ABSTRACT
This chapter provides an overview of some of the current research developments regarding the statistical modeling and characterization of microstructure. It reviews the terminology and notation of stochastic processes. The concept of microstructure is fundamental to the field of materials science and engineering. The microstructure of virtually all materials exhibit rich details that span several hierarchical length scales. The spatial correlation functions contain a great deal of information about the microstructure; however, it is not always easily interpreted. There is a strong connection between microstructure statistics and the field of stereology. Numerous other higher-order statistical and topological descriptors have been developed and utilized for characterization of complex materials and microstructures. The chord length distribution and lineal path function are two important measures of particle or grain size and the connectedness of microstructure features along a straight path.
