I have a set of points defined by their coordinates $(x_1,y_1)$ after changing some parameters of the problem I obtain a second set of points defined by their coordinates $(x_2, y_2)$. There exists a one-to-one mapping between these two sets of points. Is there a standard way to obtain the most likely mapping between these two sets of points? Consider the following sets of points: (blue, red, and green are different sets)
I would like to obtain this mapping from blue to red to green:
My first thought for solving this is to compute the nearest neighbor of blue points to each of the red points, sort these nearest neighbors by distance, remove the closest match, recompute the nearest neighbors, and repeat. However, it is easy to think of situations for which this algorithm does not work. (I don't think it works for the sets of points above.)
I'm solving a large eigenvalue problem and attempting to track eigenvalues as I vary parameters.