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Program-combinatorial approach to solving problems of error-free readout of random point images

  • Analysis and Synthesis of Signals and Images
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Optoelectronics, Instrumentation and Data Processing Aims and scope

Abstract

A novel approach is proposed for solving probability problems arising in studying reliability of readout of random point structures. The essence of this approach is based on combining specialized program-analytical and discrete-combinatorial methods of research seldom used in academic practice. The efficiency of the proposed approach is demonstrated by an example of solving a particular problem that involves two-threshold readout of random point images.

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References

  1. A. L. Reznik and V. M. Efimov, Computer Analytics and Generalized Catalan Numbers in Problems of Detection of Random Discrete Objects (Izd. Sib. Div. Ross. Akad. Nauk, Novosibirsk, 2013) [in Russian].

  2. A. L. Reznik, V. M. Efimov, A. A. Solov’ev, and A. V. Torgov, “Reliability of Readout of Random Point Fields with a Limited Number of Threshold Levels of the Scanning Aperture,” Avtometriya 50 (6), 61–68 (2014) [Optoelectron., Instrum. Data Process. 50 (6), 582–588 (2014)].

    Google Scholar 

  3. A. L. Reznik, V. M. Efimov, A. A. Solov’ev, and A. V. Torgov, “On the Reliable Readout of Random Discrete-Point Structures,” Patt. Recogn. Image Analys. Advances Math. Theory Appl. 25 (1), 84–88 (2015).

    Google Scholar 

  4. E. Parzen, Modern Probability Theory and Its Applications (John Wiley and Sons, New York, London, 1960).

    MATH  Google Scholar 

  5. S. S. Wilks, Mathematical Statistics (Wiley, New York, 1962).

    MATH  Google Scholar 

  6. A. L. Reznik, V. M. Efimov, and A. A. Solov’ev, “Computer-Analytical Calculation of the Probability Characteristics of Readout of Random Point Images,” Avtometriya 47 (1), 10–16 (2011) [Optoelectron., Instrum. Data Process. 47 (1), 7–11 (2011)].

    Google Scholar 

  7. A. L. Reznik, V. M. Efimov, A. Solov’ev, and A. V. Torgov, “Generalized Catalan Numbers in Problems of Processing of Random Discrete Images,” Avtometriya 47 (6), 11–15 (2011) [Optoelectron., Instrum. Data Process. 47 (6), 533–536 (2011)].

    Google Scholar 

  8. D. Zeilberger, “Andre’s Reflection Proof Generalized to the Many-Candidates Ballot Problem,” Discrete Math. 44 (3), 325–326 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  9. I. M. Gessel and D. Zeilberger, “Random Walk in a Weyl Chamber,” Proc. Amer. Math. Soc. 115 (1), 27–31 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  10. D. André, “Solution Directe du Problème Résola par M. Bertrand,” Comptes Rendus de l’Académie des Sciences 105, 436–437 (1887).

    Google Scholar 

  11. A. L. Reznik, V. M. Efimov, and A. A. Solov’ev, “Estimation of Reliability of Readout of Random Discrete Images with the Use of Computer Analytics Tools,” Vestnik NGU. Ser. Fizika 5 (2), 104–110 (2010).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 1, Novosibirsk, 630090, Russia

    A. L. Reznik, A. A. Solov’ev & A. V. Torgov

Authors
  1. A. L. Reznik
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  2. A. A. Solov’ev
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  3. A. V. Torgov
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Corresponding author

Correspondence to A. L. Reznik.

Additional information

Original Russian Text © A.L. Reznik, A.A. Solov’ev, A.V. Torgov, 2016, published in Avtometriya, 2016, Vol. 52, No. 2, pp. 20–27.

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Reznik, A.L., Solov’ev, A.A. & Torgov, A.V. Program-combinatorial approach to solving problems of error-free readout of random point images. Optoelectron.Instrument.Proc. 52, 121–127 (2016). https://doi.org/10.3103/S8756699016020035

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  • DOI: https://doi.org/10.3103/S8756699016020035

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