Stereological estimation of mean particle volume tensors in R³ from vertical sections

Kousholt, A.; Ziegel, Johanna F.; Kiderlen, M.; Jensen, E. B. Vedel (2017). Stereological estimation of mean particle volume tensors in R³ from vertical sections. In: Jensen, Eva B. Vedel; Kiderlen, Markus (eds.) Tensor Valuations and their applications in Stochastic Geometry and Imaging. Lecture Notes in Mathematics: Vol. 2177 (pp. 423-434). Springer

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In this chapter, we discuss stereological estimation of mean particle volume tensors in R³
from vertical sections. We consider a particle process of compact particles that can be represented as a stationary marked point process. Under the assumption that the particle distribution is invariant under rotations around a fixed axis, called the vertical axis, we show how the mean particle volume tensors can be estimated consistently (in a probabilistic sense) from observations in vertical sections through a sample of particles. In a simulation study, the new estimator has a superior behaviour compared to an earlier estimator based on observations in several optical planes.

Item Type:	Book Section (Book Chapter)
Division/Institute:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science
UniBE Contributor:	Ziegel, Johanna F.
Subjects:	500 Science > 510 Mathematics
ISSN:	0075-8434
ISBN:	978-3-319-51950-0
Series:	Lecture Notes in Mathematics
Publisher:	Springer
Language:	English
Submitter:	Johanna Ziegel
Date Deposited:	08 Nov 2017 09:18
Last Modified:	05 Dec 2022 15:07
URI:	https://boris.unibe.ch/id/eprint/105337