This may sound vague, since I am not sure if what I am looking for even exists, but please bear with me.
I am interested in a technology that would allow me to not only locate, but also identify items placed on a screen. Imagine, for example, a large screen with chess pieces on top of it. I would want to know where each piece is. Specifically, I would want to be able to identify each piece, and match that unique ID with its current location. Note that the pieces should not be the limiting factor - I'm fine with adding sensors/actuators/etc. to them as long as that actually helps the screen identify them.
My hope is that there exists an obvious technology that I just haven't thought of. In a perfect case scenario, that would be a capacitive touch screen with the identification bit done in software rather than hardware. In the worst case scenario, you'd point me to a research paper and wish me good luck in building the screen myself†.
EDIT: to clarify certain things that came up in the comments, I am indeed talking about a screen that can display images in addition to sensing objects placed on top of it. @gbulmer suggested Reactable, and that's very close to what I need (at least when it comes to its operation, the technical part of the solution of course can be very different). The screen should probably not be larger than 30 cm * 30 cm, and I'd expect up to 10 objects being on the screen at the same time.
† I've found papers on building touch screens with fingerprinting capabilities, but somehow that sounds like an overkill.