This is very similar to the cryo-electron microscopy problem: You want to image a certain macromolecule, and the scale of the macromolecule requires the use of an electron microscope. Unfortunately, such an imaging process is harmful to the specimen. In the 80s, they realized you can protect the specimen by freezing it first, but a single exposure will undo the protection. As such, they freeze a bunch of identical macromolecules (which end up at unknown orientations), and then image each one, producing a two-dimensional projection image (similar to your shadow). The cryo-EM problem is to recover the three-dimensional macromolecule from these images (see this paper and references therein)

This is very similar to the cryo-electron microscopy problem: You want to image a certain macromolecule, and the scale of the macromolecule requires the use of an electron microscope. Unfortunately, such an imaging process is harmful to the specimen. In the 80s, they realized you can protect the specimen by freezing it first, but a single exposure will undo the protection. As such, they freeze a bunch of identical macromolecules (which end up at unknown orientations), and then image each one, producing a two-dimensional projection image (similar to your shadow). The cryo-EM problem is to recover the three-dimensional macromolecule from these images (see this paper and references therein)