Mode Extraction by Multivalue Morphology for Cluster Analysis

  • A. Sbihi
  • J.-G. Postaire
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The new statistical approach to unsupervised pattern classification, developed in this paper, consists to extending the multivalue morphological concepts to multidimensional functions in order to detect the modes of the underlying probability density function, particularly when no a priori information is available as to the number of clusters and their distribution.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    DEVIJVER, P.A. et KITTLER, J. (1982) Pattern recognition: A statistical approach. Prentice-Hall, Englewood Cliffs, 448Google Scholar
  2. [2]
    GITMAN, I. (1973) An algorithm for nonsupervised pattern classification. IEEE Trans. Syst. Man. Cybern., SCM-3, 66–74Google Scholar
  3. [3]
    FUKUNAGA, K. et HOSTLER, L.D. (1975) The estimation of the gradient of a density function with applications in pattern recognition. IEEE Trans. Inf. Theory, IT-21, 1, 32–40CrossRefGoogle Scholar
  4. [4]
    KITTLER J. (1976) A local sensitive method for cluster analysis. Pattern Recognition, 8, 23–33CrossRefGoogle Scholar
  5. [5]
    VASSEUR, C.P.A. et POSTAIRE, J.G. (1980) A convexity testing method for cluster analysis. IEEE Trans. Syst. Man. Cyber., SMC-10, 3, 145–179Google Scholar
  6. [6]
    VASSEUR, C.P.A. et POSTAIRE, J.G. (1981) An approximate solution to normal mixture identification with application to unsupervised pattern classification. IEEE Trans. Pattern Anal. Machine Intell., PAMI-3, 2,163–179Google Scholar
  7. [7]
    MATHERON, G. (1975) Random sets and integral geometry. Wiley, New YorkGoogle Scholar
  8. [8]
    SERRA, J. (1982) Image analysis and mathematical morphology. Academic Press, New YorkGoogle Scholar
  9. [9]
    HARALICK, R.M., STENBERG, S.R. et ZHUNG, X. (1987) Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Machine Intell., 9, 532–550CrossRefGoogle Scholar
  10. [10]
    POSTAIRE, J.G., ZHANG, R.D. et BOTTE-LECOCQ, C. (1993) Cluster analysis by binary morphology. IEEE Trans. Pattern Anal. Machine Intell., 15, 2, 170–180CrossRefGoogle Scholar
  11. [11]
    POSTAIRE, J.G. et VASSEUR, C.P.A. (1982) A fast algorithm for non parametric probability density estimation. IEEE Trans. Pattern Anal. Machine Intell., PAMI-4, 6, 663–666CrossRefGoogle Scholar
  12. [12]
    BALL, G.H. et HALL, J.D. (1967) A clustering technique for summarizing multivariate data. Behavioral Sci., 12, 135–155CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • A. Sbihi
    • 1
  • J.-G. Postaire
    • 2
  1. 1.Morocco & „Centre d’Automatique“ of U.S.T.L.University of KenitraFrance
  2. 2.„Centre d’Automatique“University of Lille (U.S.T.L.)Villeneuve d’AscqFrance

Personalised recommendations