Random heterogeneous materials via texture synthesis

Computer models of random heterogeneous materials are becoming increasingly important in order to support the latest advances in material science, biomedical applications and manufacturing. Such models usually take the form of a microstructure whose geometry is reconstructed from a small material sample, an exemplar. A widely used traditional approach to material reconstruction relies on stochastic optimization to approximate the material descriptors of the exemplar, such as volume fraction and two-point correlation functions. This approach is computationally intensive and is limited to certain types of isotropic materials. We show that formulating material reconstruction as a Markov Random Field (MRF) texture synthesis leads to a number of advantages over the traditional optimization-based approaches. These include improved computational efficiency, preservation of many material descriptors, including correlation functions and Minkowski functionals, ability to reconstruct anisotropic materials, and direct use of the gray-scale material images and two-dimensional cross-sections. Quantifying the quality of reconstruction in terms of correlation functions as material descriptors suggests a systematic procedure for selecting a size of neighborhood, a key parameter in the texture synthesis procedure. We support our observations by experiments using implementation with Gaussian pyramid and periodic boundary conditions.