  We analyze the problem of determining whether 2 given point clouds in 2D,
with any distinct cardinality and any number of outliers, have subsets of the
same size that can be matched via a rigid motion. This problem is important,
for example, in the application of fingerprint matching with incomplete data.
We propose an algorithm that, under assumptions on the noise tolerance, allows
to find corresponding subclouds of the maximum possible size. Our procedure
optimizes a potential energy function to do so, which was first inspired in the
potential energy interaction that occurs between point charges in
electrostatics.
