Stochastic Modeling of Multidimensional Particle Properties Using Parametric Copulas

In this paper, a prediction model is proposed which allows the mineralogical characterization of particle systems observed by X-ray micro tomography (XMT). The model is calibrated using 2D image data obtained by a combination of scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) in a planar cross-section of the XMT data. To reliably distinguish between different minerals the model is based on multidimensional distributions of certain particle characteristics describing, e.g., their size, shape and texture. These multidimensional distributions are modeled using parametric Archimedean copulas, since other approaches like kernel density estimation require much larger sample sizes and are thus less practical. Parametric copulas have the advantage of describing the correlation structure of complex multidimensional distributions with only a few parameters. With the help of such distributions the proposed prediction model is able to distinguish between different types of particles among the entire XMT image.