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.