Fast Fourier transform and support-shift techniques for pore-scale microstructure classification using additive morphological measures

Abstract

The Minkowski functionals, as the full set of additive morphological measures in three dimensions (3D) consisting of volume, surface area, mean curvature, and total curvature, can be calculated directly by evaluating the local contributions of vertices of a discrete structure. They are sensitive measures of microstructure, and for microstructures generated by a Boolean process, relate to their physical properties. In this work we introduce fast numerical techniques based on the additivity of the Minkowski functionals to derive fields of regional Minkowski measures over large regional support for large 3D data sets as generated, e.g., from x-ray tomography techniques. We demonstrate the application of these 3D feature fields to microstructure classification for a set of heterogeneous microstructures using a multivariate Gaussian mixture model and a thin-bedded sandstone. It is shown that for the case of a spatially heterogeneous Boolean process the internal boundaries of the generating process are recovered with high accuracy, while for the thin-bedded sandstone, compact partitions with clear layering are extracted.