Segmentation of Crystal Defects via Local Analysis of Crystal Distortion

Matt Elsey, Benedikt Wirth

2013

Abstract

We propose a variational method to simultaneously detect dislocations and grain boundaries in an image of a crystal as well as the local crystal distortion. To this end we extract a distortion field F from the image which is nearly curl-free except at dislocations and grain boundaries. The sparsity of the curl is promoted by an L1-regularization of curlF in the employed energy functional. The structure of the functional admits a fast and parallelizable minimization such that fairly large images can be analyzed in a few minutes.

References

  1. Begau, C., Hua, J., and Hartmaier, A. (2012). A novel approach to study dislocation density tensors and lattice rotation patterns in atomistic simulations. Journal of the Mechanics and Physics of Solids, 60(4):711-722.
  2. Berkels, B., Rätz, A., Rumpf, M., and Voigt, A. (2008). Extracting grain boundaries and macroscopic deformations from images on atomic scale. J. Sci. Comput., 35(1):1-23.
  3. Boerdgen, M., Berkels, B., Rumpf, M., and Cremers, D. (2010). Convex relaxation for grain segmentation at atomic scale. In Fellner, D., editor, VMV 2010 - Vision, Modeling & Visualization, pages 179-186. Eurographics Association.
  4. Bregman, L. M. (1967). The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys., 7(2):200-217.
  5. Elder, K. R. and Grant, M. (2004). Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys. Rev. E, 70:051605.
  6. Goldstein, T. and Osher, S. (2009). The split Bregman method for L1-regularized problems. SIAM J. Imag. Sci., 2(2):323-343.
  7. Lifshitz, R. and Petrich, D. M. (1997). Theoretical model for Faraday waves with multiple-frequency forcing. Phys. Rev. Lett., 79(7):1261-1264.
  8. Osher, S., Burger, M., Goldfarb, D., Xu, J., and Yin, W. (2005). An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul., 4(2):460-489.
  9. Singer, H. M. and Singer, I. (2006). Analysis and visualization of multiply oriented lattice structures by a two-dimensional continuous wavelet transform. Phys. Rev. E, 74:031103.
  10. Strekalovskiy, E. and Cremers, D. (2011). Total variation for cyclic structures: Convex relaxation and efficient minimization. In Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on, pages 1905-1911.
  11. Stukowski, A. and Albe, K. (2010a). Dislocation detection algorithm for atomistic simulations. Modelling and Simulation in Materials Science and Engineering, 18(2):025016.
  12. Stukowski, A. and Albe, K. (2010b). Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Modelling and Simulation in Materials Science and Engineering, 18(8):085001.
  13. Wang, B., Idrissi, H., Galceran, M., Colla, M., Turner, S., Hui, S., Raskin, J., Pardoen, T., Godet, S., and Schryvers, D. (2012). Advanced TEM investigation of the plasticity mechanisms in nancrystalline freestanding palladium films with nanoscale twins. Int. J. Plast., 37:140-156.
  14. Wu, K.-A., Adland, A., and Karma, A. (2010). Phasefield-crystal model for fcc ordering. Phys. Rev. E, 81:061601.
  15. Wu, K.-A. and Voorhees, P. W. (2012). Phase field crystal simulations of nanocrystalline grain growth in two dimensions. Acta Materialia, 60(1):407-419.
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Paper Citation


in Harvard Style

Elsey M. and Wirth B. (2013). Segmentation of Crystal Defects via Local Analysis of Crystal Distortion . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013) ISBN 978-989-8565-47-1, pages 294-302. DOI: 10.5220/0004281502940302


in Bibtex Style

@conference{visapp13,
author={Matt Elsey and Benedikt Wirth},
title={Segmentation of Crystal Defects via Local Analysis of Crystal Distortion},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013)},
year={2013},
pages={294-302},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004281502940302},
isbn={978-989-8565-47-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2013)
TI - Segmentation of Crystal Defects via Local Analysis of Crystal Distortion
SN - 978-989-8565-47-1
AU - Elsey M.
AU - Wirth B.
PY - 2013
SP - 294
EP - 302
DO - 10.5220/0004281502940302