An end-to-end three-dimensional reconstruction framework of porous media from a single two-dimensional image based on deep learning

Abstract Stochastically reconstructing a three-dimensional (3D) structure of porous media from a given two-dimensional (2D) image is an outstanding problem. For such problem, despite that the big progress has been made on reconstruction methods such as optimization-based and multi-point statistics-based algorithms, however, the reconstruction of topologically complex or non-stationary materials is still not well addressed. Besides, the reconstruction efficiency is another remarkable challenge, and a 12 8 3 reconstruction using these methods generally requires several hours. In this paper, to overcome these problems, we propose a general end-to-end deep learning-based 3D reconstruction framework. Specially, the mapping (function) between a 2D slice and its 3D structure is first learned by a neural network. Then, the 3D reconstruction of a new 2D image using this mapping is instantaneous. For a 12 8 3 reconstruction, our method only requires 0 . 2 s , thus achieving a 3 . 6 × 1 0 4 speedup factor compared with the classical methods. Besides, to yield diverse 3D structures for the same 2D input, a Gaussian noise is introduced into the network. Our approach is tested on two statistically isotropic materials and a non-stationary porous material, and evaluated in terms of both visual and quantitative comparisons. Experimental results indicate that the proposed method is accurate, fast, and stable. The proposed framework also enables that theoretically an arbitrary number of constraints can be incorporated to further improve the reconstruction accuracy.