Generalized Partial Volume: An Inferior Density Estimator to Parzen Windows for Normalized Mutual Information

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.