Conditions of Generating Descriptive Image Algebras by a Set of Image Processing Operations

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


It is outlined new results of investigations into development of mathematical tools for analysis and estimation of information represented by images. It continues research of a new class of image algebras (IA) – the Descriptive Image Algebras (DIA). Practical implementation of DIA in image analysis applications requires a study of a set of operations, leading or not leading to DIA construction, having or not having physical interpretation. Operations of the ring in these algebras are both standard algebraic operations and special operations of image processing and transformation. The problem of operations that can be used for construction of DIA and of how this possibility is connected with physical interpretation of corresponding algebra operations is still open. This problem is reduced to formulation of the conditions that should be satisfied by a set of operations for construction of the DIA. The first stage of its solution is the construction of the examples of the sets of operations (having physical meaning), leading or not leading to DIA construction. The basic results of the report are both the method of testing the specified conditions and the examples of sets with various elements and the operations introduced on them (both generating algebras and not).


  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., Smetanin, Y.G., Zhuravlev, Y.I.: Descriptive Image Algebras: Determination of the Base Structures. Pattern Recognition and Image Analysis 9(4), 635–647 (1999)Google Scholar
  4. 4.
    Ritter, G.X., Wilson, J.N.: Handbook of Computer Vision Algorithms in Image Algebra, 2nd edn. CRC Press Inc., Boca Raton (2001)zbMATHGoogle Scholar
  5. 5.
    Van Der Waerden, B.L.: Algebra I,II. Springer, Heidelberg (1971, 1967) (in Russian)Google Scholar
  6. 6.
    Zhuravlev, Y.I.: Correct Algebras Over Sets of Incorrect (Heuristic) Algorithms. Cybernetics (Kiev) (4), 14–21 (1977); (6), 21–27 (1977); (2), 35–42 (1978) (in Russian) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Igor B. Gurevich
    • 1
  • Vera Yashina
    • 1
  1. 1.Scientific Council “Cybernetics” of the Russian Academy of SciencesMoscow GSP-1Russian Federation

Personalised recommendations