Turning Grain Maps into Diagrams

The present paper studies mathematical models for representing, imaging, and analyzing polycrystalline materials. We introduce various techniques for converting grain maps into diagram or tessellation representations that rely on constrained clustering. In particular, we show how to significantly accelerate the computation of generalized balanced power diagrams and how to extend it to allow for optimization over all relevant parameters. A comparison of the accuracy of the proposed approaches is given based on a three-dimensional real-world data set of 339 × 339 × 599 voxels.