Some Problems of Structural Analysis of Complex Patterns,
Abstract
The paper presents an outline of problems associated with a structural analysis and description of complex patterns for which so-called 'compactness hypothesis' does not hold. On the base of the general theory of relations, a series of concepts is formulated. They make possible to determine algebraic relationships existing for relations describing special features of patterns to be recognized. Especially, such concepts as conjunction, alternation, Cartesian product, projection, relation convolution and conditional relation are discussed. These concepts are illustrated by examples connected with the recognition of planar graphical patterns. Moreover, some relations existing for describing structures are considered. In particular, such concepts as over-, sub- and quasi-isomorphism and homeomorphism of structures are formulated. The paper gives a principle of a simplified structure description by means of a graph which illustrates logic implications holding for relations in a given structure. At the end, some problems related to the selection of structures which describe patterns are presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 21, 1971
- Accession Number
- AD0887943
Entities
People
- Juliusz Lech Kulikowski
Organizations
- National Air and Space Intelligence Center