The article continues development of the descriptive theory of image analysis proposed by the authors and opens a series of articles that will characterize the image formalization space as a mathematical object—a mathematical space. The main prerequisite for effective and, in general, practically feasible automation of image analysis and recognition in solving applied diagnostics, identification, detection, intelligent decision-making, and forecasting problems in the case of using images in the initial data is the construction and use of formalized image representations—descriptive image representations and descriptive image models. The image formalization space was introduced and defined with the aim of formalizing and standardizing the description of all admissible states and procedures involved in reducing images to a form convenient for recognition, in the form of a single model corresponding to a certain mathematical space, and allowing its implementation in it. This article (1) presents and analyzes the axioms of the descriptive theory of image analysis that underlie the definition of the image formalization space; (2) defines the problems arising in constructing a mathematical model of the image formalization space in a standard mathematical space (metric, topological, phase); (3) considers the necessary conditions that should be satisfied by models of the image formalization space when implemented in the corresponding standard mathematical space.
Gurevich et al. (Mon,) studied this question.