Prediction of mineralogical particle composition using CT data and R-vine copulas

Computed tomography (CT) can capture volumes large enough to measure a statistical meaningful number of micron-sized particles with a sufficiently good resolution to allow for the analysis of individual particles. However, the development of methods to efficiently investigate such image data and interpretably model the observed particle features is still an active field of research. When image data of particles exhibiting a wide range of shapes and sizes is considered, traditional image segmentation methods, such as the watershed algorithm, struggle to recognize particles with satisfying accuracy. Thus, more advanced methods of machine learning must be utilized for image segmentation to improve the validity of subsequent analyzes. Moreover, CT data does not include information about the mineralogical composition of particles and, therefore, additional SEM-EDS image data must be acquired. Here, micro-CT data of a particle system mostly composed of zinnwaldite-quartz composites is considered. First, an image segmentation method is applied which uses deep convolutional neural networks (CNN), namely a U-net. This has the advantage of requiring less hand-labeling than other machine learning methods, while also being more flexible with the possibility of transfer learning. Then, parameterized models based on vine copulas are designed to determine multivariate probability distributions of descriptor vectors for the size, shape, texture and composition of particles. For model fitting, the segmented three-dimensional CT data and co-registered two-dimensional SEM-EDS data are used. The models are applied to predict the mineralogical composition of particles, solely on the basis of particle descriptors observed in CT data. The power of the introduced prediction models for estimating the mineralogical composition of particles by means of CT-based descriptor vectors, are evaluated with respect to the prediction of the zinnwaldite volume fraction of particles. Results obtained for the goodness of fit and the predictive power are quantitatively assessed.