{"title":"Automation of Eye Disease Diagnoses Using Descriptive Image Algebras and Boolean Algebra Methods","authors":"I. B. Gurevich, V. V. Yashina","doi":"10.1134/s1054661824700093","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":35400,"journal":{"name":"PATTERN RECOGNITION AND IMAGE ANALYSIS","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"PATTERN RECOGNITION AND IMAGE ANALYSIS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1054661824700093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The purpose of the journal is to publish high-quality peer-reviewed scientific and technical materials that present the results of fundamental and applied scientific research in the field of image processing, recognition, analysis and understanding, pattern recognition, artificial intelligence, and related fields of theoretical and applied computer science and applied mathematics. The policy of the journal provides for the rapid publication of original scientific articles, analytical reviews, articles of the world''s leading scientists and specialists on the subject of the journal solicited by the editorial board, special thematic issues, proceedings of the world''s leading scientific conferences and seminars, as well as short reports containing new results of fundamental and applied research in the field of mathematical theory and methodology of image analysis, mathematical theory and methodology of image recognition, and mathematical foundations and methodology of artificial intelligence. The journal also publishes articles on the use of the apparatus and methods of the mathematical theory of image analysis and the mathematical theory of image recognition for the development of new information technologies and their supporting software and algorithmic complexes and systems for solving complex and particularly important applied problems. The main scientific areas are the mathematical theory of image analysis and the mathematical theory of pattern recognition. The journal also embraces the problems of analyzing and evaluating poorly formalized, poorly structured, incomplete, contradictory and noisy information, including artificial intelligence, bioinformatics, medical informatics, data mining, big data analysis, machine vision, data representation and modeling, data and knowledge extraction from images, machine learning, forecasting, machine graphics, databases, knowledge bases, medical and technical diagnostics, neural networks, specialized software, specialized computational architectures for information analysis and evaluation, linguistic, psychological, psychophysical, and physiological aspects of image analysis and pattern recognition, applied problems, and related problems. Articles can be submitted either in English or Russian. The English language is preferable. Pattern Recognition and Image Analysis is a hybrid journal that publishes mostly subscription articles that are free of charge for the authors, but also accepts Open Access articles with article processing charges. The journal is one of the top 10 global periodicals on image analysis and pattern recognition and is the only publication on this topic in the Russian Federation, Central and Eastern Europe.
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