ABSTRACT
In modeling of random morphology of heterogeneous media there are two fundamental tasks: characterization and simulation. A straightforward mathematical tool to tackle morphological problems is the theory of stochastic processes, i.e, to view each morphological pattern as a stochastic process that is completely defined by a multivariate distribution, or approximately characterized with partial statistical information such as a hierarchical order of statistical moments or correlation functions. A random field is strongly homogeneous or homogeneous in the strict sense when its probability distribution does not change with regard to a spatial shift. If only the mean and covariance are spatial invariant, it is called weakly homogeneous or homogeneous in the wide sense. As a concluding remark, the cumulative distribution function (CDF)-based translation is just one of many monotonic nonlinear operators that enable one-to-one mapping between an underlying Gaussian field and its non-Gaussian translation.
