用3D图像数据拟合广义功率图，助力虚拟材料测试
Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing
- 结合凸分析与几何聚类，构建可计算的三维分块模型
- 实测数据对比显示，非线性优化在精度上优于线性方法
- 适合材料模拟、计算几何与最优传输研究者参考
本文综述了将广义功率图拟合到三维图像数据的算法与建模方法，这是虚拟材料测试（VMT）的关键步骤。这类剖分模型不仅在材料科学中具有实际意义，还关联优化、计算几何、随机建模和最优传输等多个应用数学活跃领域。其形式融合凸分析与几何聚类思想，理论与计算交互丰富。我们系统回顾了近期应用，并定量比较了拟合 Voronoi 图、功率图及广义平衡功率图（GBPDs）的算法策略，包括线性与非线性规划、基于交叉熵法的随机优化及基于梯度的方法。在真实数据集上的对比结果揭示了算法复杂度与模型精度之间的权衡。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。