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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)

Abstract

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.

Keywords

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 

Notes

Acknowledgment

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

References

  1. 1.
    Grenander, U., Miller, M.: Pattern Theory: From Representation to Inference. Oxford Studies in Modern European Culture. Oxford University Press, Oxford (2007)zbMATHGoogle Scholar
  2. 2.
    Gurevich, I.B., Yashina, V.V.: Computer-aided image analysis based on the concepts of invariance and equivalence. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 16(4), 564–589 (2006)CrossRefGoogle Scholar
  3. 3.
    Gurevich, I.B., Yashina, V.V.: Operations of descriptive image algebras with one ring. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 16(3), 298–328 (2006)CrossRefGoogle Scholar
  4. 4.
    Gurevich, I.B., Yashina, V.V., Koryabkina, I.V., Niemann, H., Salvetti, O.: Descriptive approach to medical image mining. An algorithmic scheme for analysis of cytological specimens. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 18(4), 542–562 (2008)CrossRefGoogle Scholar
  5. 5.
    Gurevich, I.B., Yashina, V.V.: Descriptive approach to image analysis: image formalization space. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 22(4), 495–518 (2012)CrossRefGoogle Scholar
  6. 6.
    Gurevich, I.B., Yashina, V.V.: Descriptive image analysis. foundations and descriptive image algebras. Int. J. Pattern Recogn. Artif. Intell. 33(12), 25 p. (2019)CrossRefGoogle Scholar
  7. 7.
    Gurevich, I.B., Yashina, V.V.: On the interpretability of operations of descriptive image algebras. In: Proceedings of 14th International Conference on Pattern Recognition and Information Processing, Minsk, “Bestprint”, pp. 159–163 (2019)Google Scholar
  8. 8.
    Gurevich, I.B., Yashina, V.V.: Algebraic interpretation of image analysis operations. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 29(3), 389–403 (2019)CrossRefGoogle Scholar
  9. 9.
    Gurevich, I.B., Yashina, V.V.. Descriptive image analysis. II. descriptive image models. Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications 29(4) (2019)Google Scholar
  10. 10.
    Haralick, R.M., Sternberg, S.R., Zhuang, X.: Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987)CrossRefGoogle Scholar
  11. 11.
    Ritter, G.X., Wilson, J.N.: Handbook of Computer Vision Algorithms in Image Algebra, 2nd edn. CRC Press Inc., Boca Raton (2001)zbMATHGoogle Scholar
  12. 12.
    Zhuravlev Yu.I.: an algebraic approach to recognition and classification problems. Pattern Recogn. Image Anal.: Adv. Math. Theory Appl. 8, 59–100 (1998)Google Scholar

Copyright information

© 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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