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Mutual Information (MI)

Viola [] has developed a way^3.17 of finding and measuring the similarity between two images or more by repeatedly comparing pairs of images. This ability to compare images is crucial for registration of images as it robustly and accurately returns an estimate of the beneficialness of the warps applied. Chapter deals with the introduction of information theory and some of the basic measures which can explain the following in more detail. However, it is the principle that is worth understanding at this stage, rather than tedious technicality [,].

Mutual information [WWW-13] computes volumes of overlap in images. If two images are matched, the joint histogram is then expected to give an indication of where sharp grey-value peaks are located and the sharpness value of these peaks. Under the converse case which is mis-registration, the joint histogram is then expected to show peaks of low sharpness and new peaks can emerge. The algorithms and advanced information theoretic expressions that take advantage of this observation are at this stage left out entirely. At this point, it is only worth defining a joint information (or entropy) to be $H(A,B)$ and state that MI calculates $H(A)+H(B)-H(A,B)$. This means that joint information is subtracted from the sum of information present in the two individual images.