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Second-Order Characteristics of the Edge System of Random Tessellations and the PPI Value of Foams

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Abstract

The mean number of pores per inch (PPI) is widely used as a pore size characteristic for foams. Nevertheless, there is still a lack of fast and reliable methods for estimating this quantity. We propose a method for estimating the PPI value based on the Bartlett spectrum of a dark field image of the material. To this end, second-order properties of the edge systems of random tessellations are investigated in detail. In particular, we study the spectral density of the random length measure of the edges. It turns out that the location of its first local maximum is proportional to the PPI value. To determine the factor of proportionality, several random tessellation models as well as examples of real foams are investigated. To mimic the image acquisition process, 2D sections and projections of 3D tessellations are considered.

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Authors and Affiliations

  1. Department of Mathematics, University of Kaiserslautern, 67653, Kaiserslautern, Germany

    Claudia Redenbach

  2. Department of Mathematics and Natural Sciences, University of Applied Sciences Darmstadt, Schöfferstr. 3, 64295, Darmstadt, Germany

    Joachim Ohser & Ali Moghiseh

Authors
  1. Claudia Redenbach
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  2. Joachim Ohser
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  3. Ali Moghiseh
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Correspondence to Claudia Redenbach.

Additional information

This work was supported by the German Federal Ministry of Education and Research (BMBF) under grant MNT/03MS603/AMiNa.

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Redenbach, C., Ohser, J. & Moghiseh, A. Second-Order Characteristics of the Edge System of Random Tessellations and the PPI Value of Foams. Methodol Comput Appl Probab 18, 59–79 (2016). https://doi.org/10.1007/s11009-014-9403-x

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  • DOI: https://doi.org/10.1007/s11009-014-9403-x

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