Prototypes stability analysis in the design of a binning strategy for mutual information based medical image registration

The purpose of this paper is to develop and test a new approach for the selection of the number and size of bins of frequency histograms used for the evaluation of normalized mutual information. To design an efficient re-binning strategy, a notion of prototypes stability was introduced. Prototypes, which can be seen as representatives of the bins, need to be stable (i.e., they should not differ significantly in spite of small fluctuations occurring within the experimental data). In this work, prototypes stability analysis was used to find the number of clusters (or histogram bins) appropriate for normalized mutual information calculation. Once the number of bins was found, fuzzy c-means was used to achieve a natural clustering of the joint histogram. As a result, the normalized mutual information metric using variable binning was more robust to local maxima when compared to the traditional normalized mutual information with equidistant binning.