Abstract
Mapper is a topological construction similar to a Reeb graph, and is used to summarize the shape of a dataset as a (generalized) graph. Formally, mapper can be constructed for any connected space and algorithms have been developed to compute mapper for point clouds and 2D images. In this paper, we extend mapper to 3D volumetric images. We use our algorithm to compute mapper for scans of barley generated using computed tomography. We demonstrate the flexibility of the construction by highlighting different aspects of the morphology through different choices of starting parameters. Applying mapper to this type of data provides an integrated means of visualization, segmentation and clustering, and can thus be used to study the topology of any 3D object.
This project was supported by the USDA National Institute of Food and Agriculture, and by Michigan State University AgBioResearch. The work of EM was supported in part by NSF grants DMS-1800446 and CMMI-1800466.
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Acknowledgments
The authors thank Jacob Landis and Daniel Koenig for providing the barley spike and X-ray Computed Tomography data. The data set is available on the figshare repository [5].
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Chitwood, D.H., Eithun, M., Munch, E., Ophelders, T. (2019). Topological Mapper for 3D Volumetric Images. 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_7
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