Let me preface this question with the fact that two hours ago I had no idea what a cloud point was. I do however have a solid mathematical background although geometry has never been my focus. I do know a lot about search trees, distances and space partitioning which I feel like would be useful for the potential solution to a problem I'm facing.

I have a 3D scanner that with high accuracy can generate a point cloud. Let's say I have a database of a number of objects in the range of 10,000. The way these are stored depends on the solution, but they could be point clouds themselves scanned by the 3D scanner, actual 3D models or perhaps even another representation of the object.

What I'm looking for is to match the newly scanned object to the 'closest' or most resembling object from the database and preferably tell me if there is no match as well (although this could just be some threshold I have to empirically set). I don't know if this is feasible in theory, feasible computationally or even reliable but I'm very interested if this is, I don't really know what to look for or where to start.