While the microscopic structure of defected solid crystalline materials has significant impact on their physical properties, efficient and accurate determination of a given polycrystalline microstructure remains a challenge. In this paper, we present a highly generalizable and reliable variational method to achieve this goal for two-dimensional crystalline and quasicrystalline materials. The method is benchmarked and optimized successfully using a variety of large-scale systems of defected solids, including periodic structures and quasicrystalline symmetries to quantify their microstructural characteristics, e.g., grain size and lattice misorientation distributions. We find that many microstructural properties show universal features independent of the underlying symmetries.