The challenging process of 3D porous media reconstruction from a single 2D image is investigated in this paper. The reconstruction of the 3D model is based on the statistical information derived from a 2D thin image of the material, by applying a spatial correlation function. For the first time, this paper reviews the commonly used auto-correlation functions for material characterization and discusses their properties making them useful for 3D porous media reconstruction. A set of experiments is conducted in order to analyze the reconstruction capabilities of the studied correlation functions, while some useful conclusions are drawn. Finally, by taking into account the reconstruction performance of the existed correlation functions, some desirable properties that need to be satisfied by an ideal correlation function towards the improvement of the reconstruction accuracy are determined.

One of the most challenging problems that are still open in the field of materials science is the 3D reconstruction of porous media using information from a single 2D thin image of the original material. Such a reconstruction is only feasible subject to some important assumptions that need to be made as far as the statistical properties of the material are concerned. In this study, the aforementioned problem is investigated as an explicitly formulated optimization problem, with the phase of each porous material point being decided such that the resulting 3D material model shows the same statistical properties as its corresponding 2D version. Based on this problem formulation, herein for the first time, several traditional (genetic algorithms—GAs, particle swarm optimization—PSO, differential evolution—DE), as well as recently proposed (firefly algorithm—FA, artificial bee colony—ABC, gravitational search algorithm—GSA) nature-inspired optimization algorithms were applied to solve the 3D reconstruction problem. These algorithms utilized a newly proposed data representation scheme that decreased the number of unknowns searched by the optimization process. The advantages of addressing the 3D reconstruction of porous media through the application of a parallel heuristic optimization algorithm were clearly defined, while appropriate experiments demonstrating the greater performance of the GA algorithm in almost all the cases by a factor between 5%–84% (porosity accuracy) and 3%–15% (auto-correlation function accuracy) over the PSO, DE, FA, ABC, and GSA algorithms were undertaken. Moreover, this study revealed that statistical functions of a high order need to be incorporated into the reconstruction procedure to increase the reconstruction accuracy.