Differential-spectral shift-invariant image representation as applied to the Fourier–Mellin method

Потапов А.С., Аверкин А.Н. Дифференциально-спектральное инвариантное к сдвигу представление изображений применительно к методу Фурье-Меллина // Оптический журнал. 2010. Т. 77. № 4. С. 19–25.

Potapov A.S., Averkin A.N. Differential-spectral shift-invariant image representation as applied to the Fourier–Mellin method [in Russian] // Opticheskii Zhurnal. 2010. V. 77. № 4. P. 19–25.

A. S. Potapov and A. N. Averkin, "Differential-spectral shift-invariant image representation as applied to the Fourier–Mellin method," Journal of Optical Technology. 77(4), 239-244 (2010). https://doi.org/10.1364/JOT.77.000239

This paper proposes a new shift-invariant image representation, based on the operation of differentiation of the phase component of the spectrum, to replace the traditionally used operation, which totally eliminates phase information. The new representation is used to modify the Fourier-Mellin method, which is intended for the comparison of images in which a relative geometrical transformation from the similarity group is present. A sample of pairs of aerospace images is used to establish that it is more reliable to compare images by the new method, because it preserves significant information concerning the image, contained in the phase component of the spectrum.