Finding the Edge of a Poisson Forest with Inside and Outside Observations: The Discriminant Analysis Point of View

  • J. P. Rasson
  • M. Rémon
  • Fl. Henry
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The estimation of convex sets when inside and outside observations are available is often needed in current research applications. The key idea in this presentation is to try to identify a convex domain through random observations which turn to belong or not to the convex. We can think here to oil fields detection, to population polls, to pattern recognition, etc.

The solution proposed here is based on a criterion from discriminant analysis. This criterion, for deciding whether a further observation [for which we do not know if it is inside or outside the original convex set], was first proposed by Baufays and Rasson (1984), (1985). Its application here gives a robust and practical estimate of the unknown domain D.


Discriminant Analysis Poisson Process Convex Domain Allocation Rule Point Poisson Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. BAUFAYS, P., and RASSON, J.P. (1985): A new geometric discriminant rule. Computational Statistics Quaterly, vol 2, issue 1, 15–30. Google Scholar
  2. BAUFAYS, P., and RASSON, J.P. (1984): Une nouvelle règle de classement utilisant l’enveloppe convexe et la mesure de Lebesgue. Statistique et Analyse des Données, vol 9, no 2, 31–47.Google Scholar
  3. GRENANDER, U. (1973): Statistical geometry: a tool for pattern analysis. Bulletin of the American Mathematical Society, vol. 79, 829–856. CrossRefGoogle Scholar
  4. HACHTEL, G.D., MEILIJSON, I. and NADAS, A. (1981): The estimation of a convex subset of IRk and its probability content. IBM research report, Yorktown Heights N.Y.Google Scholar
  5. HAND, D.J. (1982): Kernel Discriminant Analysis. Research studies press, England.Google Scholar
  6. MOORE, M., LEMAY, Y. and ARCHAMBAULT, S. (1988): Algorithms to reconstruct a convex set from sample points. Computing Science and Statistics: Proceedings of the 20th Symposium on the Interface, Eds. E J. Wegman, D.T. Gantz and J.J. Miller, ASA, Virginia, 553–558.Google Scholar
  7. RASSON, J.P., REMON, M. and KUBUSHISHI, T. (1993): Finding the edge of a Poisson forest with inside and outside observations. Internal report 93/14, Dept. of Mathematics, FUNDP, Namur.Google Scholar
  8. REMON, M. (1994): The estimation of a convex domain when inside and outside observations are available. Supplemento ai Rendiconti del Circolo Matematico di Palermo, serie II no 35, 227–235.Google Scholar
  9. RIPLEY, B.D., and RASSON, J.P. (1977): Finding the edge of a Poisson forest. Journal of Applied Probability, 14, 483–491. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • J. P. Rasson
    • 1
  • M. Rémon
    • 1
  • Fl. Henry
    • 1
  1. 1.Département de MathématiqueFacultés Universitaires Notre-Dame de la PaixNamurBelgium

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