Variable Data Influence

The first type of inhomogeneity varies the importance attached to information content in the domain of the image pair when computing the transformation required at each point in the source. In terms of a Bayesian approach [2], where the deformation is determined by the solution of a weighted sum of likelihoods and priors, the weight assigned to the likelihood is varied according to assumptions about the relevance of the data in different regions of the image. In terms of regularisation, where the equation solved is a weighted sum of driving forces and constraints on the deformation, the influence of the driving force is weakened or strengthened relative to the deformation constraints.

By ignoring the contribution of the driving force, we can force a region to be passive, whose deformation is due solely to its proximity to active regions.

Let $\Omega = \{ \vec{x} \}$ be the domain of the image. We make the following definitions:
 

A medical application would be an intra-modality pair of which the source contains known segmented structures whose homologues are absent in the target but which may be confused, due to similarities of intensity, with regions nearby.