaranteed for XX years.
The case appears to be for a lever set movement (notch at 2 o'clock?) so it may have been re-cased at some point, or the original buyer just liked that case and chose it when they bought the watch.
If you can provide clearer photos and the diameter of the movement in millimetres it may be possible to add more info.