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 339×339×599 voxels.
@article{arxiv.2205.06650,
title = {Turning grain maps into diagrams},
author = {Andreas Alpers and Maximilian Fiedler and Peter Gritzmann and Fabian Klemm},
journal= {arXiv preprint arXiv:2205.06650},
year = {2022}
}