Topological Mapper for 3D Volumetric Images

  • Daniel H. Chitwood
  • Mitchell EithunEmail author
  • Elizabeth Munch
  • Tim Ophelders
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11564)


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.


Topological mapper Image processing Computed tomography Topological data analysis 



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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel H. Chitwood
    • 1
  • Mitchell Eithun
    • 1
    Email author
  • Elizabeth Munch
    • 1
  • Tim Ophelders
    • 1
  1. 1.Michigan State UniversityEast LansingUSA

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