5. The algebraic approaches and techniques in image analysis

Abstract

Summary form only given. Automation of image processing, analysis, estimating and understanding is one of the crucial points of theoretical computer science having decisive importance for applications, in particular, for diversification of solvable problem types and for increasing the efficiency of problem solving. Automation of image mining is one of the most important strategic goals in image analysis, recognition and understanding science and technologies. The main subgoals are developing and applying of mathematical theory for constructing image models accepted by efficient pattern recognition algorithms and for standardized representation and selection of image analysis transforms. Automation of image-mining is possible by combined application techniques for image analysis, understanding and recognition. The specificity, complexity and difficulties of image analysis and estimation (IAE) problems stem from necessity to achieve some balance between such highly contradictory factors as goals and tasks of a problem solving, the nature of visual perception, ways and means of an image acquisition, formation, reproduction and rendering, and mathematical, computational and technological means allowable for the IAE. The mathematical theory of image analysis is not finished and is passing through a developing stage. It is only recently came understanding of the fact that only intensive creating of comprehensive mathematical theory of image analysis and recognition (in addition to the mathematical theory of pattern recognition) could bring a real opportunity to solve efficiently application problems via extracting from images the information necessary for intellectual decision making. The transition to practical, reliable and efficient automation of image-mining is directly dependent on introducing and developing of mathematical means for IAE. During recent years there was accepted that algebraic techniques, in particular different kinds of image algebras, is the most prospective direction of construction of the mathematical theory of image analysis and of development of an universal algebraic language for representing image analysis transforms and image models