Image Similarity Metrics in Image Registration

Measures of image similarity that inspect the intensity probability distribution of the images have proved ex-tremely 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. Description of Purpose The use of image similarity measures that inspect the intensity distribution of each of the images has proved successful for many image alignment procedures. The combination of the Shannon entropies of the individual and joint image histograms into mutual information was discussed independently by Viola and Wells1 and Maes2. A popular normalised variant was also proposed that the authors claim is more robust to changes in image overlap, although a full theoretical justification is not given3. However, neither of these measures is strictly a metric. A later survey of the growth of image registration procedures using mutual information or its variants was produced by Pluim et al4 and later extended5. It is normally assumed that pixel intensity values in an imag