Stochastic reconstruction of 3D microstructures from 2D cross-sectional images using machine learning-based characterization

The availability of high-quality three-dimensional (3D) microstructures is an essential prerequisite to understanding the macroscopic behaviours of heterogeneous media. Considering the high cost of 3D microscopy imaging, it is an economical way to derive large numbers of virtual 3D microstructures from limited morphological information of 2D cross-sectional images. This paper presents an efficient method that incorporates machine learning-based characterization of 2D images to statistically reconstruct 3D microstructures. The latent stochasticity of 2D images is mastered by fitting supervised machine learning models, which essentially characterize the local morphological statistics. A morphology integration scheme is developed to project the 2D morphological statistics into the 3D space, and new equivalent 3D microstructures can then be synthesized by sequentially generating voxel values from probability sampling. The new method is tested on a series of heterogeneous media with distinct morphologies, and it is also compared with two classical methods (i.e. stochastic optimization-based reconstruction and Gaussian random field transformation) in terms of reconstruction accuracy and efficiency. Besides, various microstructural descriptors are used to quantify the discrepancies between the reconstructed and target microstructures. The results confirm that the proposed method provides a highly cost-effective and widely applicable way to reproduce 3D realizations that precisely preserve the statistical characteristics, geometrical irregularities, long-distance connectivity and anisotropy that exist in 2D cross-sectional images.