The above video animation shows a 2.5D Parallax effect where the subject and the background move in different directions and at different speeds. This is the very first attempt and does need some refinement such as trying different speeds, directions, etc.
The part of the process that takes the most time is the selection of the branch in the foreground, this can be done via different methods including the pen tool or quick selection tool, which ever works best.
This video will show you how to create the effect using selections and Photoshop’s built in video editor:
This will not work with every image you have but certain landscapes or subjects with a large background behind them would work quite well.