Comparative Analysis of Algorithms for the Fitting of Tessellations to 3D Image Data
This work addresses the need for efficient and accurate tessellation fitting in materials science, but it is incremental as it focuses on comparative analysis of existing methods.
This paper tackled the problem of fitting tessellation models to 3D image data of materials like polycrystals and foams by comparing optimization-based methods, and the results highlighted trade-offs in model complexity, optimization routines, and approximation quality to guide method selection.
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.