This paper discusses how the mutual spatial transformation of local segments of images affects the result of their phase correlation. The equations obtained for the noise of the cross-correlation field caused by scale mismatch of segments of the images or their relative rotation make it possible to estimate the allowable values of the coefficients of a mutual affine transformation for which the relative displacement of the segments can be reliably determined from the correlation peak. An estimate is given of the accuracy with which this displacement is determined. Based on this analysis, filtering of the spectra of the images is proposed that makes it possible to broaden the allowable range of parameters of the mutual spatial transformation. The results were applied in practice in the local-correlation method described earlier. © 2004 Optical Society of America

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