{"ID":2893152,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.14268","arxiv_id":"2507.14268","title":"Comparative Analysis of Algorithms for the Fitting of Tessellations to 3D Image Data","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.","short_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...","url_abs":"https://arxiv.org/abs/2507.14268","url_pdf":"https://arxiv.org/pdf/2507.14268v1","authors":"[\"Andreas Alpers\",\"Orkun Furat\",\"Christian Jung\",\"Matthias Neumann\",\"Claudia Redenbach\",\"Aigerim Saken\",\"Volker Schmidt\"]","published":"2025-07-18T15:28:59Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cond-mat.mtrl-sci\",\"math.OC\"]","methods":"[]","has_code":false}