Skip to main content
SpringerLink
Log in

Random planar shapes and their statistical recognition

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

A two-dimensional shape as considered in this paper is the equivalence class of closed polygons under rigid motions (rotations and translations). We discuss a model for random shapes which is used as the basis for probabilistic classifiers. A maximum-likelihood approach is used to deal with the incomplete information given by the knowledge of the equivalence class only. As an example, the problem of the recognition of species of plants from the shape of their leaves is studied.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Y. Amit, U. Grenander and M. Piccioni, Structural image restoration through deformable templates, J. Amer. Stat. Assoc. 86(1991)376–387.

    Google Scholar 

  2. A. Bengtsson and J.-O. Eklundh, Shape representation by multiscale contour approximation, IEEE Trans. PAMI 13(1991)85–93.

    Google Scholar 

  3. H. Cramer and M.R. Leadbetter,Stationary and Related Stochastic Processes (Wiley, New York, 1967).

    Google Scholar 

  4. D. Cyganski and R.F. Vaz, Generation of affine invariant local contour feature data, Pattern Recognition Lett. 11(1990)479–483.

    Google Scholar 

  5. G. Freud,Orthogonale Polynome (Birkhauser, Basel, 1969).

    Google Scholar 

  6. A. Gabe, Stationäre Gaußprozesse in der Ebene und ihre Anwendung in der Statistischen Bildanalyse, Diplomarbeit, Universität Giessen (1988).

  7. U. Grenander,Pattern Synthesis (Vol. I), Pattern Analysis (Vol. II), Applied Math. Sciences (Springer, New York, 1976–1977).

    Google Scholar 

  8. U. Grenander, Advances in Pattern Theory, The 1985 Rietz Lecture, Ann. Stat. 17(1985)1–30.

    Google Scholar 

  9. D.M. Himmelblau,Applied Nonlinear Programming (McGraw-Hill, New York, 1972).

    Google Scholar 

  10. R. Lenz, Group theoretical methods in image processing, Lecture Notes in Comp. Sci. 413 (1990).

  11. D.G. Kendall, A survey of the statistical theory of shape, Stat. Sci. 4(2)(1989)87–120.

    Google Scholar 

  12. L.H. Koopmans,The Spectral Analysis of Time Series (Academic Press, New York/London, 1974).

    Google Scholar 

  13. D.H. McLain, Vector approximation to curves, Comp. J. 21(1978)176–177, Algorithm 100.

    Google Scholar 

  14. W.J. Park, A multiparameter Gaussian process, Ann. Math. Stat. 41(1970)1582–1595.

    Google Scholar 

  15. A. Zilinskas,Global Optimization (Mokslas, Vilniusm 1986), in Russian.

    Google Scholar 

  16. Pavlidis,Structural Pattern Recognition (Springer, Berlin/Heidelberg/New York, 1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Statistics and Computer Science, University of Vienna, Vienna, Austria

    Georg Ch. Pflug

Authors
  1. Georg Ch. Pflug
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pflug, G.C. Random planar shapes and their statistical recognition. Ann Math Artif Intell 13, 267–279 (1995). https://doi.org/10.1007/BF01530831

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01530831

Keywords

Search

Navigation