Completeness Conditions of a Class of Pattern Recognition Algorithms Based on Image Equivalence

  • Igor B. Gurevich
  • Irina A. Jernova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2905)


The paper presents recent results in establishing existence conditions of a class of efficient algorithms for image recognition problem including the algorithm that correctly solves this problem. The proposed method for checking on satisfiability of these conditions is based on the new definition of image equivalence introduced for a special formulation of an image recognition problem. It is shown that the class of efficient algorithms based on estimate calculation contains the correct algorithm in its algebraic closure. The main result is an existence theorem. The obtained theoretical results will be applied to automation of lymphoid tumor diagnostics by the use of hematological specimens.


  1. 1.
    Grenander, U.: General Pattern Theory. A Mathematical Study of Regular Structures. Clarendon Press, Oxford (1993)Google Scholar
  2. 2.
    Gurevich, I.B.: The Descriptive Framework for an Image Recognition Problem. In: Proc. of the 6th Scandinavian Conf. on Image Analysis, Oulu, Finland. Pattern Recognition Society of Finland, vol. 1, pp. 220–227 (1989)Google Scholar
  3. 3.
    Gurevich, I.B., Jernova, I.A., Smetanin, Y.G.: A Method of Image Recognition Based on the Fusion of Reduced Invariant Representations: Mathematical Substantiation. In: Kasturi, R., Laurendeau, D., Suen, C. (eds.) Proceedings of the 16th International Conference on Pattern Recognition (ICPR2002), Quebec, Canada, August 11-15. The Institute of Electrical and Electronics Engineers, Inc., vol. 4,3, pp. 391–394 (2002)Google Scholar
  4. 4.
    Gurevich, I.B., Smetanin, Y.G.: On the Equivalence of Images in Pattern Recognition Problems. In: Austvoll, I. (ed.) Proceedings of the 12th Scandinavian Conference on Image Analysis, Bergen, June 11-14. Norwegian Society for Image Processing and Pattern Recognition, pp. 679–685 (2001)Google Scholar
  5. 5.
    Gurevich, I.B., Zhuravlev, Y.I.: An Image Algebra Accepting Image Models and Image Transforms. In: Greiner, G., Niemann, H., Ertl, T., Girod, B., Seidel, H.-P. (eds.) Proceedings of the 7th International Workshop Vision, Modeling, and Visualization 2002 (VMV2002), Erlangen, Germany, November 20-22, pp. 21–26. IOS Press, Amsterdam (2002)Google Scholar
  6. 6.
    Mundy, J.L., Zisserman, A.: Towards a New Framework for Vision. In: Mundy, J., Zisserman, A. (eds.) Geometric invariance in computer vision, pp. 1–39 (1992)Google Scholar
  7. 7.
    Ritter, G.X., Wilson, J.N.: Handbook of Computer Vision Algorithms in Image Algebra, 2nd edn. CRC Press Inc., Boca Raton (2001)zbMATHGoogle Scholar
  8. 8.
    Serra, J.: Image Analysis and Mathematical Morphology. L. Academic Press, London (1982)zbMATHGoogle Scholar
  9. 9.
    Sternberg, S.R.: Language and Architecture for Parallel Image Processing. In: Proceedings of the Conference on Pattern Recognition in Practice, Amsterdam (1980)Google Scholar
  10. 10.
    Zhuravlev, Y.I.: An Algebraic Approach to Recognition or Classification Problems. Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications 8(1), 59–100 (1998)Google Scholar
  11. 11.
    Zhuravlev, Y.I., Gurevitch, I.B.: Pattern Recognition and Image Recognition. Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications in the USSR 1(2), 149–181 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Igor B. Gurevich
    • 1
  • Irina A. Jernova
    • 1
  1. 1.Scientific Council “Cybernetics” of the Russian Academy of SciencesMoscow GSP-1Russian Federation

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