Pattern Recognition and Image Analysis

, Volume 28, Issue 4, pp 737–746 | Cite as

On Recognition of Graphs and Images

  • V. K. LeontievEmail author
  • E. N. Gordeev
Representation, Processing, Analysis, and Understanding of Images


This paper discusses the possibility of using the classical results of graph theory related to reconstruction and recognition of graphs and their characteristics in the field of image recognition. Two heuristic approaches are proposed to estimate the adequacy of object images. Various aspects of the problem of graph description (representation) with the use of graph invariants are analyzed. New classes of invariants that can be used to construct the heuristics mentioned above are introduced and investigated. In addition, some statements concerning two aspects of the problem—the formation of complex invariants taking into account the basic and functional dependences among invariants—are proved.


recognition feature tables heuristics reconstruction graph graph invariant chromatic number independence number external stability number and internal stability number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yu. I. Zhuravlev, “On an algebraic approach to the solution of pattern recognition and classification problems,” Problemy Kibernet. No. 33, 5–68 (1978) [in Russian].Google Scholar
  2. 2.
    K. V. Rudakov and I. Yu. Torshin, “Selection of informative feature values on the basis of solvability criteria in the problem of protein secondary structure recognition,” Dokl. Math. 84 (3), 871–874 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    I. Yu. Torshin and K. V. Rudakov, “On the application of the combinatorial theory of solvability to the analysis of chemographs. Part 1: Fundamentals of modern chemical bonding theory and the concept of the chemograph,” Pattern Recogn. Image Anal. 24 (1), 11–23 (2014).CrossRefGoogle Scholar
  4. 4.
    I. Yu. Torshin and K. V. Rudakov, “On the application of the combinatorial theory of solvability to the analysis of chemographs. Part 2: Local completeness of invariants of chemographs in view of the combinatorial theory of solvability,” Pattern Recogn. Image Anal. 24 (2), 196–208 (2014).CrossRefGoogle Scholar
  5. 5.
    M. Gary and D. Johnson, Computers and Intractability: A Guide to the Theory of NP–Completeness (Freeman, New York, 1979; Mir, Moscow, 1982).Google Scholar
  6. 6.
    W. T. Tutte, Graph Theory (Cambridge Univ. Press, 2001; Mir, Moscow, 1988).Google Scholar
  7. 7.
    A. A. Zykov, Fundamentals of Graphs Theory (Nauka, Moscow, 1986; BCS Associates, Moscow, ID, 1990).zbMATHGoogle Scholar
  8. 8.
    Ye. A. Smolenskii, “A method for the linear recording of graphs,” USSR Comput. Math. Math. Phys. 2 (2), 396–397 (1963).MathSciNetCrossRefGoogle Scholar
  9. 9.
    K. A. Zaretskii, “Constructing a tree on the basis of a set of distances between the hanging vertices,” Uspehi Mat. Nauk 20 (6), 90–92 (1965) [in Russian].MathSciNetGoogle Scholar
  10. 10.
    V. K. Leontiev, Combinatorics and Information (Mosk. Fiz.–Tekh. Inst., Moscow, 2015) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Computer Science and Control Federal Research CenterRussian Academy of SciencesMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

Personalised recommendations