Fitting the topology of synthetic particle systems with a novel graph representation

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.