Pretty simple. Extract "dog to the far right" out of all the frames, which result you with "dog to the far right" in a empty background swaying. Then re-add the background too all the frames; the dog(middle) should be removed from the background and it(the background) is a tessellation so this shouldn't be very hard. And since the background doesn't move, it should the same for every frame.
Edit: Bored... Background:
