Automation of Eye Disease Diagnoses Using Descriptive Image Algebras and Boolean Algebra Methods

Abstract

The article presents an algebraic model for solving the problem of automation of ophthalmological diagnostics written in the language of descriptive image algebras. Descriptive image algebras are an initial mathematical language for formalizing and standardizing representations and procedures for processing image models and conversions over them when extracting information from images. To construct an algebraic model for solving the problem of automation of ophthalmological diagnostics, descriptive algebras of images with one ring are mainly used. This class of algebras belongs to the class of universal linear algebras with a sigma-associative ring with identity. A series of conversions and steps of the algebraic model are described using descriptive Boolean algebras over images. Descriptive image algebras are the main section of the mathematical apparatus of descriptive image analysis, which is a logically organized set of descriptive methods and models designed for image analysis and evaluation. The article defines specialized versions of descriptive image algebras with one ring and descriptive Boolean algebras over images, over models and representations of images, and over conversions of image models and images themselves, necessary for constructing an algebraic model. The image models (representations, formalized descriptions) used in writing the article are described. An example of a descriptive algorithmic scheme for solving an applied ophthalmological problem using an algebraic model is constructed.