Point cloud comparison 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.
This is termed 3D object retrieval. There are many possible approaches to follow. First, if your meshes are nice, clean and descriptive, you could then consult the academic literature of computer graphics, while computer vision deals with more noisy scenes, partial visibility, non-meshed data. As I am a computer vision oriented person, I would be biased towards such approaches. But keep in mind that Eurographics organizes a workshop on 3d object retrieval every year, called 3DOR. Each year different problems are addressed, but it is very common to find something meeting your requirements.
The following might be good references in the direction you would like to go:


From Low-Cost Depth Sensors to CAD: Cross-Domain 3D Shape Retrieval via Regression Tree Fields

Database-Assisted Object Retrieval for Real-Time 3D Reconstruction

Feature-based Similarity Search in 3D Object Databases



There are many many more works though. For example, here are some, incorporating deep learning:


3DNet: Large-Scale Object Class Recognition from CAD Models

3D Shape Retrieval Using a Single Depth Image from Low-cost Sensors

3D ShapeNets: A Deep Representation for Volumetric Shapes