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)


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.



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


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© 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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