Registering non-corresponding point clouds

[preet]

I'm interested in the problem of registering non-corresponding (but similar) point clouds.

I have two sets of point cloud data (points in xyz) representing the same geometric shape. However, the point cloud data does not correspond -- both clouds have a different number of points and there is no relation between the two clouds other than the fact that they represent a similar geometric shape.

The goal is to register one of these point clouds to the other one using only rigid transformation (translation, rotation).

I'm not sure how to approach this problem -- a lot of the information I've found on the internet points the Iterative Closest Point algorithm, which involves defining a function to measure the disparity between the two point sets and then minimizing it to converge to a solution. However, I don't know how to define a function to measure the disparity between the two point sets I've described, since the points do not correspond.

tldr;
How do I define a 'distance' or 'disparity' function between two sets of point clouds that do not correspond but represent a similar geometric structure?

TiA,

-preet

 

[preet]

So I guess this is actually a pretty open ended question =p
For those interested, One way is to use the iterative closest point algorithm, explained really well here:

http://ais.informatik.uni-freiburg.de/teaching/ss07/robotics/slides/14.pdf

 

[mXSCNT]

One possibility is to perform a principal component analysis on both clouds of data, producing a coordinate system for each cloud. Then rotate/translate one cloud of data so that its coordinate system matches the other's.