Current Trends in Mathematical Image Analysis A Survey

摘要

The main task of the survey is to explain and discuss the opportunities and limitations of algebraic approaches in image analysis. 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 an universal algebraic language for representing image analysis transforms and image models. The main goal of the Algebraic Approach is designing of a unified scheme for representation of objects under recognition and its transforms in the form of certain algebraic structures. It makes possible to develop corresponding regular structures ready for analysis by algebraic, geometrical and topological techniques. 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 classes and types of solvable problems and for essential increasing of solution efficiency and quality.