[Insight-developers] Where mutual information works, and doesn't

[Paul Hughett]

> L2 assumes a model with gaussian image noise and so preprocessing is
> required for it to work well.  in practice, (normalized)
> cross-correlation is usually a more effective (but costly)
> alternative.

There must be something I'm not seeing here.  Once you remove all the terms
and factors that don't depend on the coordinate transform, the Pearson product
moment correlation (or the cross-correlation evaluated for a single shift
value) boils down to Exy, whereas the L2 norm boils down to the square root
of E(x-y)^2.  If anything, the cross-correlation should be faster, since it
requires only two flops per voxel, versus three for the L2 norm.

Paul Hughett