Hierarchical reconstruction of three-dimensional porous media from a single two-dimensional image with multiscale entropy statistics

Despite the development of 3D imaging technology, the reconstruction of three-dimensional (3D) microstructure from a single two-dimensional (2D) image is still a prominent problem. In this paper, we propose a hierarchical reconstruction method based on simulated annealing, which is named hierarchical simulated annealing method (HSA), with the multiscale entropy statistics as the morphological information descriptor to reconstruct its corresponding three-dimensional (3D) microstructure from a single two-dimensional (2D) image. Both hierarchical simulated annealing (HSA) method and simulated annealing (SA) method are used to perform on the 2D and 3D microstructure reconstruction from a single 2D image, where the two-point cluster function and the standard two-point correlation function are used as the measurement metrics for the reconstructed 2D and 3D structures. From the 2D reconstructions, it can be seen that all the reconstructions of HSA method and SA method not only captures the similar morphological information with the original images, but also have a good agreement with the target microstructures in two-point cluster function. For the reconstructed 3D microstructures, the comparison of two-point correlation function shows that both HSA method and SA method can effectively reconstruct its 3D microstructure and the comparison of the reconstruction time between HSA method and SA method shows that the reconstruction speed of HSA method is an order of magnitude faster than that of SA method.