Comparative Analysis of Algorithms for the Fitting of Tessellations to 3D Image Data

TL;DR

This paper compares various algorithmic strategies for fitting tessellation models to 3D image data of materials, evaluating their effectiveness and trade-offs in approximating grain structures.

Contribution

It provides a comprehensive comparison of optimization-based methods for fitting tessellations to 3D data, offering guidance on method selection based on data and application.

Findings

Different algorithms show trade-offs between accuracy and complexity.

Gradient descent and stochastic methods perform well on complex structures.

Model choice impacts fit quality and computational efficiency.

Abstract

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.