Abstract
In order to detect and analyze branching nodes in 3D images of micro-structures, the topology preserving thinning algorithm of Couprie and Zrour is jointly used with a constraint set derived from the spherical granulometry image. The branching points in the thus derived skeleton are subsequently merged guided by the local structure thickness as provided by the spherical granulometry. This enables correct merging of nodes and thus a correct calculation of the nodes’ valences. The algorithm is validated using two synthetic foam structures with known vertices and valences. Subsequently, the algorithm is applied to micro-computed tomography data of a rigid aluminium foam where the valence is known, to the pore space of polar firn samples, and to corrosion casts of mice livers.
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Acknowledgements
We thank André Liebscher for providing the foam data, Johannes Freitag and Tetsuro Taranczewski for the firn data, and Maximilian Ackermann and Willi Wagner for the mice liver data. This work was supported by the Fraunhofer High Performance Center for Simulation- and Software-Based Innovation, by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the priority programme “Antarctic Research with comparative investigations in Arctic ice areas”, grant RE 3002/3-1, and by the German Federal Ministry of Education and Research (BMBF), grant 05M16UKA (AMSCHA).
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Cheng, X., Föhst, S., Redenbach, C., Schladitz, K. (2019). Detecting Branching Nodes of Multiply Connected 3D Structures. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2019. Lecture Notes in Computer Science(), vol 11564. Springer, Cham. https://doi.org/10.1007/978-3-030-20867-7_34
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