Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes

  • Veera SundararaghavanEmail author
Part of the following topical collections:
  1. Use of Digital Data in Materials Science and Engineering


A pervasive method for reconstructing microstructures from two-dimensional microstructures imaged on orthogonal planes is presented. The algorithm reconstructs 3D images through matching of 3D slices at different voxels to the representative 2D micrographs and an optimization procedure that ensures patches from the 2D micrographs meshed together seamlessly in the 3D image. We show that the method effectively models the three-dimensional features in the microstructure using three cases (i) disperse spheres, (ii) anisotropic lamellar microstructure, and (iii) a polycrystalline microstructure. The method is validated by comparing the point probability functions of the reconstructed images to the original 2D image, as well as by comparing the elastic properties of reconstructed image to the experimental data.


Microstructure Markov random field Ising model Sampling Reconstruction Statistical descriptors 



The author would like to acknowledge the Air Force Office of Scientific Research, MURI contract FA9550-12-1-0458, for the financial support.

Supplementary material

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  1. 1.
    Sundararaghavan V, Zabaras N: Classification and reconstruction of three-dimensional microstructures using support vector machines. Compu Mater Sci 2005, 32: 223–239. 10.1016/j.commatsci.2004.07.004CrossRefGoogle Scholar
  2. 2.
    Yeong CLY, Torquato S: Reconstructing random media II. Three-dimensional media from two-dimensional cuts. Phys Rev E 1998, 58(1):224–233. 10.1103/PhysRevE.58.224CrossRefGoogle Scholar
  3. 3.
    Manwart C, Torquato S, Hilfer R: Stochastic reconstruction of sandstones. Phys Rev E 2000, 62: 893–899. 10.1103/PhysRevE.62.893CrossRefGoogle Scholar
  4. 4.
    Torquato S: Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York; 2002.CrossRefGoogle Scholar
  5. 5.
    Efros A, Leung T: Texture synthesis by non-parametric sampling. Int Conf Comput Vis 1999, 2: 1033–1038.Google Scholar
  6. 6.
    Ising E: Beitrag zur Theorie des Ferromagnetismus. Zeitschrift Physik 1925, 31: 253–258. 10.1007/BF02980577CrossRefGoogle Scholar
  7. 7.
    Besag J: Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc. Series B (Methodological) 1974, 36(2):192–236.CrossRefGoogle Scholar
  8. 8.
    Kwatra V, Essa I, Bobick A, Kwatra N: Texture optimization for example-based synthesis. ACM Trans Graph (Proc. SIGGRAPH) 2005, 24(3):795–802. 10.1145/1073204.1073263CrossRefGoogle Scholar
  9. 9.
    Altman NS: An introduction to kernel and nearest-neighbor nonparametric regression. The American Statistician 1992, 46(3):175–185.Google Scholar
  10. 10.
    Kopf J, Fu C-W, Cohen-Or D, Deussen O, Lischinski D, Wong T-T: Solid texture synthesis from 2D exemplars. Proc SIGGRAPH 2007, 2: 1–9.Google Scholar
  11. 11.
    Xu H, Dikin DA, Burkhart C, Chen W: Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput Mater Sci 2014, 85: 206–216. 10.1016/j.commatsci.2013.12.046CrossRefGoogle Scholar
  12. 12.
    Quintanilla J: Microstructure and properties of random heterogeneous materials: a review of theoretical results. Polymer Engg Sci 1999, 39: 559–585. 10.1002/pen.11446CrossRefGoogle Scholar
  13. 13.
    Umekawa S, Kotfila R, Sherby OD: Elastic properties of a tungsten-silver composite above and below the melting point of silver. J Mech Phys Solids 1965, 13(4):229–230. 10.1016/0022-5096(65)90012-8CrossRefGoogle Scholar
  14. 14.
    Roberts AP, Garboczi EJ: Elastic properties of a tungsten-silver composite by reconstruction and computation. J Mech Phys Solids 1999, 47: 2029–2055. 10.1016/S0022-5096(99)00016-2CrossRefGoogle Scholar
  15. 15.
    Roberts AP, Torquato S: Chord-distribution functions of three-dimensional random media: approximate first-passage times of Gaussian processes. Phys Rev E 1999, 59(5):4953–4963. 10.1103/PhysRevE.59.4953CrossRefGoogle Scholar
  16. 16.
    Lee PS, Piehler HR, Rollett AD, Adams BL: Texture clustering and long-range disorientation representation methods: application to 6022 aluminum sheet. Metallurgical Mater Trans A 2002, 33(12):3709–3718. 10.1007/s11661-002-0243-xCrossRefGoogle Scholar
  17. 17.
    Garboczi EJ (1998) NIST Internal Report 6269. Chapter 2. . Accessed 24 Nov 2013., []

Copyright information

© Sundararaghavan.; licensee springer. 2014

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Aerospace EngineeringUniversity of MichiganAnn ArborUSA

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