Reconstruction of three-dimensional anisotropic media based on analysis of morphological completeness

Abstract

The physical properties of porous media can be more effectively observed and understood when analyzing three-dimensional (3D) structures. The use of computer-based mathematical modeling methods has been proven effective for reconstructing 3D structures of porous media from two-dimensional (2D) images. However, reconstructing a heterogeneous 3D structure from a single 2D image is currently challenging for computer-based mathematical modeling methods. Focusing on the reconstruction of heterogeneous 3D structures from a single anisotropic training image (TI), this paper first introduces a morphological completeness analysis method, which presents a completely new approach to reconstruction in which only two sections are controlled. Then, to enhance the constraint on the simulation points in this new approach to reconstruction, a double-layer and multi-grid system (DLMGS) is proposed. The updated pattern density function simulation, based on the DLMGS, is then taken as the specific reconstruction algorithm in this work. Finally, our reconstruction method is tested using a core image, and the performance of the reconstruction result is assessed using multiple functions. Detailed experiments show that our method can successfully reconstruct a heterogeneous 3D structure from a single anisotropic image, which reduces the required dimensionality of input data for 3D reconstruction and extends the applicable scope.