Mean covariogram of cylinders and applications to Boolean random sets

  • F. Willot
Stochastic and Integral Geometry


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.


Stochastic geometry geometrical covariogram Boolean model cylinder 

MSC2010 numbers

60D05 52A22 53C65 


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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Mines ParisTechPSL Research UniversityParisFrance

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