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The degradation in acquisition probability that occurs when cross correlation is used to determine the offset of two images of the same scene that differ by a relative geometric distortion is presented. The geometric distortions considered can be represented by a general affine transformation of image coordinates. The analysis shows that for a given geometric distortion there is an image size and shape that minimizes the probability of false acquisition. The results are derived for images modeled as random patterns with arbitrary auto-correlation functions. The results are illustrated for images with Gaussian autocorrelation functions.
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Mostafavier et al. (1978) studied this question.
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