# Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing

arXiv: https://arxiv.org/abs/2507.14268 · HTML: https://mlsanity.com/paper/2507.14268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 127 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [The Geometry of Deep Networks: Power Diagram Subdivision](https://mlsanity.com/paper/1905.08443/) (2019)
- [Generalized balanced power diagrams for 3D representations of polycrystals](https://mlsanity.com/paper/1411.4535/) (2014)
- [Power-SLIC: Fast Superpixel Segmentations by Diagrams](https://mlsanity.com/paper/2012.11772/) (2020)
- [Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport](https://mlsanity.com/paper/2403.03571/) (2024)
- [Automated pebble mosaic stylization of images](https://mlsanity.com/paper/1902.02806/) (2019)
- [Laguerre tessellations and polycrystalline microstructures: A fast algorithm for generating grains of given volumes](https://mlsanity.com/paper/1912.07188/) (2019)
- [Coresets for Weight-Constrained Anisotropic Assignment and Clustering](https://mlsanity.com/paper/2203.10864/) (2022)
- [Dynamic grain models via fast heuristics for diagram representations](https://mlsanity.com/paper/2204.06430/) (2022)
- [Exploration of Gibbs-Laguerre tessellations for three-dimensional stochastic modeling](https://mlsanity.com/paper/1905.04252/) (2019)
- [On resolution coresets for constrained clustering](https://mlsanity.com/paper/2204.00893/) (2022)
- [An Analytical Representation of the 2d Generalized Balanced Power Diagram](https://mlsanity.com/paper/2303.15275/) (2023)
- [Inverting Laguerre tessellations: Recovering tessellations from the volumes and centroids of their cells using optimal transport](https://mlsanity.com/paper/2406.00871/) (2024)
- [Nonparametric inference for Poisson-Laguerre tessellations](https://mlsanity.com/paper/2501.08810/) (2025)

## Abstract (arXiv)

This paper reviews algorithmic and modeling approaches for fitting generalized power diagrams to three-dimensional image data, a key step in virtual materials testing (VMT). Beyond their practical relevance to materials science, these tessellation models connect to several active areas of applied mathematics, including optimization, computational geometry, stochastic modeling, and optimal transport. Their formulation combines concepts from convex analysis and geometric clustering, offering a rich interplay between theory and computation. We survey recent applications and quantitatively compare algorithmic strategies for fitting Voronoi diagrams, power diagrams, and generalized balanced power diagrams (GBPDs), including linear and nonlinear programming, stochastic optimization via the cross-entropy method, and gradient-based approaches. Comparative results on real datasets illustrate trade-offs between algorithmic complexity and model accuracy.