# Generalized balanced power diagrams for 3D representations of polycrystals

arXiv: https://arxiv.org/abs/1411.4535 · HTML: https://mlsanity.com/paper/1411.4535/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2014.

## Built on by (most cited first, 3 of 3)

- [Generating multi-scale NMC particles with radial grain architectures using spatial stochastics and GANs](https://mlsanity.com/paper/2407.05333/) (2024)
- [Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing](https://mlsanity.com/paper/2507.14268/) (2025)
- [Superpixel-Based Image Segmentation Using Squared 2-Wasserstein Distances](https://mlsanity.com/paper/2601.17071/) (2026)

## Abstract (arXiv)

Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its center-of-mass position, its volume and, if available, by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D x-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear program it can be computed quite efficiently. Based on verified real-world measurements we show that from the few parameters per grain (3, respectively 6 in 2D and 4, respectively 10 in 3D) we obtain excellent representations of both equiaxed and non-equiaxed structures. Hence our approach seems to capture the physical principles governing the forming of such polycrystals in the underlying process quite well.