Fitting Laguerre tessellation approximations to tomographic image data

Abstract

The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.

Keywords:

• Image processing
• microstructural characterization
• grain boundary structure
• polycrystalline
• power diagram
• inverse problem
• cross-entropy method

Notes

No potential conflict of interest was reported by the authors.

A software package including Java code and data-sets can be downloaded from https://github.com/stochastics-ulm-university/laguerre-approximation.

Additional information

Funding

This work was partially supported by the Australian Research Council [grant number DP140101956]; the Deutsche Forschungsgemeinschaft [grant number KR 1658/4-1].