Mathematical formalization of transformations in transmission via channels of telecommunication systems of graphic images

The paper considres one of the problems of representation of graphical information in intelligent telecommunication systems, images first of all. An outline analysis scheme is proposed, in which the sequence of transformation groups is ordered by the group-over-group relationship. The advantages of this scheme are briefly described. The description of transformations of graphic images is given at transmittion via telecommunication channels. A mathematical formalization of these transformations is described, including identical transformations, translations, centrifugal rotations, central-affine-axial bicompressions, motions, and non-reflex affine transformations. The properties of structural elements for various basic transformation groups are formulated. It is noted that mathematically formalized analysis of transformations makes it possible to carry out a structural description of graphic images with their geometric-topological properties, characteristics and interrelations, which is important, for example, when organizing the transmittion of graphic images through the channels of telecommunication systems and when compressing images during this transmittion.