  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 generalized balanced power diagram method from [1] and how to extend it to
allow for optimization over all relevant parameters. A comparison of the
accuracies of the proposed approaches is given based on a 3D real-world data
set of $339\times 339 \times 599$ voxels.
