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There are various ways of measuring the conjectured similarity between two images. Mean-squared-differences or sum-of-squared-differences are rather poor methods of getting a useful measure of similarity if the images are far away. Therefore, such measures are often better off used when convergence is foreseen. There are also measure that are immune to large spatial displacements or variability in form. Histograms of the intensity values in the images, where intensity values are accounted for globally (or locally, inside regions that require greater emphasis), would be far better measures under most circumstances. Extra strategic steps, such as the removal of empty bins in such histograms, are taken to make the histograms more powerful indicators of similarity. Active research repeatedly reveals better algorithms as will be described in brevity below.
Although the correlation ratio is still occasionally used to measure similarity, it is less relevant to this report and goes back over half a century ago [30]. Mutual information and normalised mutual information, as described by Studholme, give good measures that see high usage in existing non-rigid registration algorithms. Each one will be dealt with in turn.