The degradation in acquisition probability that occurs when cross correlation is used to determine the offset of two images of the same scene thatIdiffer 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 autocorrelation functions. The results are illustrated for images with Gaussian autocorrelation functions.
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