Turning grain maps into diagrams

TL;DR

This paper develops and compares methods for converting 3D grain maps of polycrystalline materials into diagram representations, enhancing the efficiency and accuracy of generalized balanced power diagrams.

Contribution

It introduces accelerated algorithms and extensions for power diagram methods, enabling better optimization and analysis of complex grain structures.

Findings

Significant speed-up of the generalized balanced power diagram method.

Extension of the method to optimize over all relevant parameters.

Empirical validation on a large 3D real-world dataset.

Abstract

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.