Descriptive image analysis: Genesis and current trends

This paper is devolved to descriptive image analysis, an important, if not a leading, direction in the modern mathematical theory of image analysis. Descriptive image analysis is a logically organized set of descriptive methods and models meant for analyzing and estimating the information represented in the form of images, as well as for automating the extraction (from images) of knowledge and data needed for intelligent decision making about the real-world scenes reflected and represented by images under analysis. The basic idea of descriptive image analysis consists in reducing all processes of analysis (processing, recognition, and understanding) of images to (1) construction of models (representations and formalized descriptions) of images; (2) definition of transformations over image models; (3) construction of models (representations and formalized descriptions) of transformations over models and representations of images; and (4) construction of models (representations and formalized descriptions) of schemes of transformations over models and representations of images that provide the solution to image analysis problems. The main fundamental sources that predetermined the origination and development of descriptive image analysis, or had a significant influence thereon, are considered. In addition, a brief description of the current state of descriptive image analysis that reflects the main results of the descriptive approach to analysis and understanding of images is presented. The opportunities and limitations of algebraic approaches to image analysis are discussed. During recent years, it was accepted that algebraic techniques, particularly, different kinds of image algebras, are the most promising direction of construction of the mathematical theory of image analysis and of the development of a universal algebraic language for representing image analysis transforms, as well as image representations and models. The main goal of the algebraic approaches is designing a unified scheme for representation of objects under recognition and its transforms in the form of certain algebraic structures. This makes it possible to develop the corresponding regular structures ready for analysis by algebraic, geometrical, and topological techniques. The development of this line of image analysis and pattern recognition is of crucial importance for automatic image mining and application problems solving, in particular, for diversification of the classes and types of solvable problems, as well as for significant improvement of the efficiency and quality of solutions. The main subgoals of the paper are (1) to set forth the-state-of-the-art of the mathematical theory of image analysis; (2) to consider the algebraic approaches and techniques suitable for image analysis; and (3) to present a methodology, as well as mathematical and computational techniques, for automation of image mining on the basis of the descriptive approach to image analysis (DAIA). The main trends and problems in the promising basic researches focused on the development of a descriptive theory of image analysis are described.