Revisiting overlap invariance in medical image alignment

In Studholme et al. introduced normalized mutual information (NMI) as an overlap invariant generalization of mutual information (MI). Even though Studholme showed how NMI could be used effectively in multimodal medical image alignment, the overlap invariance was only established empirically on a few simple examples. In this paper, we illustrate a simple example in which NMI fails to be invariant to changes in overlap size, as do other standard similarity measures including MI, cross correlation (CCorr), correlation coefficient (CCoeff), correlation ratio (CR), and entropy correlation coefficient (ECC). We then derive modified forms of all of these similarity measures that are proven to be invariant to changes in overlap size. This is done by making certain assumptions about background statistics. Experiments on multimodal rigid registration of brain images show that 1) most of the modified similarity measures outperform their standard forms, and 2) the modified version of MI exhibits superior performance over any of the other similarity measures for both CT/MR and PET/MR registration.