[Numpy-discussion] shift for optimal superimposition of two 3D matrices according to correlation computed using FFT

[Klaus Kopec]

Hello everybody,

I have two 3D density maps (meaning volumetric data, each one 
essentially a IxJxK matrix containing real values that sum to one) and 
want to find translation of between the two that maximises correlation. 
This can be done by computing the correlation between the two 
(correlation theorem -> I use FFT for this) and then shifting one of the 
two maps by the vector that corresponds to the index of the maximum in 
the 3D correlation matrix.

My problem with this method is, however, that the shift wraps around the 
edges of the matrix. e.g: for a 30x30x30 matrix that needs to be 
slightly shifted to fit the seconds 3D matrix, sometimes shift vectors 
like (0, 29, 0) appear, that actually mean a shift by (0, -1, 0). This 
means that the size of the matrix needs to be subtracted from some 
components of the shift vector in special cases.

So far, I have been unable to determine the cutoff value, outside of 
which I need to subtract the matrix size from a component of the shift 
vector, as this cutoff seems to vary between different data sets.

Can anybody help me out with this? Best regards,
Klaus