Petrich Lukas, Staněk Jakub, Wang Mingyan, Westhoff Daniel, Heller Luděk, Šittner Petr, Krill Carl E, Beneš Viktor, Schmidt Volker
Institute of Stochastics, Faculty of Mathematics and Economics, Ulm University,89069 Ulm,Germany.
Department of Mathematics Education,Faculty of Mathematics and Physics, Charles University,18675 Prague,Czech Republic.
Microsc Microanal. 2019 Jun;25(3):743-752. doi: 10.1017/S1431927619000485. Epub 2019 Apr 30.
Far-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries-and, therefore, individual grain shapes-are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.
