Estimating Particle Shape and Orientation Using Volume Tensors

Ziegel, Johanna F.; Nyengaard, Jens R.; Vedel Jensen, Eva B. (2015). Estimating Particle Shape and Orientation Using Volume Tensors. Scandinavian journal of statistics, 42(3), pp. 813-831. Blackwell 10.1111/sjos.12138

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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.

Item Type:

Journal Article (Original Article)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ziegel, Johanna F.


300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics








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Date Deposited:

25 Aug 2015 10:17

Last Modified:

05 Dec 2022 14:49

Publisher DOI:


Uncontrolled Keywords:

ellipsoidal approximation, local stereology, optical rotator, particle cover density, particle orientation, particle shape, volume tensors




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