Recognition of Geometric Images by Linguistic Method

Abstract

Image recognition is currently one of the fastest-growing areas in applied mathematics. Of the many methods for solving problems in this area, the grammatical (linguistic) method of pattern recognition is the least studied. The essence of the grammar method is to construct appropriate grammar for object classes. In this case, the object recognition problem is related to the language generated by the given grammar. Using the linguistic method, an algorithm and software for recognizing geometric images have been developed. While the development the following tasks were solved. Methods have been developed for describing geometric images (triangles, squares, polygons) and corresponding grammars have been constructed for them so that the chains generated by this grammar represent objects of this class. The problems of constructing given classes of geometric images, as well as constructing a grammar for each class, are solved.

At the training stage, classes are considered, each of which is described by a finite set of chains. To classify a new image, that is, to determine which class it belongs to, a parsing of the corresponding chain of this image was performed using grammars. Thus, the belonging of the chain to the language born by this grammar was clarified.