Mutual Information (MI) and normalized mutual information
(NMI) are popular choices as similarity measure for multimodal
image registration. Presently, one of two approaches is often used for
estimating these measures: The Parzen Window (PW) and the Generalized
Partial Volume (GPV). Their theoretical relation has so far been
unexplored. We present the direct connection between PW and GPV
for NMI in the case of rigid and non-rigid image registration. Through
step-by-step derivations of PW and GPV we clarify the difference and
show that GPV is algorithmically inferior to PW from a model point
of view as well as w.r.t. computational complexity. Finally, we present
algorithms for both approaches for NMI which is comparable in speed
to Sum of Squared Differences (SSD), and we illustrate the differences
between PW and GPV on a number of registration examples.