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Application of the principle of maximum likelihood to the problem of image registration is shown to yield an optimum process which is analogous to that of conventional cross correlation but in which the product function is replaced by a new function that has been called the `likelihood correlationÂ¿ function. This function is defined by the separate and joint probability distributions of the contents of the two pictures to be registered. The form of the likelihood correlation function is particularly simple in two special cases of practical interest and a suitable embodiment is described. It is shown that a number of algorithms described in the literature are special cases of the likelihood correlation function. Possible embodiments of this function in the general case are outlined. It is suggested that the likelihood correlation function has wider applicability than just for image registration.