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Unsupervised and Accurate Extraction of Primitive Unit Cells from Crystal Images

  • Niklas Mevenkamp
  • Benjamin Berkels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9358)

Abstract

We present a novel method for the unsupervised estimation of a primitive unit cell, i.e. a unit cell that can’t be further simplified, from a crystal image. Significant peaks of the projective standard deviations of the image serve as candidate lattice vector angles. Corresponding fundamental periods are determined by clustering local minima of a periodicity energy. Robust unsupervised selection of the number of clusters is obtained from the likelihoods of multi-variance cluster models induced by the Akaike information criterion. Initial estimates for lattice angles and periods obtained in this manner are refined jointly using non-linear optimization. Results on both synthetic and experimental images show that the method is able to estimate complex primitive unit cells with sub-pixel accuracy, despite high levels of noise.

Notes

Acknowledgments

The authors would like to thank P.M. Voyles for providing experimental STEM images.

References

  1. 1.
    Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Boerdgen, M., Berkels, B., Rumpf, M., Cremers, D.: Convex relaxation for grain segmentation at atomic scale. In: Fellner, D. (ed.) Vision, Modeling and Visualization, pp. 179–186. Eurographics Association (2010)Google Scholar
  3. 3.
    Bragg, W.L.: The determination of parameters in crystal structures by means of fourier series. Proc. Roy. Soc. Lond. A Math. Phys. Eng. Sci. 123, 537–559 (1929)CrossRefzbMATHGoogle Scholar
  4. 4.
    Browning, N., Chisholm, M., Pennycook, S.: Atomic-resolution chemical analysis using a scanning transmission electron microscope. Nature 366(6451), 143–146 (1993)CrossRefGoogle Scholar
  5. 5.
    Buades, A., Coll, B., Morel, J.M.: Image denoising methods: a new nonlocal principle. SIAM Rev. 52(1), 113–147 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Burnham, K.P., Anderson, D.R.: Multimodel inference understanding AIC and BIC in model selection. Sociol. Methods Res. 33(2), 261–304 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cava, R., Ji, H., Fuccillo, M., Gibson, Q., Hor, Y.: Crystal structure and chemistry of topological insulators. J. Mater. Chem. C 1(19), 3176–3189 (2013)CrossRefGoogle Scholar
  8. 8.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    De La Cuadra, P., Master, A., Sapp, C.: Efficient pitch detection techniques for interactive music. In: Proceedings of the 2001 International Computer Music Conference, pp. 403–406 (2001)Google Scholar
  10. 10.
    Elsey, M., Wirth, B.: Fast automated detection of crystal distortion and crystal defects in polycrystal images. Multiscale Model. Simul. 12(1), 1–24 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hamerly, G., Elkan, C.: Learning the k in k-means. In: Neural Information Processing Systems, p. 2003. MIT Press (2003)Google Scholar
  12. 12.
    Hanson, M.A., Roth, C.B., Jo, E., Griffith, M.T., Scott, F.L., Reinhart, G., Desale, H., Clemons, B., Cahalan, S.M., Schuerer, S.C., et al.: Crystal structure of a lipid g protein-coupled receptor. Science 335(6070), 851–855 (2012)CrossRefGoogle Scholar
  13. 13.
    Kimoto, K., Asaka, T., Yu, X., Nagai, T., Matsui, Y., Ishizuka, K.: Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy. Ultramicroscopy 110(7), 778–782 (2010)CrossRefGoogle Scholar
  14. 14.
    Klug, A.: Image analysis and reconstruction in the electron microscopy of biological macromolecules. Chemica Scripta 14, 245–256 (1978–1979)Google Scholar
  15. 15.
    Klug, H.P., Alexander, L.E., et al.: X-ray Diffraction Procedures, vol. 2. Wiley, New York (1954)zbMATHGoogle Scholar
  16. 16.
    Mevenkamp, N., Binev, P., Dahmen, W., Voyles, P.M., Yankovich, A.B., Berkels, B.: Poisson noise removal from high-resolution stem images based on periodic block matching. Adv. Struct. Chem. Imag. 1(1), 1–19 (2015)CrossRefGoogle Scholar
  17. 17.
    Pelleg, D., Moore, A.W.: X-means: extending k-means with efficient estimation of the number of clusters. In: ICML, pp. 727–734 (2000)Google Scholar
  18. 18.
    Putnis, A.: An Introduction to Mineral Sciences. Cambridge University Press, Cambridge (1992)CrossRefGoogle Scholar
  19. 19.
    Sang, X., LeBeau, J.M.: Revolving scanning transmission electron microscopy: correcting sample drift distortion without prior knowledge. Ultramicroscopy 138, 28–35 (2014)CrossRefGoogle Scholar
  20. 20.
    Wang, Z., Song, Y., Shi, H., Wang, Z., Chen, Z., Tian, H., Chen, G., Guo, J., Yang, H., Li, J.: Microstructure and ordering of iron vacancies in the superconductor system k y fe x se 2 as seen via transmission electron microscopy. Phys. Rev. B 83(14), 140505 (2011)CrossRefGoogle Scholar
  21. 21.
    Williams, D.B., Carter, C.B.: The Transmission Electron Microscope. Springer, New York (1996)CrossRefGoogle Scholar
  22. 22.
    Zeng, Y.M., Wu, Z.Y., Liu, H.B., Zhou, L.: Modified amdf pitch detection algorithm. In: 2003 International Conference on Machine Learning and Cybernetics, vol. 1, pp. 470–473. IEEE (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.AICES Graduate SchoolRWTH Aachen UniversityAachenGermany

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