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Statistics and Computing

, Volume 10, Issue 2, pp 121–132 | Cite as

Random texture models for material structures

  • Dominique Jeulin
Article

Abstract

We consider the construction and properties of some basic random structure models (point processes, random sets and random function models) for the description and for the simulation of heterogeneous materials. They can be specialized to three dimensional Euclidean space. Their implementation requires the use of image analysis tools.

random sets random structures Boolean model Boolean random functions dead leaves model simulation image analysis 

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References

  1. Aubert A. and Jeulin D. 2000. Estimation of the influence of second and third order moments on random sets reconstructions. Pattern Recognition 33(6): 1083–1103.Google Scholar
  2. Bretheau T. and Jeulin D. 1989. Caractéristiques morphologiques des constituants et comportement à la limite élastique d'un matériau biphasé Fe/Ag. Revue Phys. Appl. 24: 861–869.Google Scholar
  3. Charollais F., Bauer M., Coster M., Jeulin D., and Trotabas M. 1997. Modelling the structure of a nuclear ceramic obtained by solid phase sintering. Acta Stereologica 16(3): 315–321.Google Scholar
  4. Cox D.R. and Isham V. 1980. Point Processes. Chapman and Hall, New York.Google Scholar
  5. Cressie N. 1991. Spatial Statistics. J. Wiley, New York.Google Scholar
  6. Demarty C.H., Grillon F., and Jeulin D. 1996. Study of the contact permeability between rough surfaces from confocal microscopy. Microscopy, Microanalysis, Microstructure 7: 505–511.Google Scholar
  7. Jeulin D. 1987. Random structure analysis and modelling by mathematical morphology. In: Spencer A.J.M. (Ed.), Proc. CMDS5, Balkema, Rotterdam, pp. 217–226.Google Scholar
  8. Jeulin D. 1991. Modèles morphologiques de structures aléatoires et de changement d'échelle. Thèse de Doctorat d'Etat, University of Caen.Google Scholar
  9. Jeulin D. 1993a. Damage simulation in heterogeneous materials from geodesic propagations. Engineering Computations 10: 81–91.Google Scholar
  10. Jeulin D. 1993b. Random models for the morphological analysis of powders. Journal of Microscopy 172 (Part 1): 13–21.Google Scholar
  11. Jeulin D. 1994. Random structure models for composite media and fracture statistics. In: Markov K.Z. (Ed.), Advances in Mathematical Modelling of Composite Materials. World Scientific Company, Advances in Mathematics for Applied Sciences, Vol. 15, pp. 239–289.Google Scholar
  12. Jeulin D. (Ed.). 1997. In: Proceedings of the Symposium on the Advances in the Theory and Applications of Random Sets, Fontainebleau, 9–11 October 1996. World Scientific Publishing Company.Google Scholar
  13. Jeulin D. 1998. Morphological modeling of surfaces, Surface Engineering 14(3): 199–204.Google Scholar
  14. Jeulin D. In press. Morphological Models of Random Structures. CRC Press.Google Scholar
  15. Jeulin D. and Le Coënt A. 1996. Morphological modeling of random composites. In: Markov K.Z. (Ed.), Proceedings of the CMDS8 Conference, Varna, 11–16 June 1995. World Scientific Company, pp. 199–206.Google Scholar
  16. Jeulin D. and Laurenge P. 1997. Simulation of rough surfaces by morphological random functions. Journal of Electronic Imaging 6(1): 16–30.Google Scholar
  17. Jeulin D. and Savary L. 1997. Effective complex permitivity of random composites. Journal de Physique I, Section Condensed Matter, September 1997, pp. 1123–1142.Google Scholar
  18. Matheron G. 1967. Eléments pour une théorie des milieux poreux. Masson, Paris.Google Scholar
  19. Matheron G. 1968. Composition des perméabilités en milieu poreux hétérogène: critique de la règle de pondération géométrique. Revue de l'IFP 23: 201–218.Google Scholar
  20. Matheron G. 1969. Théorie des Ensembles Aléatoires, Cahiers du Centre de Morphologie Mathématique. Fascicule 4, Paris School of Mines publication.Google Scholar
  21. Matheron G. 1975. Random Sets and Integral Geometry. J. Wiley, New York.Google Scholar
  22. Miller M. 1969. Bounds for the effective electrical, thermal and magnetic properties of heterogeneous materials. Journal of Mathematical Physics 10: 1988–2004.Google Scholar
  23. Molchanov I.S. 1997. Statistics of the Boolean Model for Practitioners and Mathematicians. J. Wiley, New York.Google Scholar
  24. Norberg T. 1986. Random capacities and their distributions. Probability Theory and Related Fields 73: 281–297.Google Scholar
  25. Quenec'h J.L., Chermant J.L., Coster M., and Jeulin D. 1994. Liquid phase sintered materials modelling by random closed sets. In: Serra J. and Soille P. (Eds.), Mathematical Morphology and its Applications to Image Processing. Kluwer Academic Pub., Dordrecht, pp. 225–232.Google Scholar
  26. Rintoul M.D. and Torquato S. 1997. Precise determination of the critical threshold and exponents in a three-dimensional continuum percolation model. Journal of Physics A: Mathematical and General, 30: L585–L592.Google Scholar
  27. Savary L., Jeulin D., and Thorel A. 1999. Morphological analysis of carbon-polymer composite materials from thick sections. Acta Stereol. 18(3): 297–303.Google Scholar
  28. Serra J. 1982. Image Analysis and Mathematical Morphology. Academic Press, London.Google Scholar
  29. Serra J. (Ed.). 1988. Image Analysis and Mathematical Morphology, Vol. 2. Academic Press, London.Google Scholar
  30. Stoyan D., Kendall W.S., and Mecke J. 1987. Stochastic Geometry and its Applications. J. Wiley, New York.Google Scholar
  31. Vervaat W. 1988. Narrow and vague convergence of set functions. Statistics and Probability Letters 6: 295–298.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Dominique Jeulin
    • 1
  1. 1.Centre de Morphologie MathématiqueEcole des Mines de ParisFontainebleauFrance

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