[RESOLVED] Register by rotation: a tough one (thawing out though)

[krtxmrtz]

I want to register 2 polygons P and P' of arbitrary shapes with vertices of coordinates
(x_k, y_k) and (x'_k, y'_k), k=1,...,N
such that
x'_k = x_k + a
y'_k = y_k + b
for all k, where a and b are unknown, i.e. P' has the same shape as P but it is displaced.

However, because the coordinates x' and y' for polygon P' come from experimental measurements they do not exactly match the theoretically calculated (x,y) but they are very close. Therefore, what I do is calculate the center of mass for both polygons to find average values for a and b as the difference of the CoM coordinates.

So far so good. Now the difficult part is that sometimes the P' polygon is slightly rotated with respect to P. So the question is, what parameter could I check to guess the approximate angle of rotation (in a similar manner to the center of mass calculation to account for the shift)?