Journal of Materials Science

, Volume 45, Issue 4, pp 888–896 | Cite as

Determination of the fibre orientation in composites using the structure tensor and local X-ray transform

  • M. KrauseEmail author
  • J. M. Hausherr
  • B. Burgeth
  • C. Herrmann
  • W. Krenkel


Computed tomography is a non-destructive testing technique based on X-ray absorption that permits the 3D-visualisation of materials at micron-range resolutions. In this article, computed tomography is used to investigate fibre orientation and fibre position in various fibre-reinforced materials such as ceramic matrix composites, glass fibre-reinforced plastics or reinforced concrete. The goal of this article is to determine the quantitative orientation of fibres in fibre-reinforced materials. For this purpose, a mathematical technique based on the structure tensor is used to determine the local orientation of fibres. The structure tensor is easy to implement and results in a fast algorithm relying solely on local properties of the given reconstruction. In addition, the local X-ray transform is used to denoise fibres and to segment them from the matrix.


Fibre Orientation Structure Tensor Orientation Vector Ceramic Matrix Composite Gaussian Smoothing 



The authors gratefully acknowledge the support of the ’Bayrische Forschungsstiftung’ (BFS) for funding this research in respect of the project ’Kontisilizierung’ (Förderkennzeichen AZ-719-06).


  1. 1.
    Stock SR (2009) Micro computed tomography. CRC Press, Boca Raton, FlGoogle Scholar
  2. 2.
    Buffiére JY, Maire E, Cloetens P, Lormand G, Fougeres R (1999) Acta Mater 47:1613CrossRefGoogle Scholar
  3. 3.
    Buffière JY, Savelli S, Maire E (2000) Characterisation of MMCp and cast aluminium alloys. X-ray tomography in materials science. Hermes Science Publications, Paris, pp 103–114Google Scholar
  4. 4.
    Martín-Herrero J, Germain C (2007) Carbon 45:1242CrossRefGoogle Scholar
  5. 5.
    Babout L, Marrow TJ, Engelberg D, Withers PJ (2006) Mater Sci Techol 22(9):1068CrossRefGoogle Scholar
  6. 6.
    Hausherr JM, Fischer F, Krenkel W, Altstädt V (2006) In: Proceedings of conference on damage in composite material, Stuttgart. Accessed 24 Aug 2009
  7. 7.
    Hausherr J, Krenkel W (2008) Ceramics matrix composites. Wiley VCH, Weinheim, pp 261–286CrossRefGoogle Scholar
  8. 8.
    Herrmann C, Hausherr JM, Krenkel W (2009) In: Verbundwerkstoffe, Wiley VCH, New York, pp 249–256Google Scholar
  9. 9.
    Feldkamp LA, Davis LC, Kress JW (1984) J Opt Soc Am 1(6):612CrossRefGoogle Scholar
  10. 10.
    Natterer F (1986) The mathematics of computerized tomography. Teubner, Wiley, Stuttgart, ChichesterGoogle Scholar
  11. 11.
    Natterer F, Wübbeling F (2001) Mathematical methods in image reconstruction. SIAM, Philadelphia, PACrossRefGoogle Scholar
  12. 12.
    Kak AC, Slaney M (2001) Principles of computerized tomographic imaging. SIAM, Roberto’Malley, USACrossRefGoogle Scholar
  13. 13.
    Hausherr JM, Meinhardt J, Hassink B, Herrmann C, Daimer J, Raether G, Krenkel W (2009) In: Proceedings of 11th international conference on European ceramic society, ECERS, KrakowGoogle Scholar
  14. 14.
    Kastner J, Pfeifer F, Heinzl C, Freytag R (2008) In: DACH-Jahrestagung 2008 in St. Gallen, Accessed 26 Aug 2009
  15. 15.
    Robb K, Wirjadi O, Schladitz K (2007) In: HIS, pp 320–325Google Scholar
  16. 16.
    Lampert CH, Wirjadi O (2006) IEEE Trans Image Process 15(11):3501CrossRefGoogle Scholar
  17. 17.
    Knutsson H (1989) In: The 6th Scandinavian conference on image analysis, Oulu, Finland, p 244, Report LiTH-ISY-I-1019, Computer Vision Laboratory, Linköping University, SwedenGoogle Scholar
  18. 18.
    Van Ginkel M (2002) Image analysis using orientation space based on steerable filters, Delft University of Technology, PhD thesisGoogle Scholar
  19. 19.
    Van Kempen GMP, van den Brink N, van Vliet LJ, Van Ginkel M, Verbeek PW, Blonk H (1999) In: Proceedings of the 11th Scandinavian conference on image analysis SCIA’99, Kangerlussuaq, Greenland, pp 447–455Google Scholar
  20. 20.
    Axelsson M (2008) In: ICPR, IEEE, pp 1–4Google Scholar
  21. 21.
    Mulat C, Donias M, Baylou P, Vignoles G, Germain C (2008) J Electron Imaging 17:031108CrossRefGoogle Scholar
  22. 22.
    Zeyun Y, Bajaj C (2006) In: IEEE international conference on image processing, pp 2513–2516Google Scholar
  23. 23.
    Krause M, Alles RM, Burgeth B, Weickert J (2008) Retinal vessel detection via second derivative of local radon transform. Universität des Saarlandes Technical Report No. 212. Accessed 28 Oct 2009
  24. 24.
    Louis AK (1996) Inverse Probl 12:175Google Scholar
  25. 25.
    Cormack AM (1963) J Appl Phys 34:2722CrossRefGoogle Scholar
  26. 26.
    Hounsfield GN (1973) Computerized transverse axial scanning (tomography): part 1. description of system. Br J Radiol 46:1016CrossRefGoogle Scholar
  27. 27.
    Louis AK (2009) Inverse problems and imaging. Accessed 27 Aug 2009
  28. 28.
    Fischer G (2005) Lineare algebra. Vieweg+Teubner, WiesbadenCrossRefGoogle Scholar
  29. 29.
    Deuflhard P (2002) Numerische Mathematik 1. Gruyter, BerlinGoogle Scholar
  30. 30.
    Otsu N (1979) IEEE Trans Syst Man Cybernet 9(1):62CrossRefGoogle Scholar
  31. 31.
    Rohde M, Fischer F, Altstädt V, Herrmann C, Krenkel W, Hausherr JM (2009) IMC-Spritzgiesscompounder-Potentiale der Langfaserverstärkung. In: Verbundwerkstoffe, Wiley, VCH, New York, pp 483–66Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • M. Krause
    • 1
    Email author
  • J. M. Hausherr
    • 1
    • 2
  • B. Burgeth
    • 3
  • C. Herrmann
    • 2
  • W. Krenkel
    • 1
    • 2
  1. 1.Ceramic Materials EngineeringUniversity of BayreuthBayreuthGermany
  2. 2.Fraunhofer Projektgruppe Keramische VerbundstrukturenBayreuthGermany
  3. 3.Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany

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