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Optical Area Correlation with Magnification and Rotation

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Abstract

A relationship exists between the autocorrelation function of a pictorial image and the cross-correlation function of the image and a magnified or rotated copy of it. This relationship is derived under the assumption that the image is a stationary isotropic function of transmittance or reflectance. The derived relationship is used to calculate the cross-correlation functions of scenes possessing exponential autocorrelation peaks with different widths, for varying degrees of rotation and magnification. These cross-correlation functions are measured on actual aerial scenes which have nearly exponential autocorrelation peaks. The results are compared with computed values and the changes induced in the correlation peak are found to agree qualitatively with the calculations.

© 1970 Optical Society of America

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Corrections

Martin J. Lahart, "Erratum," J. Opt. Soc. Am. 61, 985_1-985 (1971)
https://opg.optica.org/josa/abstract.cfm?uri=josa-61-7-985_1

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Equations (24)

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