Reconstruction of three-dimensional heterogeneous media from a single two-dimensional section via co-occurrence correlation function

Abstract

Accurately modeling and reconstructing three-dimensional (3D) microstructure of heterogeneous media from limited morphological information obtained from a single two-dimensional (2D) section remains an outstanding problem. Specially, based on simulated annealing (SA) procedure, two-point correlation function S2 is widely used to reconstruct various 3D microstructures in many different cases. However, two-point correlation function is a lower-order statistical descriptor and is generally not sufficient to accurately characterize a microstructure. From the perspective of texture description, a co-occurrence correlation function (CCF) based on gray-level co-occurrence matrix is presented, and four feature functions are derived from it and used as objective function in SA procedure. Moreover, the CCF can be both manageably measured from a single 2D image and embody non-trivial higher-order morphological information. Furthermore, to avoid completely re-computing the CCF in the reconstruction, a fast updating method for CCF is proposed, and thus accelerating the reconstruction process. The four feature functions are utilized to reconstruct different types of media, including square array of nonoverlapping disks, anode microstructure of solid oxide fuel cell and sandstone core. Meanwhile, the two-point correlation function reconstructions are used for comparison. Unconstrained functions including lineal-path function and two-point cluster function are used to quantitatively ascertain the accuracy of the reconstructions, and the comparison of run time is also demonstrated. The results indicate that the proposed method can accurately reconstruct the microstructures with correlation functions being in good agreement with those of the target.