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Morse theory-based segmentation and fabric quantification of granular materials

Karran Pandey, Talha Bin Masood, Saurabh Singh, Ingrid Hotz, Vijay Natarajan, and Tejas G. Murthy.
Granular Matter, 24(1), 2022, 27:1-20.
[Springer link]


This article presents a robust Morse theory-based framework for segmenting 3D x-ray computed tomography image (CT) and computing the fabric, relative arrangement of particles, of granular ensembles. The framework includes an algorithm for computing the segmentation, a data structure for storing the segmentation and representing both individual particles and the connectivity network, and visualizations of topological descriptors of the CT image that enable interactive exploration. The Morse theory-based framework produces superior quality segmentation of a granular ensemble as compared to prior approaches based on the watershed transform. The accuracy of the connectivity network also improves. Further, the framework supports the efficient computation of various distribution statistics on the segmentation and the connectivity network. Such a comprehensive characterization and quantification of the fabric of granular ensembles is the first step towards a multiple length scale understanding of the behavior.