Abstract
This paper presents a comparative analysis of algorithmic strategies for fitting tessellation models to 3D image data of materials such as polycrystals and foams. In this steadily advancing field, we review and assess optimization-based methods -- including linear and nonlinear programming, stochastic optimization via the cross-entropy method, and gradient descent -- for generating Voronoi, Laguerre, and generalized balanced power diagrams (GBPDs) that approximate voxelbased grain structures. The quality of fit is evaluated on real-world datasets using discrepancy measures that quantify differences in grain volume, surface area, and topology. Our results highlight trade-offs between model complexity, the complexity of the optimization routines involved, and the quality of approximation, providing guidance for selecting appropriate methods based on data characteristics and application needs.
Abstract (translated)
本文对用于拟合多晶材料和泡沫等材料的3D图像数据的镶嵌模型的算法策略进行了比较分析。在这一不断发展的领域中，我们回顾并评估了基于优化的方法（包括线性和非线性规划、通过交叉熵方法进行的随机优化以及梯度下降）以生成Voronoi图、Laguerre图和广义平衡功率图（GBPDs），这些图形可以近似于体素基粒结构。我们使用差异测量指标来评估拟合质量，这些指标量化了颗粒体积、表面积及拓扑结构的差异。我们的研究结果突出了模型复杂性与优化流程复杂性以及近似质量之间的权衡，并为基于数据特性和应用需求选择合适方法提供了指导。
URL
https://arxiv.org/abs/2507.14268
