Pattern Analysis of Multidimensional Digital Spaces, Homotopy Theory Approach

Abstract

Large scale and very large scale systems are considered in computer sciences, economics, ecology, biology, engineering, cybernetics and many other areas. Interconnection of their elements, sels or subsystems and complexity of their topological structure is not less important than their quantative characteristics or parameters. In this paper we give brief review of topological methods of pattern analysis of n-dimensional digital images in finite spaces, which was presented on two previous SMS conferences and in some other publications, New properties of digital fundamental group, which are important for their calculation, are investigated. Digital fundamental group of product spaces is calculated through fundamental group of multipliers. Some other higher dimensional invariants of finite digital spaces are considered and their application to pattern analysis is investigated. These methods of algebraic topological shape analysis uniquely characterize digital patterns with precision to homotopy equivalence. It shows that pattern analysis has to be conducted on interdisciplinary basis.