AI 中文总结
研究旨在用持久同调拟合粒子系统拓扑，因3D图像数据量大使现有方法计算不可行。通过引入新型图形表示法，将持久同调计算转移到图形域，得到与生成方法无关的后处理方法，改善与真实粒子系统的一致性并保留形态特征。
AI 中文摘要
材料中粒子的形状和排列决定其宏观性质。生成具有不同粒子结构的合成数据（常表示为3D体素图像）并结合宏观性质模拟可揭示结构 - 性质关系。多数粒子生成模型关注单粒子特征。本文旨在用持久同调工具拟合粒子系统拓扑，但所需3D图像数据量大使现有方法计算不可行。为此引入新型图形表示法，将持久同调计算从图像域转移到图形域，得到一种粒子系统合成图像的后处理方法，该方法与底层生成方法无关，能改善与真实粒子系统的拓扑和几何一致性，同时保留如粒子尺寸分布等形态特征。
英文摘要
The shape and arrangement of particles in a material determine its macroscopic properties. The generation of synthetic data with varying particle structure, often represented as 3D voxel images, combined with simulation of macroscopic properties reveals structure-property relations. Most particle generation models focus on single-particle characteristics like shape and size. We aim at fitting the topology of the particle system using tools from persistent homology. However, the large size of the required 3D image data makes existing methods computationally infeasible. We bridge this gap by introducing a novel graph representation of particle systems and transferring the computation of persistent homology from the image domain to the graph domain. This yields a postprocessing method for synthetic images of particle systems, that is independent of the underlying generation method and improves topological and geometrical agreement with real particle systems while preserving morphological characteristics such as the particle size distribution.
Comments27 pages, 5 figures, 6 tables
