A Markov Random Field Approach for Microstructure Synthesis

We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure generally ‘look alike’. To enable computation of such a probability distribution, we represented microstructures in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, we developed algorithms to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. We artificially synthesized 2D microstructures using the sampled probabilities. We found that the statistical features such as grain size distribution and shape moment invariants closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using finite element method and were also found to match the experimental values.