We consider a two-phases model to describe a porous medium; an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase. Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato).
KRATZ, M., ESTRADE, A. and IRIBARREN, I. (2006). Funciones de distribucion de cuerdas en medios porosos. In: Rencontres France-Espagne-Venezuela de probabilité et statistique mathématique. Choroni.