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Local Stereology of Tensors of Convex Bodies

Author

Listed:
  • Eva B. Vedel Jensen

    (Aarhus University)

  • Johanna F. Ziegel

    (University of Bern)

Abstract

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

Suggested Citation

  • Eva B. Vedel Jensen & Johanna F. Ziegel, 2014. "Local Stereology of Tensors of Convex Bodies," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 263-282, June.
  • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9337-8
    DOI: 10.1007/s11009-013-9337-8
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    References listed on IDEAS

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    1. Zbyněk Pawlas & Jens R. Nyengaard & Eva B. Vedel Jensen, 2009. "Particle Sizes from Sectional Data," Biometrics, The International Biometric Society, vol. 65(1), pages 216-224, March.
    2. L. M. Cruz‐Orive & H. Hoppeler & O. Mathieu & E. R. Weibel, 1985. "Stereological Analysis of Anisotropic Structures Using Directional Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(1), pages 14-32, March.
    3. C. Beisbart & M. S. Barbosa & H. Wagner & L. da F. Costa, 2006. "Extended morphometric analysis of neuronal cells with Minkowski valuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(4), pages 531-546, August.
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    1. Johanna F. Ziegel & Jens R. Nyengaard & Eva B. Vedel Jensen, 2015. "Estimating Particle Shape and Orientation Using Volume Tensors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 813-831, September.

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