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Lattice Metric Space Application to Grain Defect Detection

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Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

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Abstract

We propose a new model for grain defect detection based on the theory of lattice metric space [7]. The lattice metric space \((\mathscr {L},d_{\mathscr {L}})\) shows outstanding advantages in representing lattices. Utilizing this advantage, we propose a new algorithm, Lattice clustering algorithm (LCA). After over-segmentation using regularized k-means, the merging stage is built upon the lattice equivalence relation. Since LCA is built upon \((\mathscr {L},d_{\mathscr {L}})\), it is robust against missing particles, deficient hexagonal cells, and can handle non-hexagonal lattices without any modification. We present various numerical experiments to validate our method and investigate interesting properties.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA

    Yuchen He & Sung Ha Kang

Authors
  1. Yuchen He
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  2. Sung Ha Kang
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Correspondence to Yuchen He .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of Lübeck, Lübeck, Germany

    Jan Modersitzki

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He, Y., Kang, S.H. (2019). Lattice Metric Space Application to Grain Defect Detection. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_30

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  • DOI: https://doi.org/10.1007/978-3-030-22368-7_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

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