Mean covariogram of cylinders and applications to Boolean random sets

Abstract

This work focuses on the variance properties of isotropic Boolean random sets containing randomly-oriented cylinders with circular cross-section. Emphasis is put on cylinders with large aspect ratios, of the oblate and prolate types. A link is established between the power law decay of the covariance function and the variance of the estimates of the volume fraction of cylinders. The covariance and integral range of the Boolean mixtures are expressed in terms of the orientation-averaged covariogram of cylinders, for which exact analytical formulas and approximate expressions are provided.

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Correspondence to F. Willot.

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Original Russian Text © F. Willot, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 6, pp. 62-76.

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Willot, F. Mean covariogram of cylinders and applications to Boolean random sets. J. Contemp. Mathemat. Anal. 52, 305–315 (2017). https://doi.org/10.3103/S1068362317060061

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MSC2010 numbers

  • 60D05
  • 52A22
  • 53C65

Keywords

  • Stochastic geometry
  • geometrical covariogram
  • Boolean model
  • cylinder