Reconstruction of random heterogeneous media

Stochastic reconstruction is a technique to generate samples of random structures with prescribed distributional properties in the sense that certain of their statistical summary characteristics match target values or forms. This technique can be used to produce structures of any wanted size for further statistical analysis starting from small samples, which may be even only lower dimensional, for instance, when three-dimensional imaging techniques are not available. In this review we explain the main ideas of stochastic reconstruction, concentrating on the most important case of digitized binary media and with a particular emphasis on stereological reconstruction.