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Picture processing and alteration for the purpose of quantification and map matching are discussed and the mathematics thereof derived. The statistics of such pictures, reduced to a black-and-white state, are developed. The theoretical derivation of the autocorrelation and crosscorrelation of any two-level pictures is described on the basis of their measured statistics. The importance of such correlation to scene classification and to map matching for the purposes of navigation and homing guidance is shown. The effects of various types of noise that may corrupt one or both copies of the pictures to be correlated are assessed. Finally, the validity of the theory is demonstrated by applying it to specific cases of synthetic radar maps as well as to other displays.