Abstract
This paper is devoted to the study of the key concepts of the mathematical theory of image recognition—the invariance and equivalence of images. To provide a computer-aided choice of invariants for constructing partial descriptions of images, a classification of invariants is proposed that takes into account the basic features of invariants and systematizes their properties. Group invariants, methods for constructing invariants, and various image invariants are described. Various methods for determining equivalence on the set of images are considered. The relation between equivalence and invariance of images is analyzed. It is proved that, under certain constraints on image transformations, the problem of image recognition in the standard statement can be reduced to a problem for which there exists a correct algorithm within the algebraic closure of algorithms for calculating estimates.
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