A wide spectrum of Random Function models, based on the theory of Random sets, are introduced to simulate single or multivariate signals as encountered in the common practice of electron probe microscopy.
These models are built in three steps, combining the choice of a family of primary random functions and of Poisson varieties in the n-dimensional space for their implantation. For electron microscopy images, they can describe the following situations:
- topography (as obtained from stereo pair images in fractography) simulated by Boolean and by alternate sequential random functions;
- thick slices (as in the case of Transmission Electron Microscope (TEM) and Scanning Transmission Electron Microscope (STEM) specimens) for the dilution random functions;
- perspective views (e.g. secondary electron images in the SEM from non planar samples, such as powder samples) for the Dead Leaves model;
- multispectral mappings on polished sections. Their main strength is to enable the estimation of parameters (namely the statistical properties of the structural unit made of primary random functions, and the density of its implantation in space) from simple operations and measurements on grey level images based on Mathematical Morphology, without any segmentation of images. This purpose is illustrated by the main properties of the models with reference to electron microscopy and microprobe situations, and by simulations.
"Random Image Models for Microstructure Analysis and Simulation,"
Scanning Microscopy: Vol. 1992
, Article 11.
Available at: https://digitalcommons.usu.edu/microscopy/vol1992/iss6/11