Stochastic Modeling of Multidimensional Particle Properties Using Parametric Copulas

In this paper, prediction models are proposed which allow the mineralogical characterization of particle systems observed by X-ray micro tomography (XMT). The models are calibrated using 2D image data obtained by a combination of scanning electron microscopy and energy dispersive X-ray spectroscopy in a planar cross-section of the XMT data. To reliably distinguish between different minerals the models are based on multidimensional distributions of certain particle characteristics describing, for example, their size, shape, and texture. These multidimensional distributions are modeled using parametric Archimedean copulas which are able to describe the correlation structure of complex multidimensional distributions with only a few parameters. Furthermore, dimension reduction of the multidimensional vectors of particle characteristics is utilized to make non-parametric approaches such as the computation of distributions via kernel density estimation viable. With the help of such distributions the proposed prediction models are able to distinguish between different types of particles among the entire XMT image.