Sensitivity of the local measures to deviations of the typical grain shape in Boolean models - Mines Saint-Étienne Access content directly
Conference Papers Year : 2021

Sensitivity of the local measures to deviations of the typical grain shape in Boolean models

Abstract

The method of the typical grain elongation ratio estimation based on the local measures distributions is proposed. The local measures are straightforward generalizations of the Minkowski functionals (MFs) (in R2 coincide up to normalization with classical geometric measurements: Euler-Poincar ́e characteristic, perimeter and area). Consider a random structure ̃Ξ in Rd, and take values of the Minkowski functionals for ̃Ξ ∩ Br( ̃x), where Br( ̃x) is a ball of radius r positioned in a uniformly randomly distributed point ̃x. For the different realizations of ̃x the different values are obtained, which provide d + 1 measures in the sense of the measure theory: mappings which assign real numbers to sets and which become “random measures”. These localizations of MFs previously were used to characterize the porous structure of a Fontainebleau sandstone.
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Dates and versions

emse-03537220 , version 1 (20-01-2022)

Identifiers

  • HAL Id : emse-03537220 , version 1

Cite

Tatyana Eremina, Johan Debayle, Frédéric Gruy, Jean-Charles Pinoli. Sensitivity of the local measures to deviations of the typical grain shape in Boolean models. ECSIA'2021 : The 13th European Congress for Stereology and Image Analysis, Mines Saint-Etienne - Institut Mines Telecom (IMT), Jun 2021, Saint-Etienne, France. ⟨emse-03537220⟩
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