Topological Mapper for 3D Volumetric Images

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.