Fitting Laguerre tessellation approximations to tomographic image data

TL;DR

This paper presents a robust stochastic optimization method using the cross-entropy technique to efficiently fit Laguerre tessellations to complex tomographic image data of polycrystalline materials.

Contribution

It introduces a new formulation of the fitting problem and applies the cross-entropy method for fast, reliable approximation of grain structures in tomographic images.

Findings

Effective fitting of Laguerre tessellations demonstrated on real and synthetic data

The method avoids local minima and converges quickly

Improves accuracy of grain structure analysis in materials science

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.