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The authors present image descriptors and spatial filters based on the circular Fourier and radial Mellin transforms. The Fourier-Mellin descriptors have advantage in terms of the noise sensitivity. The Fourier-Mellin filters generate the shift invariant Fourier-Mellin transforms optically. An opto-neural system using the Fourier-Mellin filters and a back-propagation neural network shows shift, scale and rotation invariant pattern recognition.
Sheng et al. (Sun,) studied this question.