On the accuracy of approximations in the error analysis of registration systems

The similarity functions used to register images are often approximated for the purposes of statistical analysis. An extension of a theorem for one-dimensional signals is presented that can assess the effects of approximations used in the statistical analysis of a registration system. The extended theorem facilitates the selection of an approximation that is sure to yield a pessimistic, or, if so preferred, an optimistic, variance of registration error. This method can be applied to a broad class of similarity functions that includes cross-correlation-based and linear-filter-based similarity functions.<
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