Second-order Moments in Stereological Study of Random Forms

Dieter König and Detrich Stoyan

Mining Academy Freiberg, Department of Mathematics

Keywords: Second-order moment, stereology, random form

Abstract. Traditional stereology consists nearly completely in the determination of particle size distributions' and mean values such as V_v and S_v. However, for the description of the "inner" structure of random structures second-order characteristics such as pair correlation function or reduced second moment function are useful. In the present paper stereological estimation of second-order quantities for centres of random sphere systems and for random fibre systems is considered. In the case of sphere systems stereological formulae are given which connect the pair correlation function of the sphere centres with quantities available from planar, linear and thin sections. For random fibre systems some exact and approximate stereological methods are suggested which enable the determination of secon-dorder quantities from planar and thin sections.