Abstract

Many variants of MI exist in the literature. These vary pri- marily in how the joint histogram is populated. This paper places the four main variants of MI: Standard sampling, Partial Volume Estima- tion (PVE), In-Parzen Windowing and Post-Parzen Windowing into a single mathematical framework. Jacobians and Hessians are derived in each case. A particular contribution is that the non-linearities implicit to standard sampling and post-Parzen windowing are explicitly dealt with. These non-linearities are a barrier to their use in optimisation. Side-by- side comparison of the MI variants is made using eight diverse data-sets, considering computational expense and convergence. In the experiments, PVE was generally the best performer, although standard sampling of- ten performed nearly as well (if a higher sample rate was used). The widely used sum of squared differences metric performed as well as MI unless large occlusions and non-linear intensity relationships occurred. The binaries and scripts used for testing are available online.