Stereological determination of particle size distributions for similar convex bodies

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Abstract

Consider an opaque medium that contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a planar section of the medium we obtain a sample of observed 2D section profile areas of the intersected particles. In this paper, the distribution of interest is the underlying 3D particle size distribution for which an identifiability result is obtained. Moreover, a non-parametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.

Original languageEnglish
Pages (from-to)742-774
Number of pages33
JournalElectronic Journal of Statistics
Volume18
Issue number1
DOIs
Publication statusPublished - 2024

Keywords

  • consistency
  • EM
  • iterative convex minorant
  • Mellin transform
  • particle system
  • Stereology

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