How do I combine images with the same composition into one?

It can be done without a mask by aligning the Layers. making a selection and deleting half the top image as shown and flatten..

I think to automate this meaningfully one might need an image of the empty table. 

Whether is worth the trouble to automate it at all seems dubious, though. 

Hi

Not without masking, but it is an extremely simple masking job - Select Subject the Layaer> Layer Mask from Selection and a couple of brush strokes to ensure the shadow is included

Dave