Irrelation of Mathematical and Functional Aspects of Descriptive Image Algebras with One Ring Operations Interpretability

  • Igor Gurevich
  • Vera YashinaEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1055)


The study is continued investigation of 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. The interpretation is considered as a transition from a meaningful description of the operation to its mathematical or algorithmic implementation. The main types of interpretability are defined, and examples of interpretability of operations of the descriptive image algebras with one ring, are given.


Computer Vision Descriptive Image Algebras Algebraic Interpretation Physical, semantic, and Functional Interpretability of Image Processing Operations Interpretation Domains of Operations Interpretability of Operations Image Analysis, Recognition, and Processing Automated Image-mining 



This work was supported in part by the Russian Foundation for Basic Research (Project No. 18-57-00013).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussian Federation

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