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Estimating Particle Shape and Orientation Using Volume Tensors

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  • Johanna F. Ziegel
  • Jens R. Nyengaard
  • Eva B. Vedel Jensen

Abstract

type="main" xml:id="sjos12138-abs-0001"> We develop statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles. We focus on the case where particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle shape and orientation, and we derive stereological estimators of the tensors. These estimators are combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends on the orientation and shape of the particles. For instance, if the distribution of the typical particle is invariant under rotations, then the covariance matrix is proportional to the identity matrix. We develop a non-parametric test for such isotropy. A flexible Lévy-based particle model is proposed, which may be analysed using a generalized method of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:3:p:813-831
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    File URL: http://hdl.handle.net/10.1111/sjos.12138
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    References listed on IDEAS

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    1. 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. 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.

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