Skip to main content
SpringerLink
Log in

Structural Pattern Recognition: A Random Graph Approach

  • Conference paper
Pattern Recognition Theory and Applications

Part of the book series: NATO ASI Series ((NATO ASI F,volume 30))

Abstract

This paper presents the notion of random graphs and their associated probability distributions. It addresses both the structural and probabilistic aspects of structural pattern recognition. A structural pattern can be explicitly represented in the form of attributed graphs and an ensemble of such representations can be considered as outcomes of a mapping, called random graph mapping. To account for the variation of structural patterns in the ensemble, a lower order probability distribution is used to approximate the high order joint probability. To synthesize an ensemble of attributed graphs into a probability distribution (or a set of distributions) of a random graph, we introduce a distance measure together with a hierarchical clustering algorithm. The distance measure is defined as the minimum change of a specially defined Shannon’s entropy before and after the merging of the distributions. With this new formulation, both supervised and unsupervised classification of structural patterns can be achieved.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wong, A.K.C. and Goldfarb, L., 1978, “Modeling Systems and Multilevel Hierarchical Relational Structures,” in Savage, G.J. and Roe, P.H., ed., Large Engineering Systems 2, Sanford Educational Press, Waterloo, Ontario, pp. 37–44.

    Google Scholar 

  2. Tsai, W.H. and Fu, K.S., 1979, “Error-Correcting Isomorphism of Attributed Relational Graphs for Pattern Analysis”, IEEE Trans, on Systems, Man and Cybernetics, vol. SMC-13, pp. 353–362.

    MathSciNet  Google Scholar 

  3. Wong, A.K.C. and You, M.L., 1986, “Entropy and Distance of Random Graphs with Application to Structural Pattern Recognition,” IEEE Trans, on Pattern Analysis and Machine Intelligence, vol. PAMI-7, pp. 599–609.

    Article  Google Scholar 

  4. Shaw, A.C., 1969, “A Formal Picture Description Scheme as a Basis for Picture Processing Systems,” Information and Control, vol. 14, pp. 9–52.

    Article  MATH  Google Scholar 

  5. Shaw, A.C., 1970, “Parsing of Graph-Represent able Pictures,” Journal of ACM, vol. 17, pp. 453–481.

    Article  MATH  Google Scholar 

  6. Pavlidis, T., 1977, Structural Pattern Recognition, Springer-Verlag.

    MATH  Google Scholar 

  7. Pavlidis, T., 1980, “Structural Description and Graph Grammars,” in Chang, S.K. and Fu, K.S., ed.,Pictorial Information Systems, Springer-Verlag, pp. 86–103.

    Chapter  Google Scholar 

  8. Sanfeliu, A. and Fu, K.S., 1983, “A Distance Measure Between Attributed Relational Graphs for Pattern Recognition,” IEEE Trans, on Systems, Man, and Cybernetics, vol. SMC-13, pp. 353–362.

    Google Scholar 

  9. Wong, A.K.C. and Ghahraman, D.E., 1980, “Random Graphs: Structural- Contextual Dichotomy,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. PAMI-2, pp. 341–348.

    Article  Google Scholar 

  10. Ghahraman, D.E., Wong, A.K.C. and AU, T., 1980, “Graph Optimal Monomor- phism Algorithms,” IEEE Trans, on Systems, Man and Cybernetics, vol. SMC-10, pp. 189–196.

    Google Scholar 

  11. Shapiro, L.G. and Haralick, R.M., 1981, “Structural Descriptions and Inexact Matching,” IEEE Trans, on Pattern Analysis and Machine Intelligence, vol. PAMI-3, pp. 504–519.

    Article  Google Scholar 

  12. Ghahraman, D.E., Wong, A.K.C. and Au, T., 1980, “Graph Monomorphism Algorithm,” IEEE Trans, on Syst., Man Cybern., vol. SMC-10, pp. 181–196.

    Article  Google Scholar 

  13. You, M.L. and Wong, A.K.C., 1984, “An Algorithm for Graph Optimal Isomorphsim,” Proc. of the Seventh International Conference on Pattern Recognition, pp. 316–319.

    Google Scholar 

  14. Masumi, A.E., 1973, Picture Analysis of Graph Transformation, Ph.D. Thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign.

    Google Scholar 

  15. Fu, K.S., 1980, “Picture Syntax,” in Chang, S.K. and Fu, K.S., ed.,Pictorial Information Systems, Springer-Verlag, pp. 104–127.

    Chapter  Google Scholar 

  16. Niemann, H., 1980, “Hierarchical Graphs in Pattern Analysis,” Proc. 1980 Int. Conf. on Pattern Recognition, pp. 213–216.

    Google Scholar 

  17. You, M., 1983, A Random Graph Approach to Pattern Recognition, Ph. D. Thesis, Dept. of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, pp. 37–44.

    Google Scholar 

  18. Wong, A.K.C., Reichert, T.A., Cohen, D.N., and Aygun, B.O., 1974, “A Generalized Method for Matching Informational Macromolecular Code Sequences,” Com- put. Biol. Med., vol. 4, pp. 43–57.

    Article  Google Scholar 

  19. Cohen, D.N., Reichert, T.A., and Wong, A.K.C., 1975, “Matching Code Sequences Utilizing Context Free Quality Measures,” Mathematical Biosciences, vol. 24, pp. 25–30.

    Article  MathSciNet  MATH  Google Scholar 

  20. Fu, K.S., 1983, “A Step Towards Unification of Syntactic and Statistic Pattern Recognition,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol PAMI-5, pp. 200–205.

    Google Scholar 

  21. Abe, K. and Sugita, N., 1982, “Distance between Strings of Symbols — Review and Remarks,” Proc. 1982 Int. Conf. on Pattern Recognition, vol. 1, pp. 172–174.

    Google Scholar 

  22. Fu, K.S., 1982, Syntactic Pattern Recognition and Applications, Prentice-Hall.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Systems Design Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Andrew K. C. Wong

Authors
  1. Andrew K. C. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Philips Research Laboratory, Avenue Em. Van Becelaere 2, Box 8, B-1170, Brussels, Belgium

    Pierre A. Devijver

  2. Department of Electronic and Electrical Engineering, University of Surrey, GU2 5XH, Guildford, UK

    Josef Kittler

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wong, A.K.C. (1987). Structural Pattern Recognition: A Random Graph Approach. In: Devijver, P.A., Kittler, J. (eds) Pattern Recognition Theory and Applications. NATO ASI Series, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83069-3_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83069-3_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83071-6

  • Online ISBN: 978-3-642-83069-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation