Multi-modal medical image registration: from information theory to optimization objective

A relatively large class of information theoretical measures, including e.g. mutual information or normalized entropy, has been used in multi-modal medical image registration. Even though the mathematical foundations of the different measures were very similar, the final expressions turned out to be surprisingly different. Therefore one of the main aims of this paper is to enlight the relationship of different objective functions by introducing a mathematical framework from which several known optimization objectives can be deduced. Furthermore we extend existing measures in order to be applicable on image features different than image intensities and introduce "feature efficiency" as a very general concept to qualify such features. The presented framework is very general and not at all restricted to medical images. Still we want to discuss the possible impact of our theoretical framework for the particular problem of medical image registration, where the feature space has traditionally been fixed to image intensities. Our theoretical approach is very general though and can be used for any kind of multi-modal signals, such as for the broad field of multi-media applications.