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Measures of image similarity that inspect the intensity probability distribution of the images have proved extremely popular in image registration applications. The joint entropy of the intensity distributions and the marginal entropies of the individual images are combined to produce properties such as resistance to loss of information in one image and invariance to changes in image overlap during registration. However information theoretic cost functions are largely used empirically. This work attempts to describe image similarity measures within a formal mathematical metric framework. Redefining mutual information as a metric is shown to lead naturally to the standardised variant, normalised mutual information. © 2010 Copyright SPIE - The International Society for Optical Engineering.

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