A normalised entropy measure for multi-modality image alignment

Automated multi-modality 3D medical image alignment has been an active area of research for many years. There have been a number of recent papers proposing and investigating the use of entropy derived measures of brain image alignment. Any registration measure must allow us to choose between transformation estimates based on the similarity of images within their volume of overlap. Since 3D medical images often have a limited extent and overlap, the similarity measure for the two transformation estimates may be derived from two very different regions within the images. Direct measures of information such as the joint entropy and mutual information will therefore be a function of, not only image similarity in the region of overlap, but also of the local image content within the overlap. In this paper we present a new measure, normalised mutual information, which is simply the ratio of the sum of the marginal entropies and the joint entropy. The effect of changing overlap on current entropy measures and this normalised measure are compared using a simple image model and experiments on clinical MR-PET and MR-CT image data. Results indicate that the normalised entropy measure provides significantly improved behaviour over a range of imaged fields of view.