Chord Length Distribution: relationship between Distribution Moments and Minkowski Functionals

Frédéric Gruy (1, 2, 3)

1 SPIN-ENSMSE - Centre Sciences des Processus Industriels et Naturels
2 LGF-ENSMSE - Laboratoire Georges Friedel
3 PMMG-ENSMSE - Département Procédés de Mise en oeuvre des Milieux Granulaires

the chord length distribution (CLD) and its nth moments ( ) have been calculated for a set of 3D-convex bodies. From these data, an empirical relation between the CLD moments and the Minkowski functionals is proposed for the second and third order CLD moments based on the Cauchy formula initially established for the first and fourth order moments in three-dimensional space. The approximation is improved by considering an additional parameter as the number of body vertices. Moreover it is shown that the data set and the empirical expression respect the inclusion inequalities recently found by L. Heinrich (Applied Mathematical Sciences, 8(2014)8257-8269).

Mots clés: Electromagnetic Wave Scattering; Monte Carlo Simulation; Chord Length Distribution; Minkowski’s functionals; Integral Geometry; Minkowski's functionals; Integral Geometry; Monte Carlo Simulation; Electromagnetic Wave Scattering

Domaines: Physique mathématique [math-ph]

Frédéric Gruy. Chord Length Distribution: relationship between Distribution Moments and Minkowski Functionals . 2017. ⟨hal-01637703⟩