Abstract

This paper considers an algebraic method of digital images processing, based on the representation of images as functions on "finite complex planes" called complex discrete tori. Properties of such tori are studied; in particular, the concept of complex rotation of a digital image is introduced. The concept of modular logarithm is introduced and used to define a new invertible discrete transform called modular Mellin transform. Next, the modular Fourier-Mellin transform, which is invariant under circular shifts, scaling, and complex rotations of digital images, is defined.

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