Reconstruction of 3D Microstructures from 2D Images via Transfer Learning

Computational analysis, modeling, and prediction of many phenomena in materials require a three-dimensional (3D) microstructure sample that embodies the salient features of the material system under study. Since acquiring 3D microstructural images is expensive and time-consuming, an alternative approach is to extrapolate a 2D image (aka exemplar) into a virtual 3D sample and thereafter use the 3D image in the analyses and design. In this paper, we introduce an efficient and novel approach based on transfer learning to accomplish this extrapolation-based reconstruction for a wide range of microstructures including alloys, porous media, and polycrystalline. We cast the reconstruction task as an optimization problem where a random 3D image is iteratively refined to match its microstructural features to those of the exemplar. VGG19, a pre-trained deep convolutional neural network, constitutes the backbone of this optimization where it is used to obtain the microstructural features and construct the objective function. By augmenting the architecture of VGG19 with a permutation operator, we enable it to take 3D images as inputs and generate a collection of 2D features that approximate an underlying 3D feature map. We demonstrate the applications of our approach with nine examples on various microstructure samples and image types (grayscale, binary, and RGB). As measured by independent statistical metrics, our approach ensures the statistical equivalency between the 3D reconstructed samples and the corresponding 2D exemplar quite well.