Stereological reconstructions of 3D cellular microstructures by combining adversarial learning and Voronoi tessellations.

A novel stereological framework to generate synthetic three-dimensional cellular material structures using Voronoi tessellations is presented. While conventional investigations of microstructural features rely on costly and often destructive three-dimensional imaging techniques, our method enables the reconstruction of 3D cellular structures from two-dimensional planar-sectional image data. By representing 3D cell architectures through Voronoi tessellations, we obtain an analytical representation requiring only three parameters per cell, ensuring efficient storage and computational processing. Our framework employs a differentiable approximation of Voronoi tessellations combined with a discriminator neural network in an adversarial learning context, enabling gradient-based optimization of tessellation parameters to generate random 3D cellular structures with statistically similar 2D planar sections as observed in measured 2D image data. We demonstrate the framework on image data of various cellular materials including metallic alloys, biological cells, and foam structures. The presented framework shows state-of-the-art capability of stereologically reconstructing 3D cellular microstructures, while introducing a low-parameter representation, preserving physical interpretability, and ensuring computational efficiency.