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01-07-2019 | REPRESENTATION, PROCESSING, ANALYSIS, AND UNDERSTANDING OF IMAGES | Issue 3/2019

Pattern Recognition and Image Analysis 3/2019

Algebraic Interpretation of Image Analysis Operations

Journal:
Pattern Recognition and Image Analysis > Issue 3/2019
Authors:
I. B. Gurevich, V. V. Yashina
Important notes
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Igor B. Gurevich. Born August 24, 1938. Dr.-Eng. diploma engineer (automatic control and electrical engineering), 1961, National Research University “Moscow Power Engineering Institute, Moscow, USSR; Dr. (mathematical cybernetics), 1975, Moscow Institute of Physics and Technology (State University), Moscow, USSR. Leading researcher at the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, the Russian Federation. He has worked from 1960 till now as an engineer and researcher in industry, medicine, and universities, and from 1985 in the USSR/Russian Academy of Sciences. Area of expertise: mathematical theory of image analysis, image-mining, image understanding, mathematical theory of pattern recognition, theoretical computer science, medical informatics, applications of pattern recognition and image analysis techniques in biology, medicine and in automation of scientific research, and knowledge-based systems.
I.B. Gurevich suggested, proved and developed with his pupils the descriptive approach to image analysis and recognition (DAIA). Within DAIA a new class of image algebra was introduced, defined and investigated (descriptive image algebras); new types of image models were introduced, classified and investigated; axioms of descriptive theory of image analysis were introduced; a common model of image recognition process was defined and investigated; new settings of image analysis and recognition problems were introduced; a notion “image equivalence” was introduced and investigated; new classes of image recognition algorithms were defined and investigated; an image formalization space was introduced, defined and investigated.
Listed results were used in development of software kits for image analysis and recognition and for solution of important and difficult applied problems of automated bio-medical image analysis.
I.B. Gurevich is an author of 2 monographs and of 301 papers in peer reviewed journals and proceedings indexed in Web of Science, Scopus and Russian Science Citation Index on the platform of Web of Science, 31 invited papers at international conferences, holder of 7 patents. Web of Science: 22 papers; SCOPUS: 70 papers, 214 citations in 125 documents; Hirsh index is 8; Russian Science Citation Index on the platform of Web of Science: 84 papers; 426 citations; Hirsh index is 7.
Vice-Chairman of the National Committee for Pattern Recognition and Image Analysis of the Presidium of the Russian Academy of Sciences, Member of the International Association for Pattern Recognition (IAPR) Governing Board (representative from RF), IAPR Fellow. He has been the PI of 62 R&D projects as part of national and international research programs. Vice-Editor-in-Chief of the “Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications” international journal of the RAS, member of editorial boards of several international scientific journals, member of the program and technical committees of many international scientific conferences. Teaching experience: Moscow Lomonosov State University, RF (assistant professor), Dresden Technical University, Germany (visiting professor), George Mason University, USA (research fellow). He was supervisor of 6 PhD students and many graduate and master students.
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Vera V. Yashina. Born 13.09.1980. Diploma mathematician, Moscow Lomonosov State University (2002). Dr. (Theoretical Foundations of Informatics), 2009, Dorodnicyn Computing Center of the Russian Academy of Sciences, Moscow. Leading researcher at the Department “Recognition, security and analysis of information” at the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, the Russian Federation. She has worked from 2001 until now in the Russian Academy of Sciences. Scientific expertise: mathematical theory of image analysis, image algebras, models and medical informatics.
The main results were obtained in mathematical theory of image analysis: descriptive image algebras with one ring were defined, classified and investigated; a new topological image formalization space was specified and investigated; descriptive generating trees were defined, classified and investigated. Listed results were applied in bio-medical image analysis.
She is scientific secretary of the National Committee for Pattern Recognition and Image Analysis of the Presidium of the Russian Academy of Sciences. She is a member of the Educational Committee of the International Association for Pattern Recognition. She has been the member of many R&D projects as part of national and international research programs. Member of editorial board of “Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications” international journal of the RAS. Author of 77 papers in peer reviewed journals, conference and workshop proceedings. Web of Science: 11 papers; Hirsh index is 4; SCOPUS: 31 papers, 98 citations; Hirsh index is 7; Russian Science Citation Index on the platform of Web of Science: 42 papers; 97 citations; Hirsh index is 7. She was awarded several times for the best young scientist papers presented at the international conferences. Teaching experience: Moscow State Lomonosov University, RF. She was supervisor of several graduate and master students.

Abstract

The study is devoted to mathematical and functional/physical interpretation of image analysis and processing operations used as sets of operations (ring elements) in descriptive image algebras (DIA) with one ring. The main result is the determination and characterization of interpretation domains of DIA operations: image algebras that make it possible to operate with both the main image models and main models of transformation procedures that ensure effective synthesis and realization of the basic procedures involved in the formal description, processing, analysis, and recognition of images. The applicability of DIAs in practice is determined by the realizability—the possibility of interpretation—of its operations. Since DIAs represent an algebraic language for the mathematical description of image processing, analysis, and understanding procedures using image transformation operations and their representations and models, the authors consider an algebraic interpretation. These procedures are formulated and implemented in the form of descriptive algorithmic schemes (DAS), which are correct expressions of the DIA language. The latter are constructed from the processing and transformation of images and other mathematical operations included in the corresponding DIA ring. The mathematical and functional properties of DIA operations are of considerable interest for optimizing procedures of processing and analyzing images and constructing specialized DAS libraries. Since not all mathematical operations have a direct physical equivalent, the construction of an efficient DAS for image analysis involves the problem of interpreting operations for DAS content. Research into this problem leads to the selection and study of interpretation domains of DIA operations. The proposed method for studying the interpretability of DIA operations is based on the establishment of correspondence between the content description of the operation function and its mathematical realization. The main types of interpretability are defined and examples given of the interpretability/uninterpretability of operations of a standard image algebra, which is a restriction of the DIA with one ring.

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