A bound on mutual information for image registration

An upper bound is derived for the mutual information between a fixed image and a deformable template containing a fixed number of gray-levels. The bound can be calculated by maximizing the entropy of the template under the constraint that the conditional entropy of the template, given the fixed image, be zero. This bound provides useful insight into the properties of mutual information as a similarity metric for deformable image registration. Specifically, it indicates that maximizing mutual information may not necessarily produce an optimal solution when the deformable transform is too flexible.